From ffacf61e8a6855c009bb180a444e498d5de22b42 Mon Sep 17 00:00:00 2001
From: Mamy Ratsimbazafy <mamy_github@numforge.co>
Date: Sun, 27 Feb 2022 01:49:08 +0100
Subject: [PATCH] Don't dump all in "backend" (#184)

* backend -> math

* towers -> extension fields

* move ISA and compiler specific code out of math/

* fix export
---
 README.md                                     |   4 +-
 benchmarks/bench_blueprint.nim                |   2 +-
 benchmarks/bench_ec_g1.nim                    |   8 +-
 benchmarks/bench_ec_g2.nim                    |  10 +-
 benchmarks/bench_elliptic_template.nim        |  11 +-
 benchmarks/bench_fields_template.nim          |   9 +-
 benchmarks/bench_fp.nim                       |  10 +-
 benchmarks/bench_fp12.nim                     |   4 +-
 benchmarks/bench_fp2.nim                      |   4 +-
 benchmarks/bench_fp4.nim                      |   4 +-
 benchmarks/bench_fp6.nim                      |   4 +-
 benchmarks/bench_fp_double_precision.nim      |   7 +-
 benchmarks/bench_hash_to_curve.nim            |  12 +-
 benchmarks/bench_pairing_bls12_377.nim        |   6 +-
 benchmarks/bench_pairing_bls12_381.nim        |   6 +-
 benchmarks/bench_pairing_bn254_nogami.nim     |   6 +-
 benchmarks/bench_pairing_bn254_snarks.nim     |   6 +-
 benchmarks/bench_pairing_template.nim         |  15 +-
 benchmarks/bench_sha256.nim                   |   2 +-
 benchmarks/bench_summary_bls12_377.nim        |   6 +-
 benchmarks/bench_summary_bls12_381.nim        |   6 +-
 benchmarks/bench_summary_bn254_nogami.nim     |   6 +-
 benchmarks/bench_summary_bn254_snarks.nim     |   6 +-
 benchmarks/bench_summary_template.nim         |  16 +-
 constantine.nimble                            | 246 +++++++++---------
 constantine/backend/primitives/static_for.nim |  36 ---
 constantine/blssig_pop_on_bls12381_g2.nim     |  21 +-
 constantine/ethereum_evm_precompiles.nim      |  15 +-
 .../{backend => }/hash_to_curve/README.md     |   0
 .../hash_to_curve/h2c_hash_to_field.nim       |   9 +-
 .../h2c_isogeny_maps.nim                      |   9 +-
 .../hash_to_curve/h2c_map_to_isocurve_swu.nim |   7 +-
 .../hash_to_curve/hash_to_curve.nim           |  11 +-
 constantine/{backend => }/hashes.nim          |   0
 constantine/{backend => }/hashes/h_sha256.nim |   4 +-
 constantine/{backend => math}/arithmetic.nim  |   0
 .../{backend => math}/arithmetic/README.md    |   0
 .../limbs_asm_modular_dbl_prec_x86.nim        |   3 +-
 .../assembly/limbs_asm_modular_x86.nim        |   3 +-
 .../assembly/limbs_asm_mul_mont_x86.nim       |   3 +-
 .../limbs_asm_mul_mont_x86_adx_bmi2.nim       |   3 +-
 .../arithmetic/assembly/limbs_asm_mul_x86.nim |   3 +-
 .../assembly/limbs_asm_mul_x86_adx_bmi2.nim   |   6 +-
 .../assembly/limbs_asm_redc_mont_x86.nim      |   3 +-
 .../limbs_asm_redc_mont_x86_adx_bmi2.nim      |   3 +-
 .../arithmetic/assembly/limbs_asm_x86.nim     |   3 +-
 .../{backend => math}/arithmetic/bigints.nim  |   4 +-
 .../arithmetic/bigints_montgomery.nim         |   3 +-
 .../arithmetic/finite_fields.nim              |   6 +-
 .../finite_fields_double_precision.nim        |   4 +-
 .../arithmetic/finite_fields_square_root.nim  |   4 +-
 .../{backend => math}/arithmetic/limbs.nim    |   4 +-
 .../arithmetic/limbs_division.nim             |   4 +-
 .../arithmetic/limbs_extmul.nim               |   3 +-
 .../arithmetic/limbs_invmod.nim               |   3 +-
 .../arithmetic/limbs_montgomery.nim           |   3 +-
 .../arithmetic/limbs_unsaturated.nim          |   4 +-
 .../{backend => math}/config/README.md        |   0
 .../{backend => math}/config/curves.nim       |   0
 .../config/curves_declaration.nim             |   2 +-
 .../config/curves_derived.nim                 |   0
 .../config/curves_parser_curve.nim            |   0
 .../config/curves_parser_field.nim            |   0
 .../config/curves_prop_curve.nim              |   0
 .../config/curves_prop_field_core.nim         |   3 +-
 .../config/curves_prop_field_derived.nim      |   3 +-
 .../{backend => math}/config/precompute.nim   |   4 +-
 .../{backend => math}/config/type_bigint.nim  |   2 +-
 .../{backend => math}/config/type_ff.nim      |   2 +-
 .../{backend => math}/curves/README.md        |   0
 .../curves/bandersnatch_sqrt.nim              |   2 +-
 .../curves/bls12_377_constants.nim            |   2 +-
 .../curves/bls12_377_endomorphisms.nim        |   2 +-
 .../curves/bls12_377_frobenius.nim            |   4 +-
 .../curves/bls12_377_pairing.nim              |   7 +-
 .../curves/bls12_377_sqrt.nim                 |   2 +-
 .../curves/bls12_377_subgroups.nim            |   8 +-
 .../curves/bls12_381_constants.nim            |   2 +-
 .../curves/bls12_381_endomorphisms.nim        |   2 +-
 .../curves/bls12_381_frobenius.nim            |   4 +-
 .../curves/bls12_381_g2_hash_to_curve.nim     |   2 +-
 .../curves/bls12_381_generators.nim           |   4 +-
 .../curves/bls12_381_pairing.nim              |   7 +-
 .../curves/bls12_381_sqrt.nim                 |   0
 .../curves/bls12_381_sqrt_fp2.nim             |   2 +-
 .../curves/bls12_381_subgroups.nim            |   8 +-
 .../curves/bn254_nogami_constants.nim         |   2 +-
 .../curves/bn254_nogami_endomorphisms.nim     |   2 +-
 .../curves/bn254_nogami_frobenius.nim         |   4 +-
 .../curves/bn254_nogami_pairing.nim           |   7 +-
 .../curves/bn254_nogami_sqrt.nim              |   0
 .../curves/bn254_nogami_sqrt_fp2.nim          |   2 +-
 .../curves/bn254_nogami_subgroups.nim         |   8 +-
 .../curves/bn254_snarks_constants.nim         |   2 +-
 .../curves/bn254_snarks_endomorphisms.nim     |   2 +-
 .../curves/bn254_snarks_frobenius.nim         |   4 +-
 .../curves/bn254_snarks_pairing.nim           |   7 +-
 .../curves/bn254_snarks_sqrt.nim              |   0
 .../curves/bn254_snarks_sqrt_fp2.nim          |   2 +-
 .../curves/bn254_snarks_subgroups.nim         |   8 +-
 .../curves/bw6_761_constants.nim              |   0
 .../curves/bw6_761_endomorphisms.nim          |   2 +-
 .../curves/bw6_761_frobenius.nim              |   6 +-
 .../curves/bw6_761_pairing.nim                |   7 +-
 .../{backend => math}/curves/bw6_761_sqrt.nim |   0
 .../curves/bw6_761_subgroups.nim              |   8 +-
 .../curves/curve25519_sqrt.nim                |   6 +-
 .../{backend => math}/curves/jubjub_sqrt.nim  |   2 +-
 .../curves/zoo_constants.nim                  |   0
 .../curves/zoo_endomorphisms.nim              |   4 +-
 .../curves/zoo_frobenius.nim                  |   0
 .../curves/zoo_generators.nim                 |   0
 .../curves/zoo_hash_to_curve.nim              |   0
 .../{backend => math}/curves/zoo_pairings.nim |   0
 .../curves/zoo_square_roots.nim               |   4 +-
 .../curves/zoo_square_roots_fp2.nim           |   0
 .../curves/zoo_subgroups.nim                  |   0
 .../{backend => math}/ec_shortweierstrass.nim |   0
 .../{backend => math}/elliptic/README.md      |   0
 .../elliptic/ec_endomorphism_accel.nim        |   8 +-
 .../elliptic/ec_scalar_mul.nim                |   6 +-
 .../elliptic/ec_shortweierstrass_affine.nim   |   8 +-
 .../elliptic/ec_shortweierstrass_jacobian.nim |   6 +-
 .../ec_shortweierstrass_projective.nim        |   6 +-
 .../elliptic/ec_twistededwards_affine.nim     |   8 +-
 .../elliptic/ec_twistededwards_projective.nim |   6 +-
 .../towers.nim => math/extension_fields.nim}  |   6 +-
 .../extension_fields}/README.md               |   0
 .../assembly/fp2_asm_x86_adx_bmi2.nim         |   4 +-
 .../extension_fields}/exponentiations.nim     |   5 +-
 .../extension_fields}/square_root_fp2.nim     |   6 +-
 .../extension_fields/towers.nim}              |   6 +-
 constantine/{backend => math}/io/README.md    |   0
 .../{backend => math}/io/io_bigints.nim       |   7 +-
 constantine/{backend => math}/io/io_ec.nim    |   6 +-
 .../io/io_extfields.nim}                      |   6 +-
 .../{backend => math}/io/io_fields.nim        |   5 +-
 .../isogeny => math/isogenies}/README.md      |   0
 .../isogeny => math/isogenies}/frobenius.nim  |   4 +-
 .../{backend => math}/pairing/README.md       |   0
 .../pairing/cyclotomic_subgroup.nim           |   8 +-
 .../{backend => math}/pairing/lines_eval.nim  |   6 +-
 .../pairing/miller_loops.nim                  |   2 +-
 .../pairing/multi_pairing.md                  |   0
 .../pairing/pairing_bls12.nim                 |   7 +-
 .../{backend => math}/pairing/pairing_bn.nim  |   6 +-
 .../pairing/pairing_bw6_761.nim               |   6 +-
 constantine/{backend => math}/pairings.nim    |   2 +-
 .../primitives => platforms}/README.md        |   0
 .../common.nim => platforms/abstractions.nim} |   8 +-
 .../primitives => platforms}/bithacks.nim     |   0
 .../compilers}/addcarry_subborrow.nim         |   2 +-
 .../compilers}/extended_precision.nim         |   4 +-
 .../extended_precision_64bit_uint128.nim      |   2 +-
 .../extended_precision_x86_64_gcc.nim         |   2 +-
 .../extended_precision_x86_64_msvc.nim        |   2 +-
 .../constant_time/ct_routines.nim}            |   2 +-
 .../constant_time/ct_types.nim}               |   0
 .../constant_time}/multiplexers.nim           |   2 +-
 .../{backend/io => platforms}/endians.nim     |   2 +-
 .../isa}/cpuinfo_x86.nim                      |   0
 .../isa}/macro_assembler_x86.nim              |   0
 .../{backend => platforms}/primitives.nim     |  24 +-
 .../{backend => }/signatures/README.md        |   0
 .../signatures/bls_signatures.nim             |   6 +-
 docs/optimizations.md                         |   2 +-
 helpers/prng_unsafe.nim                       |  12 +-
 helpers/static_for.nim                        |   8 +
 metering/m_pairings.nim                       |  10 +-
 research/kzg_poly_commit/fft_fr.nim           |   9 +-
 research/kzg_poly_commit/fft_g1.nim           |  11 +-
 research/kzg_poly_commit/fft_lut.nim          |   7 +-
 .../kzg_poly_commit/kzg_single_proofs.nim     |  10 +-
 research/kzg_poly_commit/polynomials.nim      |  11 +-
 sage/derive_endomorphisms.sage                |   2 +-
 sage/derive_frobenius.sage                    |  10 +-
 sage/derive_hash_to_curve.sage                |   2 +-
 sage/derive_pairing.sage                      |   2 +-
 sage/derive_square_root.sage                  |   2 +-
 sage/g2_params.sage                           |   2 +-
 tests/{backend => math}/support/canaries.nim  |   7 +-
 .../support/ec_reference_scalar_mult.nim      |   4 +-
 tests/{backend => math}/t_bigints.nim         |   7 +-
 .../t_bigints_mod_vs_gmp.nim                  |   8 +-
 .../t_bigints_mul_high_words_vs_gmp.nim       |   7 +-
 .../t_bigints_mul_vs_gmp.nim                  |   7 +-
 .../{backend => math}/t_bigints_multimod.nim  |   7 +-
 tests/{backend => math}/t_ec_conversion.nim   |   6 +-
 tests/{backend => math}/t_ec_frobenius.nim    |  11 +-
 .../{backend => math}/t_ec_sage_bls12_377.nim |   8 +-
 .../{backend => math}/t_ec_sage_bls12_381.nim |   8 +-
 .../t_ec_sage_bn254_nogami.nim                |   8 +-
 .../t_ec_sage_bn254_snarks.nim                |   8 +-
 .../t_ec_sage_bw6_761_g1.nim                  |   6 +-
 .../t_ec_sage_bw6_761_g2.nim                  |   6 +-
 .../{backend => math}/t_ec_sage_template.nim  |  13 +-
 .../t_ec_shortw_jac_g1_add_double.nim         |   4 +-
 .../t_ec_shortw_jac_g1_mixed_add.nim          |   6 +-
 .../t_ec_shortw_jac_g1_mul_distri.nim         |   4 +-
 .../t_ec_shortw_jac_g1_mul_sanity.nim         |   8 +-
 .../t_ec_shortw_jac_g1_mul_vs_ref.nim         |   4 +-
 ..._ec_shortw_jac_g2_add_double_bls12_377.nim |   6 +-
 ..._ec_shortw_jac_g2_add_double_bls12_381.nim |   6 +-
 ..._shortw_jac_g2_add_double_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_jac_g2_add_double_bw6_761.nim |   4 +-
 ...t_ec_shortw_jac_g2_mixed_add_bls12_377.nim |   6 +-
 ...t_ec_shortw_jac_g2_mixed_add_bls12_381.nim |   6 +-
 ...c_shortw_jac_g2_mixed_add_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_jac_g2_mixed_add_bw6_761.nim  |   4 +-
 ..._ec_shortw_jac_g2_mul_distri_bls12_377.nim |   6 +-
 ..._ec_shortw_jac_g2_mul_distri_bls12_381.nim |   6 +-
 ..._shortw_jac_g2_mul_distri_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_jac_g2_mul_distri_bw6_761.nim |   4 +-
 ..._ec_shortw_jac_g2_mul_sanity_bls12_377.nim |   6 +-
 ..._ec_shortw_jac_g2_mul_sanity_bls12_381.nim |   6 +-
 ..._shortw_jac_g2_mul_sanity_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim |   4 +-
 ..._ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim |   6 +-
 ..._ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim |   6 +-
 ..._shortw_jac_g2_mul_vs_ref_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim |   4 +-
 .../t_ec_shortw_prj_edge_cases.nim            |  11 +-
 .../t_ec_shortw_prj_g1_add_double.nim         |   4 +-
 .../t_ec_shortw_prj_g1_mixed_add.nim          |   6 +-
 .../t_ec_shortw_prj_g1_mul_distri.nim         |   4 +-
 .../t_ec_shortw_prj_g1_mul_sanity.nim         |   8 +-
 .../t_ec_shortw_prj_g1_mul_vs_ref.nim         |   4 +-
 ..._ec_shortw_prj_g2_add_double_bls12_377.nim |   6 +-
 ..._ec_shortw_prj_g2_add_double_bls12_381.nim |   6 +-
 ..._shortw_prj_g2_add_double_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_prj_g2_add_double_bw6_761.nim |   4 +-
 ...t_ec_shortw_prj_g2_mixed_add_bls12_377.nim |   6 +-
 ...t_ec_shortw_prj_g2_mixed_add_bls12_381.nim |   6 +-
 ...c_shortw_prj_g2_mixed_add_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_prj_g2_mixed_add_bw6_761.nim  |   4 +-
 ..._ec_shortw_prj_g2_mul_distri_bls12_377.nim |   6 +-
 ..._ec_shortw_prj_g2_mul_distri_bls12_381.nim |   6 +-
 ..._shortw_prj_g2_mul_distri_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_prj_g2_mul_distri_bw6_761.nim |   4 +-
 ..._ec_shortw_prj_g2_mul_sanity_bls12_377.nim |   6 +-
 ..._ec_shortw_prj_g2_mul_sanity_bls12_381.nim |   6 +-
 ..._shortw_prj_g2_mul_sanity_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim |   4 +-
 ..._ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim |   6 +-
 ..._ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim |   6 +-
 ..._shortw_prj_g2_mul_vs_ref_bn254_snarks.nim |   6 +-
 .../t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim |   4 +-
 .../t_ec_subgroups_bls12_377.nim              |   6 +-
 .../t_ec_subgroups_bls12_381.nim              |   6 +-
 .../t_ec_subgroups_bn254_nogami.nim           |   6 +-
 .../t_ec_subgroups_bn254_snarks.nim           |   6 +-
 tests/{backend => math}/t_ec_template.nim     |  15 +-
 .../t_ec_twedwards_prj_add_double.nim         |   8 +-
 .../t_ec_twedwards_prj_mul_distri.nim         |   8 +-
 .../t_ec_twedwards_prj_mul_sanity.nim         |   8 +-
 .../t_ec_twedwards_prj_mul_vs_ref.nim         |   8 +-
 tests/{backend => math}/t_finite_fields.nim   |  18 +-
 .../{backend => math}/t_finite_fields.nim.cfg |   0
 ...t_finite_fields_conditional_arithmetic.nim |   7 +-
 .../t_finite_fields_double_precision.nim      |  31 +--
 .../t_finite_fields_double_precision.nim.cfg  |   0
 .../t_finite_fields_mulsquare.nim             |  17 +-
 .../t_finite_fields_mulsquare.nim.cfg         |   0
 .../t_finite_fields_powinv.nim                |  12 +-
 .../t_finite_fields_powinv.nim.cfg            |   0
 .../t_finite_fields_sqrt.nim                  |  11 +-
 .../t_finite_fields_sqrt.nim.cfg              |   0
 .../t_finite_fields_vs_gmp.nim                |  10 +-
 .../t_fp12_anti_regression.nim                |  10 +-
 tests/{backend => math}/t_fp12_bls12_377.nim  |   4 +-
 tests/{backend => math}/t_fp12_bls12_381.nim  |   4 +-
 .../{backend => math}/t_fp12_bn254_snarks.nim |   4 +-
 .../t_fp12_exponentiation.nim                 |  10 +-
 tests/{backend => math}/t_fp12_frobenius.nim  |   6 +-
 tests/{backend => math}/t_fp2.nim             |   3 +-
 tests/{backend => math}/t_fp2_frobenius.nim   |   6 +-
 tests/{backend => math}/t_fp2_sqrt.nim        |  10 +-
 tests/{backend => math}/t_fp4.nim             |   6 +-
 tests/{backend => math}/t_fp4_frobenius.nim   |   6 +-
 tests/{backend => math}/t_fp6_bls12_377.nim   |   4 +-
 tests/{backend => math}/t_fp6_bls12_381.nim   |   4 +-
 .../{backend => math}/t_fp6_bn254_snarks.nim  |   4 +-
 tests/{backend => math}/t_fp6_bw6_761.nim     |   4 +-
 tests/{backend => math}/t_fp6_frobenius.nim   |   6 +-
 tests/{backend => math}/t_fp_cubic_root.nim   |   8 +-
 .../t_fp_tower_frobenius_template.nim         |  11 +-
 .../{backend => math}/t_fp_tower_template.nim |  11 +-
 tests/{backend => math}/t_fr.nim              |   7 +-
 tests/{backend => math}/t_hash_to_curve.nim   |  14 +-
 tests/{backend => math}/t_hash_to_field.nim   |  10 +-
 tests/{backend => math}/t_io_bigints.nim      |   6 +-
 tests/{backend => math}/t_io_fields.nim       |   8 +-
 tests/{backend => math}/t_io_fields.nim.cfg   |   0
 tests/{backend => math}/t_io_unsaturated.nim  |  17 +-
 .../t_pairing_bls12_377_gt_subgroup.nim       |   4 +-
 .../t_pairing_bls12_377_line_functions.nim    |  14 +-
 .../t_pairing_bls12_377_optate.nim            |   4 +-
 .../t_pairing_bls12_381_gt_subgroup.nim       |   4 +-
 .../t_pairing_bls12_381_line_functions.nim    |  14 +-
 .../t_pairing_bls12_381_multi.nim             |  13 +-
 .../t_pairing_bls12_381_optate.nim            |   4 +-
 .../t_pairing_bn254_nogami_gt_subgroup.nim    |   4 +-
 .../t_pairing_bn254_nogami_optate.nim         |   4 +-
 .../t_pairing_bn254_snarks_gt_subgroup.nim    |   4 +-
 .../t_pairing_bn254_snarks_optate.nim         |   4 +-
 .../t_pairing_bw6_761_gt_subgroup.nim         |   4 +-
 .../t_pairing_bw6_761_optate.nim              |   4 +-
 .../t_pairing_cyclotomic_subgroup.nim         |  14 +-
 .../t_pairing_mul_fp12_by_lines.nim           |  12 +-
 .../{backend => math}/t_pairing_template.nim  |  23 +-
 tests/{backend => math}/t_primitives.nim      |   3 +-
 .../t_primitives_extended_precision.nim       |   3 +-
 .../vectors/tv_BLS12_377_scalar_mul_G1.json   |   0
 .../vectors/tv_BLS12_377_scalar_mul_G2.json   |   0
 .../vectors/tv_BLS12_381_scalar_mul_G1.json   |   0
 .../vectors/tv_BLS12_381_scalar_mul_G2.json   |   0
 .../tv_BN254_Nogami_scalar_mul_G1.json        |   0
 .../tv_BN254_Nogami_scalar_mul_G2.json        |   0
 .../tv_BN254_Snarks_scalar_mul_G1.json        |   0
 .../tv_BN254_Snarks_scalar_mul_G2.json        |   0
 .../vectors/tv_BW6_761_scalar_mul_G1.json     |   0
 .../vectors/tv_BW6_761_scalar_mul_G2.json     |   0
 ...7_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json |   0
 ...8_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json |   0
 .../README.md                                 |   0
 ...0000000000000000000000000000000000000.json |   0
 ...6565656565656565656565656565656565656.json |   0
 ...babababababababababababababababababab.json |   0
 .../aggregate_infinity_signature.json         |   0
 .../aggregate/aggregate_na_signatures.json    |   0
 .../aggregate/aggregate_single_signature.json |   0
 .../aggregate_verify_infinity_pubkey.json     |   0
 ...ify_na_pubkeys_and_infinity_signature.json |   0
 ...te_verify_na_pubkeys_and_na_signature.json |   0
 .../aggregate_verify_tampered_signature.json  |   0
 .../aggregate_verify_valid.json               |   0
 ...h_verify_invalid_forged_signature_set.json |   0
 ...tch_verify_valid_simple_signature_set.json |   0
 ...tion_fails_infinity_with_false_b_flag.json |   0
 ...ation_fails_infinity_with_true_b_flag.json |   0
 .../deserialization_fails_not_in_G1.json      |   0
 .../deserialization_fails_not_in_curve.json   |   0
 .../deserialization_fails_too_few_bytes.json  |   0
 .../deserialization_fails_too_many_bytes.json |   0
 ...ion_fails_with_b_flag_and_a_flag_true.json |   0
 ...ation_fails_with_b_flag_and_x_nonzero.json |   0
 ...serialization_fails_with_wrong_c_flag.json |   0
 ...erialization_fails_x_equal_to_modulus.json |   0
 ...lization_fails_x_greater_than_modulus.json |   0
 ...eserialization_succeeds_correct_point.json |   0
 ...on_succeeds_infinity_with_true_b_flag.json |   0
 ...tion_fails_infinity_with_false_b_flag.json |   0
 ...ation_fails_infinity_with_true_b_flag.json |   0
 .../deserialization_fails_not_in_G2.json      |   0
 .../deserialization_fails_not_in_curve.json   |   0
 .../deserialization_fails_too_few_bytes.json  |   0
 .../deserialization_fails_too_many_bytes.json |   0
 ...ion_fails_with_b_flag_and_a_flag_true.json |   0
 ...ation_fails_with_b_flag_and_x_nonzero.json |   0
 ...serialization_fails_with_wrong_c_flag.json |   0
 ...ialization_fails_xim_equal_to_modulus.json |   0
 ...zation_fails_xim_greater_than_modulus.json |   0
 ...ialization_fails_xre_equal_to_modulus.json |   0
 ...zation_fails_xre_greater_than_modulus.json |   0
 ...eserialization_succeeds_correct_point.json |   0
 ...on_succeeds_infinity_with_true_b_flag.json |   0
 ..._verify_extra_pubkey_4f079f946446fabf.json |   0
 ..._verify_extra_pubkey_5a38e6b4017fe4dd.json |   0
 ..._verify_extra_pubkey_a698ea45b109f303.json |   0
 ...fast_aggregate_verify_infinity_pubkey.json |   0
 ...ify_na_pubkeys_and_infinity_signature.json |   0
 ...te_verify_na_pubkeys_and_na_signature.json |   0
 ...y_tampered_signature_3d7576f3c0e3570a.json |   0
 ...y_tampered_signature_5e745ad0c6199a6c.json |   0
 ...y_tampered_signature_652ce62f09290811.json |   0
 ...gregate_verify_valid_3d7576f3c0e3570a.json |   0
 ...gregate_verify_valid_5e745ad0c6199a6c.json |   0
 ...gregate_verify_valid_652ce62f09290811.json |   0
 .../hash_to_G2__2782afaa8406d038.json         |   0
 .../hash_to_G2__7590bd067999bbfb.json         |   0
 .../hash_to_G2__a54942c8e365f378.json         |   0
 .../hash_to_G2__c938b486cf69e8f7.json         |   0
 .../sign/sign_case_11b8c7cad5238946.json      |   0
 .../sign/sign_case_142f678a8d05fcd1.json      |   0
 .../sign/sign_case_37286e1a6d1f6eb3.json      |   0
 .../sign/sign_case_7055381f640f2c1d.json      |   0
 .../sign/sign_case_84d45c9c7cca6b92.json      |   0
 .../sign/sign_case_8cd3d4d0d9a5b265.json      |   0
 .../sign/sign_case_c82df61aa3ee60fb.json      |   0
 .../sign/sign_case_d0e28d7e76eb6e9c.json      |   0
 .../sign/sign_case_f2ae1097e7d0e18b.json      |   0
 .../sign/sign_case_zero_privkey.json          |   0
 ...nfinity_pubkey_and_infinity_signature.json |   0
 ...pered_signature_case_195246ee3bd3b6ec.json |   0
 ...pered_signature_case_2ea479adf8c40300.json |   0
 ...pered_signature_case_2f09d443ab8a3ac2.json |   0
 ...pered_signature_case_3208262581c8fc09.json |   0
 ...pered_signature_case_6b3b17f6962a490c.json |   0
 ...pered_signature_case_6eeb7c52dfd9baf0.json |   0
 ...pered_signature_case_8761a0b7e920c323.json |   0
 ...pered_signature_case_d34885d766d5f705.json |   0
 ...pered_signature_case_e8a50c445c855360.json |   0
 .../verify_valid_case_195246ee3bd3b6ec.json   |   0
 .../verify_valid_case_2ea479adf8c40300.json   |   0
 .../verify_valid_case_2f09d443ab8a3ac2.json   |   0
 .../verify_valid_case_3208262581c8fc09.json   |   0
 .../verify_valid_case_6b3b17f6962a490c.json   |   0
 .../verify_valid_case_6eeb7c52dfd9baf0.json   |   0
 .../verify_valid_case_8761a0b7e920c323.json   |   0
 .../verify_valid_case_d34885d766d5f705.json   |   0
 .../verify_valid_case_e8a50c445c855360.json   |   0
 ...fy_wrong_pubkey_case_195246ee3bd3b6ec.json |   0
 ...fy_wrong_pubkey_case_2ea479adf8c40300.json |   0
 ...fy_wrong_pubkey_case_2f09d443ab8a3ac2.json |   0
 ...fy_wrong_pubkey_case_3208262581c8fc09.json |   0
 ...fy_wrong_pubkey_case_6b3b17f6962a490c.json |   0
 ...fy_wrong_pubkey_case_6eeb7c52dfd9baf0.json |   0
 ...fy_wrong_pubkey_case_8761a0b7e920c323.json |   0
 ...fy_wrong_pubkey_case_d34885d766d5f705.json |   0
 ...fy_wrong_pubkey_case_e8a50c445c855360.json |   0
 ...rifycase_one_privkey_47117849458281be.json |   0
 tests/t_blssig_pop_on_bls12381_g2.nim         |   4 +-
 tests/t_ethereum_evm_precompiles.nim          |   6 +-
 tests/t_hash_sha256_vs_openssl.nim            |   2 +-
 424 files changed, 971 insertions(+), 1000 deletions(-)
 delete mode 100644 constantine/backend/primitives/static_for.nim
 rename constantine/{backend => }/hash_to_curve/README.md (100%)
 rename constantine/{backend => }/hash_to_curve/h2c_hash_to_field.nim (97%)
 rename constantine/{backend/isogeny => hash_to_curve}/h2c_isogeny_maps.nim (97%)
 rename constantine/{backend => }/hash_to_curve/h2c_map_to_isocurve_swu.nim (98%)
 rename constantine/{backend => }/hash_to_curve/hash_to_curve.nim (97%)
 rename constantine/{backend => }/hashes.nim (100%)
 rename constantine/{backend => }/hashes/h_sha256.nim (99%)
 rename constantine/{backend => math}/arithmetic.nim (100%)
 rename constantine/{backend => math}/arithmetic/README.md (100%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_modular_dbl_prec_x86.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_modular_x86.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_mul_mont_x86.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_mul_mont_x86_adx_bmi2.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_mul_x86.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_redc_mont_x86.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_redc_mont_x86_adx_bmi2.nim (99%)
 rename constantine/{backend => math}/arithmetic/assembly/limbs_asm_x86.nim (99%)
 rename constantine/{backend => math}/arithmetic/bigints.nim (99%)
 rename constantine/{backend => math}/arithmetic/bigints_montgomery.nim (99%)
 rename constantine/{backend => math}/arithmetic/finite_fields.nim (99%)
 rename constantine/{backend => math}/arithmetic/finite_fields_double_precision.nim (99%)
 rename constantine/{backend => math}/arithmetic/finite_fields_square_root.nim (99%)
 rename constantine/{backend => math}/arithmetic/limbs.nim (99%)
 rename constantine/{backend => math}/arithmetic/limbs_division.nim (99%)
 rename constantine/{backend => math}/arithmetic/limbs_extmul.nim (99%)
 rename constantine/{backend => math}/arithmetic/limbs_invmod.nim (99%)
 rename constantine/{backend => math}/arithmetic/limbs_montgomery.nim (99%)
 rename constantine/{backend => math}/arithmetic/limbs_unsaturated.nim (99%)
 rename constantine/{backend => math}/config/README.md (100%)
 rename constantine/{backend => math}/config/curves.nim (100%)
 rename constantine/{backend => math}/config/curves_declaration.nim (99%)
 rename constantine/{backend => math}/config/curves_derived.nim (100%)
 rename constantine/{backend => math}/config/curves_parser_curve.nim (100%)
 rename constantine/{backend => math}/config/curves_parser_field.nim (100%)
 rename constantine/{backend => math}/config/curves_prop_curve.nim (100%)
 rename constantine/{backend => math}/config/curves_prop_field_core.nim (96%)
 rename constantine/{backend => math}/config/curves_prop_field_derived.nim (98%)
 rename constantine/{backend => math}/config/precompute.nim (99%)
 rename constantine/{backend => math}/config/type_bigint.nim (98%)
 rename constantine/{backend => math}/config/type_ff.nim (98%)
 rename constantine/{backend => math}/curves/README.md (100%)
 rename constantine/{backend => math}/curves/bandersnatch_sqrt.nim (95%)
 rename constantine/{backend => math}/curves/bls12_377_constants.nim (97%)
 rename constantine/{backend => math}/curves/bls12_377_endomorphisms.nim (98%)
 rename constantine/{backend => math}/curves/bls12_377_frobenius.nim (99%)
 rename constantine/{backend => math}/curves/bls12_377_pairing.nim (98%)
 rename constantine/{backend => math}/curves/bls12_377_sqrt.nim (99%)
 rename constantine/{backend => math}/curves/bls12_377_subgroups.nim (98%)
 rename constantine/{backend => math}/curves/bls12_381_constants.nim (97%)
 rename constantine/{backend => math}/curves/bls12_381_endomorphisms.nim (98%)
 rename constantine/{backend => math}/curves/bls12_381_frobenius.nim (99%)
 rename constantine/{backend => math}/curves/bls12_381_g2_hash_to_curve.nim (99%)
 rename constantine/{backend => math}/curves/bls12_381_generators.nim (96%)
 rename constantine/{backend => math}/curves/bls12_381_pairing.nim (98%)
 rename constantine/{backend => math}/curves/bls12_381_sqrt.nim (100%)
 rename constantine/{backend => math}/curves/bls12_381_sqrt_fp2.nim (98%)
 rename constantine/{backend => math}/curves/bls12_381_subgroups.nim (98%)
 rename constantine/{backend => math}/curves/bn254_nogami_constants.nim (97%)
 rename constantine/{backend => math}/curves/bn254_nogami_endomorphisms.nim (98%)
 rename constantine/{backend => math}/curves/bn254_nogami_frobenius.nim (99%)
 rename constantine/{backend => math}/curves/bn254_nogami_pairing.nim (97%)
 rename constantine/{backend => math}/curves/bn254_nogami_sqrt.nim (100%)
 rename constantine/{backend => math}/curves/bn254_nogami_sqrt_fp2.nim (98%)
 rename constantine/{backend => math}/curves/bn254_nogami_subgroups.nim (98%)
 rename constantine/{backend => math}/curves/bn254_snarks_constants.nim (97%)
 rename constantine/{backend => math}/curves/bn254_snarks_endomorphisms.nim (98%)
 rename constantine/{backend => math}/curves/bn254_snarks_frobenius.nim (99%)
 rename constantine/{backend => math}/curves/bn254_snarks_pairing.nim (97%)
 rename constantine/{backend => math}/curves/bn254_snarks_sqrt.nim (100%)
 rename constantine/{backend => math}/curves/bn254_snarks_sqrt_fp2.nim (98%)
 rename constantine/{backend => math}/curves/bn254_snarks_subgroups.nim (98%)
 rename constantine/{backend => math}/curves/bw6_761_constants.nim (100%)
 rename constantine/{backend => math}/curves/bw6_761_endomorphisms.nim (98%)
 rename constantine/{backend => math}/curves/bw6_761_frobenius.nim (98%)
 rename constantine/{backend => math}/curves/bw6_761_pairing.nim (98%)
 rename constantine/{backend => math}/curves/bw6_761_sqrt.nim (100%)
 rename constantine/{backend => math}/curves/bw6_761_subgroups.nim (94%)
 rename constantine/{backend => math}/curves/curve25519_sqrt.nim (89%)
 rename constantine/{backend => math}/curves/jubjub_sqrt.nim (95%)
 rename constantine/{backend => math}/curves/zoo_constants.nim (100%)
 rename constantine/{backend => math}/curves/zoo_endomorphisms.nim (97%)
 rename constantine/{backend => math}/curves/zoo_frobenius.nim (100%)
 rename constantine/{backend => math}/curves/zoo_generators.nim (100%)
 rename constantine/{backend => math}/curves/zoo_hash_to_curve.nim (100%)
 rename constantine/{backend => math}/curves/zoo_pairings.nim (100%)
 rename constantine/{backend => math}/curves/zoo_square_roots.nim (91%)
 rename constantine/{backend => math}/curves/zoo_square_roots_fp2.nim (100%)
 rename constantine/{backend => math}/curves/zoo_subgroups.nim (100%)
 rename constantine/{backend => math}/ec_shortweierstrass.nim (100%)
 rename constantine/{backend => math}/elliptic/README.md (100%)
 rename constantine/{backend => math}/elliptic/ec_endomorphism_accel.nim (99%)
 rename constantine/{backend => math}/elliptic/ec_scalar_mul.nim (99%)
 rename constantine/{backend => math}/elliptic/ec_shortweierstrass_affine.nim (97%)
 rename constantine/{backend => math}/elliptic/ec_shortweierstrass_jacobian.nim (99%)
 rename constantine/{backend => math}/elliptic/ec_shortweierstrass_projective.nim (99%)
 rename constantine/{backend => math}/elliptic/ec_twistededwards_affine.nim (97%)
 rename constantine/{backend => math}/elliptic/ec_twistededwards_projective.nim (99%)
 rename constantine/{backend/towers.nim => math/extension_fields.nim} (83%)
 rename constantine/{backend/tower_field_extensions => math/extension_fields}/README.md (100%)
 rename constantine/{backend/tower_field_extensions => math/extension_fields}/assembly/fp2_asm_x86_adx_bmi2.nim (98%)
 rename constantine/{backend/tower_field_extensions => math/extension_fields}/exponentiations.nim (99%)
 rename constantine/{backend/tower_field_extensions => math/extension_fields}/square_root_fp2.nim (98%)
 rename constantine/{backend/tower_field_extensions/extension_fields.nim => math/extension_fields/towers.nim} (99%)
 rename constantine/{backend => math}/io/README.md (100%)
 rename constantine/{backend => math}/io/io_bigints.nim (99%)
 rename constantine/{backend => math}/io/io_ec.nim (97%)
 rename constantine/{backend/io/io_towers.nim => math/io/io_extfields.nim} (98%)
 rename constantine/{backend => math}/io/io_fields.nim (98%)
 rename constantine/{backend/isogeny => math/isogenies}/README.md (100%)
 rename constantine/{backend/isogeny => math/isogenies}/frobenius.nim (98%)
 rename constantine/{backend => math}/pairing/README.md (100%)
 rename constantine/{backend => math}/pairing/cyclotomic_subgroup.nim (99%)
 rename constantine/{backend => math}/pairing/lines_eval.nim (99%)
 rename constantine/{backend => math}/pairing/miller_loops.nim (99%)
 rename constantine/{backend => math}/pairing/multi_pairing.md (100%)
 rename constantine/{backend => math}/pairing/pairing_bls12.nim (98%)
 rename constantine/{backend => math}/pairing/pairing_bn.nim (98%)
 rename constantine/{backend => math}/pairing/pairing_bw6_761.nim (98%)
 rename constantine/{backend => math}/pairings.nim (97%)
 rename constantine/{backend/primitives => platforms}/README.md (100%)
 rename constantine/{backend/config/common.nim => platforms/abstractions.nim} (94%)
 rename constantine/{backend/primitives => platforms}/bithacks.nim (100%)
 rename constantine/{backend/primitives => platforms/compilers}/addcarry_subborrow.nim (99%)
 rename constantine/{backend/primitives => platforms/compilers}/extended_precision.nim (99%)
 rename constantine/{backend/primitives => platforms/compilers}/extended_precision_64bit_uint128.nim (99%)
 rename constantine/{backend/primitives => platforms/compilers}/extended_precision_x86_64_gcc.nim (98%)
 rename constantine/{backend/primitives => platforms/compilers}/extended_precision_x86_64_msvc.nim (99%)
 rename constantine/{backend/primitives/constant_time.nim => platforms/constant_time/ct_routines.nim} (99%)
 rename constantine/{backend/primitives/constant_time_types.nim => platforms/constant_time/ct_types.nim} (100%)
 rename constantine/{backend/primitives => platforms/constant_time}/multiplexers.nim (99%)
 rename constantine/{backend/io => platforms}/endians.nim (99%)
 rename constantine/{backend/primitives => platforms/isa}/cpuinfo_x86.nim (100%)
 rename constantine/{backend/primitives => platforms/isa}/macro_assembler_x86.nim (100%)
 rename constantine/{backend => platforms}/primitives.nim (69%)
 rename constantine/{backend => }/signatures/README.md (100%)
 rename constantine/{backend => }/signatures/bls_signatures.nim (98%)
 rename tests/{backend => math}/support/canaries.nim (80%)
 rename tests/{backend => math}/support/ec_reference_scalar_mult.nim (95%)
 rename tests/{backend => math}/t_bigints.nim (99%)
 rename tests/{backend => math}/t_bigints_mod_vs_gmp.nim (97%)
 rename tests/{backend => math}/t_bigints_mul_high_words_vs_gmp.nim (97%)
 rename tests/{backend => math}/t_bigints_mul_vs_gmp.nim (96%)
 rename tests/{backend => math}/t_bigints_multimod.nim (98%)
 rename tests/{backend => math}/t_ec_conversion.nim (91%)
 rename tests/{backend => math}/t_ec_frobenius.nim (98%)
 rename tests/{backend => math}/t_ec_sage_bls12_377.nim (81%)
 rename tests/{backend => math}/t_ec_sage_bls12_381.nim (81%)
 rename tests/{backend => math}/t_ec_sage_bn254_nogami.nim (81%)
 rename tests/{backend => math}/t_ec_sage_bn254_snarks.nim (81%)
 rename tests/{backend => math}/t_ec_sage_bw6_761_g1.nim (86%)
 rename tests/{backend => math}/t_ec_sage_bw6_761_g2.nim (86%)
 rename tests/{backend => math}/t_ec_sage_template.nim (96%)
 rename tests/{backend => math}/t_ec_shortw_jac_g1_add_double.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_jac_g1_mixed_add.nim (89%)
 rename tests/{backend => math}/t_ec_shortw_jac_g1_mul_distri.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_jac_g1_mul_sanity.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_jac_g1_mul_vs_ref.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_add_double_bls12_377.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_add_double_bls12_381.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_add_double_bw6_761.nim (85%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim (85%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim (86%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim (92%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim (92%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim (92%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim (86%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim (86%)
 rename tests/{backend => math}/t_ec_shortw_prj_edge_cases.nim (95%)
 rename tests/{backend => math}/t_ec_shortw_prj_g1_add_double.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_prj_g1_mixed_add.nim (89%)
 rename tests/{backend => math}/t_ec_shortw_prj_g1_mul_distri.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_prj_g1_mul_sanity.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_prj_g1_mul_vs_ref.nim (91%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_add_double_bls12_377.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_add_double_bls12_381.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_add_double_bw6_761.nim (85%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim (85%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim (84%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim (86%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim (92%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim (92%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim (92%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim (86%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim (83%)
 rename tests/{backend => math}/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim (86%)
 rename tests/{backend => math}/t_ec_subgroups_bls12_377.nim (85%)
 rename tests/{backend => math}/t_ec_subgroups_bls12_381.nim (85%)
 rename tests/{backend => math}/t_ec_subgroups_bn254_nogami.nim (85%)
 rename tests/{backend => math}/t_ec_subgroups_bn254_snarks.nim (85%)
 rename tests/{backend => math}/t_ec_template.nim (98%)
 rename tests/{backend => math}/t_ec_twedwards_prj_add_double.nim (84%)
 rename tests/{backend => math}/t_ec_twedwards_prj_mul_distri.nim (85%)
 rename tests/{backend => math}/t_ec_twedwards_prj_mul_sanity.nim (85%)
 rename tests/{backend => math}/t_ec_twedwards_prj_mul_vs_ref.nim (85%)
 rename tests/{backend => math}/t_finite_fields.nim (95%)
 rename tests/{backend => math}/t_finite_fields.nim.cfg (100%)
 rename tests/{backend => math}/t_finite_fields_conditional_arithmetic.nim (87%)
 rename tests/{backend => math}/t_finite_fields_double_precision.nim (92%)
 rename tests/{backend => math}/t_finite_fields_double_precision.nim.cfg (100%)
 rename tests/{backend => math}/t_finite_fields_mulsquare.nim (94%)
 rename tests/{backend => math}/t_finite_fields_mulsquare.nim.cfg (100%)
 rename tests/{backend => math}/t_finite_fields_powinv.nim (97%)
 rename tests/{backend => math}/t_finite_fields_powinv.nim.cfg (100%)
 rename tests/{backend => math}/t_finite_fields_sqrt.nim (96%)
 rename tests/{backend => math}/t_finite_fields_sqrt.nim.cfg (100%)
 rename tests/{backend => math}/t_finite_fields_vs_gmp.nim (97%)
 rename tests/{backend => math}/t_fp12_anti_regression.nim (97%)
 rename tests/{backend => math}/t_fp12_bls12_377.nim (90%)
 rename tests/{backend => math}/t_fp12_bls12_381.nim (90%)
 rename tests/{backend => math}/t_fp12_bn254_snarks.nim (90%)
 rename tests/{backend => math}/t_fp12_exponentiation.nim (96%)
 rename tests/{backend => math}/t_fp12_frobenius.nim (89%)
 rename tests/{backend => math}/t_fp2.nim (92%)
 rename tests/{backend => math}/t_fp2_frobenius.nim (89%)
 rename tests/{backend => math}/t_fp2_sqrt.nim (94%)
 rename tests/{backend => math}/t_fp4.nim (95%)
 rename tests/{backend => math}/t_fp4_frobenius.nim (89%)
 rename tests/{backend => math}/t_fp6_bls12_377.nim (90%)
 rename tests/{backend => math}/t_fp6_bls12_381.nim (90%)
 rename tests/{backend => math}/t_fp6_bn254_snarks.nim (90%)
 rename tests/{backend => math}/t_fp6_bw6_761.nim (90%)
 rename tests/{backend => math}/t_fp6_frobenius.nim (89%)
 rename tests/{backend => math}/t_fp_cubic_root.nim (83%)
 rename tests/{backend => math}/t_fp_tower_frobenius_template.nim (94%)
 rename tests/{backend => math}/t_fp_tower_template.nim (98%)
 rename tests/{backend => math}/t_fr.nim (95%)
 rename tests/{backend => math}/t_hash_to_curve.nim (93%)
 rename tests/{backend => math}/t_hash_to_field.nim (96%)
 rename tests/{backend => math}/t_io_bigints.nim (97%)
 rename tests/{backend => math}/t_io_fields.nim (96%)
 rename tests/{backend => math}/t_io_fields.nim.cfg (100%)
 rename tests/{backend => math}/t_io_unsaturated.nim (86%)
 rename tests/{backend => math}/t_pairing_bls12_377_gt_subgroup.nim (81%)
 rename tests/{backend => math}/t_pairing_bls12_377_line_functions.nim (92%)
 rename tests/{backend => math}/t_pairing_bls12_377_optate.nim (83%)
 rename tests/{backend => math}/t_pairing_bls12_381_gt_subgroup.nim (81%)
 rename tests/{backend => math}/t_pairing_bls12_381_line_functions.nim (92%)
 rename tests/{backend => math}/t_pairing_bls12_381_multi.nim (87%)
 rename tests/{backend => math}/t_pairing_bls12_381_optate.nim (83%)
 rename tests/{backend => math}/t_pairing_bn254_nogami_gt_subgroup.nim (82%)
 rename tests/{backend => math}/t_pairing_bn254_nogami_optate.nim (84%)
 rename tests/{backend => math}/t_pairing_bn254_snarks_gt_subgroup.nim (82%)
 rename tests/{backend => math}/t_pairing_bn254_snarks_optate.nim (84%)
 rename tests/{backend => math}/t_pairing_bw6_761_gt_subgroup.nim (81%)
 rename tests/{backend => math}/t_pairing_bw6_761_optate.nim (83%)
 rename tests/{backend => math}/t_pairing_cyclotomic_subgroup.nim (93%)
 rename tests/{backend => math}/t_pairing_mul_fp12_by_lines.nim (97%)
 rename tests/{backend => math}/t_pairing_template.nim (89%)
 rename tests/{backend => math}/t_primitives.nim (98%)
 rename tests/{backend => math}/t_primitives_extended_precision.nim (95%)
 rename tests/{backend => math}/vectors/tv_BLS12_377_scalar_mul_G1.json (100%)
 rename tests/{backend => math}/vectors/tv_BLS12_377_scalar_mul_G2.json (100%)
 rename tests/{backend => math}/vectors/tv_BLS12_381_scalar_mul_G1.json (100%)
 rename tests/{backend => math}/vectors/tv_BLS12_381_scalar_mul_G2.json (100%)
 rename tests/{backend => math}/vectors/tv_BN254_Nogami_scalar_mul_G1.json (100%)
 rename tests/{backend => math}/vectors/tv_BN254_Nogami_scalar_mul_G2.json (100%)
 rename tests/{backend => math}/vectors/tv_BN254_Snarks_scalar_mul_G1.json (100%)
 rename tests/{backend => math}/vectors/tv_BN254_Snarks_scalar_mul_G2.json (100%)
 rename tests/{backend => math}/vectors/tv_BW6_761_scalar_mul_G1.json (100%)
 rename tests/{backend => math}/vectors/tv_BW6_761_scalar_mul_G2.json (100%)
 rename tests/{backend => math}/vectors/tv_h2c_v7_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json (100%)
 rename tests/{backend => math}/vectors/tv_h2c_v8_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/README.md (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate/aggregate_0x0000000000000000000000000000000000000000000000000000000000000000.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate/aggregate_0x5656565656565656565656565656565656565656565656565656565656565656.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate/aggregate_0xabababababababababababababababababababababababababababababababab.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate/aggregate_infinity_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate/aggregate_na_signatures.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate/aggregate_single_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate_verify/aggregate_verify_infinity_pubkey.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate_verify/aggregate_verify_na_pubkeys_and_infinity_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate_verify/aggregate_verify_na_pubkeys_and_na_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate_verify/aggregate_verify_tampered_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/aggregate_verify/aggregate_verify_valid.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/batch_verify/batch_verify_invalid_forged_signature_set.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/batch_verify/batch_verify_valid_simple_signature_set.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_infinity_with_false_b_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_infinity_with_true_b_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_not_in_G1.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_not_in_curve.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_too_few_bytes.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_too_many_bytes.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_with_b_flag_and_a_flag_true.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_with_b_flag_and_x_nonzero.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_with_wrong_c_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_x_equal_to_modulus.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_fails_x_greater_than_modulus.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_succeeds_correct_point.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G1/deserialization_succeeds_infinity_with_true_b_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_infinity_with_false_b_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_infinity_with_true_b_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_not_in_G2.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_not_in_curve.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_too_few_bytes.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_too_many_bytes.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_with_b_flag_and_a_flag_true.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_with_b_flag_and_x_nonzero.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_with_wrong_c_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_xim_equal_to_modulus.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_xim_greater_than_modulus.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_xre_equal_to_modulus.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_fails_xre_greater_than_modulus.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_succeeds_correct_point.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/deserialization_G2/deserialization_succeeds_infinity_with_true_b_flag.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_4f079f946446fabf.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_5a38e6b4017fe4dd.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_a698ea45b109f303.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_infinity_pubkey.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_infinity_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_na_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_3d7576f3c0e3570a.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_5e745ad0c6199a6c.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_652ce62f09290811.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_valid_3d7576f3c0e3570a.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_valid_5e745ad0c6199a6c.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/fast_aggregate_verify/fast_aggregate_verify_valid_652ce62f09290811.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/hash_to_G2/hash_to_G2__2782afaa8406d038.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/hash_to_G2/hash_to_G2__7590bd067999bbfb.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/hash_to_G2/hash_to_G2__a54942c8e365f378.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/hash_to_G2/hash_to_G2__c938b486cf69e8f7.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_11b8c7cad5238946.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_142f678a8d05fcd1.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_37286e1a6d1f6eb3.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_7055381f640f2c1d.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_84d45c9c7cca6b92.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_8cd3d4d0d9a5b265.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_c82df61aa3ee60fb.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_d0e28d7e76eb6e9c.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_f2ae1097e7d0e18b.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/sign/sign_case_zero_privkey.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_infinity_pubkey_and_infinity_signature.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_195246ee3bd3b6ec.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_2ea479adf8c40300.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_2f09d443ab8a3ac2.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_3208262581c8fc09.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_6b3b17f6962a490c.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_6eeb7c52dfd9baf0.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_8761a0b7e920c323.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_d34885d766d5f705.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_tampered_signature_case_e8a50c445c855360.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_195246ee3bd3b6ec.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_2ea479adf8c40300.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_2f09d443ab8a3ac2.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_3208262581c8fc09.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_6b3b17f6962a490c.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_6eeb7c52dfd9baf0.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_8761a0b7e920c323.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_d34885d766d5f705.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_valid_case_e8a50c445c855360.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_195246ee3bd3b6ec.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_2ea479adf8c40300.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_2f09d443ab8a3ac2.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_3208262581c8fc09.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_6b3b17f6962a490c.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_6eeb7c52dfd9baf0.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_8761a0b7e920c323.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_d34885d766d5f705.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verify_wrong_pubkey_case_e8a50c445c855360.json (100%)
 rename tests/{blssig_pop_on_bls12381_g2_test_vectors_v0.1.1 => protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1}/verify/verifycase_one_privkey_47117849458281be.json (100%)

diff --git a/README.md b/README.md
index 2be6e97..1a74d3a 100644
--- a/README.md
+++ b/README.md
@@ -66,7 +66,7 @@ After [installation](#installation), the available high-level protocols are:
 _The backend, unlike protocols, is not public. Here be dragons._
 
 At the moment the following curves are implemented, adding a new curve only requires adding the prime modulus
-and its bitsize in [constantine/config/curves.nim](constantine/backend/config/curves_declaration.nim).
+and its bitsize in [constantine/config/curves.nim](constantine/math/config/curves_declaration.nim).
 
 The following curves are configured:
 
@@ -81,7 +81,7 @@ The following curves are configured:
   - Jubjub, a curve embedded in BLS12-381 scalar field to be used in zk-SNARKS circuits.
   - Bandersnatch, a more efficient curve embedded in BLS12-381 scalar field to be used in zk-SNARKS circuits.
 - Other curves
-  - Curve25519, used in ed25519 and X25519 from TLS 1.3 protocol and the Signal protocol.
+  - Edwards25519, used in ed25519 and X25519 from TLS 1.3 protocol and the Signal protocol.
   With Ristretto, it can be used in bulletproofs.
 
 ## Installation
diff --git a/benchmarks/bench_blueprint.nim b/benchmarks/bench_blueprint.nim
index b11ad0c..e6c0999 100644
--- a/benchmarks/bench_blueprint.nim
+++ b/benchmarks/bench_blueprint.nim
@@ -14,7 +14,7 @@
 
 import
   # Internal
-  ../constantine/backend/config/common,
+  ../constantine/platforms/abstractions,
   # Helpers
   ../helpers/prng_unsafe,
   ./platforms,
diff --git a/benchmarks/bench_ec_g1.nim b/benchmarks/bench_ec_g1.nim
index 79a3eb5..ca23181 100644
--- a/benchmarks/bench_ec_g1.nim
+++ b/benchmarks/bench_ec_g1.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/elliptic/[
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/elliptic/[
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian],
   # Helpers
@@ -34,7 +34,7 @@ const AvailableCurves = [
   # P224,
   BN254_Nogami,
   BN254_Snarks,
-  # Curve25519,
+  # Edwards25519,
   # P256,
   # Secp256k1,
   BLS12_377,
diff --git a/benchmarks/bench_ec_g2.nim b/benchmarks/bench_ec_g2.nim
index 5290b18..00cd37f 100644
--- a/benchmarks/bench_ec_g2.nim
+++ b/benchmarks/bench_ec_g2.nim
@@ -8,10 +8,10 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
-  ../constantine/backend/elliptic/[
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
+  ../constantine/math/elliptic/[
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian],
   # Helpers
@@ -35,7 +35,7 @@ const AvailableCurves = [
   # P224,
   BN254_Nogami,
   BN254_Snarks,
-  # Curve25519,
+  # Edwards25519,
   # P256,
   # Secp256k1,
   BLS12_377,
diff --git a/benchmarks/bench_elliptic_template.nim b/benchmarks/bench_elliptic_template.nim
index 68b2702..b2ed489 100644
--- a/benchmarks/bench_elliptic_template.nim
+++ b/benchmarks/bench_elliptic_template.nim
@@ -14,10 +14,11 @@
 
 import
   # Internals
-  ../constantine/backend/config/[curves, common],
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/io/io_bigints,
-  ../constantine/backend/elliptic/[
+  ../constantine/platforms/abstractions,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/io/io_bigints,
+  ../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian,
@@ -27,7 +28,7 @@ import
   ./platforms,
   ./bench_blueprint,
   # Reference unsafe scalar multiplication
-  ../tests/backend/support/ec_reference_scalar_mult
+  ../tests/math/support/ec_reference_scalar_mult
 
 export notes
 proc separator*() = separator(177)
diff --git a/benchmarks/bench_fields_template.nim b/benchmarks/bench_fields_template.nim
index b6ec393..e1527a4 100644
--- a/benchmarks/bench_fields_template.nim
+++ b/benchmarks/bench_fields_template.nim
@@ -14,10 +14,11 @@
 
 import
   # Internals
-  ../constantine/backend/config/[common, curves],
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
-  ../constantine/backend/curves/zoo_square_roots,
+  ../constantine/platforms/abstractions,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
+  ../constantine/math/curves/zoo_square_roots,
   # Helpers
   ../helpers/prng_unsafe,
   ./bench_blueprint
diff --git a/benchmarks/bench_fp.nim b/benchmarks/bench_fp.nim
index 8566024..18eae36 100644
--- a/benchmarks/bench_fp.nim
+++ b/benchmarks/bench_fp.nim
@@ -8,10 +8,10 @@
 
 import
   # Internals
-  ../constantine/backend/config/[curves, common],
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/io/io_bigints,
-  ../constantine/backend/curves/zoo_square_roots,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/io/io_bigints,
+  ../constantine/math/curves/zoo_square_roots,
   # Helpers
   ../helpers/static_for,
   ./bench_fields_template
@@ -29,7 +29,7 @@ const AvailableCurves = [
   # P224,
   BN254_Nogami,
   BN254_Snarks,
-  Curve25519,
+  Edwards25519,
   Bandersnatch,
   P256,
   Secp256k1,
diff --git a/benchmarks/bench_fp12.nim b/benchmarks/bench_fp12.nim
index 8fd3b7f..381e20d 100644
--- a/benchmarks/bench_fp12.nim
+++ b/benchmarks/bench_fp12.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_fields_template,
diff --git a/benchmarks/bench_fp2.nim b/benchmarks/bench_fp2.nim
index 71ba783..69447fd 100644
--- a/benchmarks/bench_fp2.nim
+++ b/benchmarks/bench_fp2.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_fields_template,
diff --git a/benchmarks/bench_fp4.nim b/benchmarks/bench_fp4.nim
index 089cca8..2250bb5 100644
--- a/benchmarks/bench_fp4.nim
+++ b/benchmarks/bench_fp4.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_fields_template,
diff --git a/benchmarks/bench_fp6.nim b/benchmarks/bench_fp6.nim
index 1d0a892..28327b5 100644
--- a/benchmarks/bench_fp6.nim
+++ b/benchmarks/bench_fp6.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_fields_template,
diff --git a/benchmarks/bench_fp_double_precision.nim b/benchmarks/bench_fp_double_precision.nim
index eef7e3c..f03e109 100644
--- a/benchmarks/bench_fp_double_precision.nim
+++ b/benchmarks/bench_fp_double_precision.nim
@@ -14,9 +14,10 @@
 
 import
   # Internals
-  ../constantine/backend/config/[curves, common],
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/platforms/abstractions,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/[prng_unsafe, static_for],
   ./platforms,
diff --git a/benchmarks/bench_hash_to_curve.nim b/benchmarks/bench_hash_to_curve.nim
index 541f8ce..e574072 100644
--- a/benchmarks/bench_hash_to_curve.nim
+++ b/benchmarks/bench_hash_to_curve.nim
@@ -8,13 +8,15 @@
 
 import
   # Internals
-  ../constantine/backend/config/[common, curves, type_bigint, type_ff],
-  ../constantine/backend/[towers, hashes],
-  ../constantine/backend/io/[io_bigints, io_ec],
-  ../constantine/backend/elliptic/[
+  ../constantine/platforms/abstractions,
+  ../constantine/math/config/curves,
+  ../constantine/math/extension_fields,
+  ../constantine/math/io/[io_bigints, io_ec],
+  ../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective],
-  ../constantine/backend/hash_to_curve/hash_to_curve,
+  ../constantine/hash_to_curve/hash_to_curve,
+  ../constantine/hashes,
   # Helpers
   ../helpers/prng_unsafe,
   ./bench_blueprint
diff --git a/benchmarks/bench_pairing_bls12_377.nim b/benchmarks/bench_pairing_bls12_377.nim
index fc5594e..b7ce8b1 100644
--- a/benchmarks/bench_pairing_bls12_377.nim
+++ b/benchmarks/bench_pairing_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_pairing_template,
diff --git a/benchmarks/bench_pairing_bls12_381.nim b/benchmarks/bench_pairing_bls12_381.nim
index a280e0c..2854b9d 100644
--- a/benchmarks/bench_pairing_bls12_381.nim
+++ b/benchmarks/bench_pairing_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_pairing_template,
diff --git a/benchmarks/bench_pairing_bn254_nogami.nim b/benchmarks/bench_pairing_bn254_nogami.nim
index 0152133..ffd0653 100644
--- a/benchmarks/bench_pairing_bn254_nogami.nim
+++ b/benchmarks/bench_pairing_bn254_nogami.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_pairing_template,
diff --git a/benchmarks/bench_pairing_bn254_snarks.nim b/benchmarks/bench_pairing_bn254_snarks.nim
index 9b1330c..1625029 100644
--- a/benchmarks/bench_pairing_bn254_snarks.nim
+++ b/benchmarks/bench_pairing_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_pairing_template,
diff --git a/benchmarks/bench_pairing_template.nim b/benchmarks/bench_pairing_template.nim
index 4ea6f21..ee03345 100644
--- a/benchmarks/bench_pairing_template.nim
+++ b/benchmarks/bench_pairing_template.nim
@@ -14,18 +14,19 @@
 
 import
   # Internals
-  ../constantine/backend/config/[curves, common],
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
-  ../constantine/backend/ec_shortweierstrass,
-  ../constantine/backend/curves/zoo_subgroups,
-  ../constantine/backend/pairing/[
+  ../constantine/platforms/abstractions,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
+  ../constantine/math/ec_shortweierstrass,
+  ../constantine/math/curves/zoo_subgroups,
+  ../constantine/math/pairing/[
     cyclotomic_subgroup,
     lines_eval,
     pairing_bls12,
     pairing_bn
   ],
-  ../constantine/backend/curves/zoo_pairings,
+  ../constantine/math/curves/zoo_pairings,
   # Helpers
   ../helpers/prng_unsafe,
   ./bench_blueprint
diff --git a/benchmarks/bench_sha256.nim b/benchmarks/bench_sha256.nim
index 98882e9..b10d6da 100644
--- a/benchmarks/bench_sha256.nim
+++ b/benchmarks/bench_sha256.nim
@@ -1,6 +1,6 @@
 import
   # Internals
-  ../constantine/backend/hashes,
+  ../constantine/hashes,
   # Helpers
   ../helpers/prng_unsafe,
   ./bench_blueprint
diff --git a/benchmarks/bench_summary_bls12_377.nim b/benchmarks/bench_summary_bls12_377.nim
index 2759b32..107e01b 100644
--- a/benchmarks/bench_summary_bls12_377.nim
+++ b/benchmarks/bench_summary_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_summary_template,
diff --git a/benchmarks/bench_summary_bls12_381.nim b/benchmarks/bench_summary_bls12_381.nim
index 788bbb2..7e7abf6 100644
--- a/benchmarks/bench_summary_bls12_381.nim
+++ b/benchmarks/bench_summary_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_summary_template,
diff --git a/benchmarks/bench_summary_bn254_nogami.nim b/benchmarks/bench_summary_bn254_nogami.nim
index 129c098..2703b92 100644
--- a/benchmarks/bench_summary_bn254_nogami.nim
+++ b/benchmarks/bench_summary_bn254_nogami.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_summary_template,
diff --git a/benchmarks/bench_summary_bn254_snarks.nim b/benchmarks/bench_summary_bn254_snarks.nim
index 6450095..8582b30 100644
--- a/benchmarks/bench_summary_bn254_snarks.nim
+++ b/benchmarks/bench_summary_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../constantine/backend/config/curves,
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/towers,
+  ../constantine/math/config/curves,
+  ../constantine/math/arithmetic,
+  ../constantine/math/extension_fields,
   # Helpers
   ../helpers/static_for,
   ./bench_summary_template,
diff --git a/benchmarks/bench_summary_template.nim b/benchmarks/bench_summary_template.nim
index 99cf85c..6d13176 100644
--- a/benchmarks/bench_summary_template.nim
+++ b/benchmarks/bench_summary_template.nim
@@ -14,21 +14,23 @@
 
 import
   # Internals
-  ../constantine/backend/config/[curves, common],
-  ../constantine/backend/[arithmetic, hashes, towers],
-  ../constantine/backend/elliptic/[
+  ../constantine/platforms/abstractions,
+  ../constantine/math/config/curves,
+  ../constantine/math/[arithmetic, extension_fields],
+  ../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian,
     ec_scalar_mul, ec_endomorphism_accel],
-  ../constantine/backend/curves/zoo_subgroups,
-  ../constantine/backend/hash_to_curve/hash_to_curve,
-  ../constantine/backend/pairing/[
+  ../constantine/math/curves/zoo_subgroups,
+  ../constantine/math/pairing/[
     cyclotomic_subgroup,
     pairing_bls12,
     pairing_bn
   ],
-  ../constantine/backend/curves/zoo_pairings,
+  ../constantine/math/curves/zoo_pairings,
+  ../constantine/hashes,
+  ../constantine/hash_to_curve/hash_to_curve,
   # Helpers
   ../helpers/[prng_unsafe, static_for],
   ./bench_blueprint
diff --git a/constantine.nimble b/constantine.nimble
index 58e60f9..786b3eb 100644
--- a/constantine.nimble
+++ b/constantine.nimble
@@ -1,7 +1,7 @@
 packageName   = "constantine"
 version       = "0.0.1"
 author        = "Status Research & Development GmbH"
-description   = "This library provides constant time big int primitives."
+description   = "This library provides thoroughly tested and highly-optimized implementations of cryptography protocols."
 license       = "MIT or Apache License 2.0"
 
 # Dependencies
@@ -23,166 +23,166 @@ const buildParallel = "test_parallel.txt"
 const testDesc: seq[tuple[path: string, useGMP: bool]] = @[
   # Primitives
   # ----------------------------------------------------------
-  ("tests/backend/t_primitives.nim", false),
-  ("tests/backend/t_primitives_extended_precision.nim", false),
+  ("tests/math/t_primitives.nim", false),
+  ("tests/math/t_primitives_extended_precision.nim", false),
   # Big ints
   # ----------------------------------------------------------
-  ("tests/backend/t_io_bigints.nim", false),
-  ("tests/backend/t_io_unsaturated.nim", false),
-  ("tests/backend/t_bigints.nim", false),
-  ("tests/backend/t_bigints_multimod.nim", false),
-  ("tests/backend/t_bigints_mod_vs_gmp.nim", true),
-  ("tests/backend/t_bigints_mul_vs_gmp.nim", true),
-  ("tests/backend/t_bigints_mul_high_words_vs_gmp.nim", true),
+  ("tests/math/t_io_bigints.nim", false),
+  ("tests/math/t_io_unsaturated.nim", false),
+  ("tests/math/t_bigints.nim", false),
+  ("tests/math/t_bigints_multimod.nim", false),
+  ("tests/math/t_bigints_mod_vs_gmp.nim", true),
+  ("tests/math/t_bigints_mul_vs_gmp.nim", true),
+  ("tests/math/t_bigints_mul_high_words_vs_gmp.nim", true),
   # Field
   # ----------------------------------------------------------
-  ("tests/backend/t_io_fields", false),
-  ("tests/backend/t_finite_fields.nim", false),
-  ("tests/backend/t_finite_fields_conditional_arithmetic.nim", false),
-  ("tests/backend/t_finite_fields_mulsquare.nim", false),
-  ("tests/backend/t_finite_fields_sqrt.nim", false),
-  ("tests/backend/t_finite_fields_powinv.nim", false),
-  ("tests/backend/t_finite_fields_vs_gmp.nim", true),
-  ("tests/backend/t_fp_cubic_root.nim", false),
+  ("tests/math/t_io_fields", false),
+  ("tests/math/t_finite_fields.nim", false),
+  ("tests/math/t_finite_fields_conditional_arithmetic.nim", false),
+  ("tests/math/t_finite_fields_mulsquare.nim", false),
+  ("tests/math/t_finite_fields_sqrt.nim", false),
+  ("tests/math/t_finite_fields_powinv.nim", false),
+  ("tests/math/t_finite_fields_vs_gmp.nim", true),
+  ("tests/math/t_fp_cubic_root.nim", false),
   # Double-precision finite fields
   # ----------------------------------------------------------
-  ("tests/backend/t_finite_fields_double_precision.nim", false),
+  ("tests/math/t_finite_fields_double_precision.nim", false),
   # Towers of extension fields
   # ----------------------------------------------------------
-  ("tests/backend/t_fp2.nim", false),
-  ("tests/backend/t_fp2_sqrt.nim", false),
-  ("tests/backend/t_fp4.nim", false),
-  ("tests/backend/t_fp6_bn254_snarks.nim", false),
-  ("tests/backend/t_fp6_bls12_377.nim", false),
-  ("tests/backend/t_fp6_bls12_381.nim", false),
-  ("tests/backend/t_fp6_bw6_761.nim", false),
-  ("tests/backend/t_fp12_bn254_snarks.nim", false),
-  ("tests/backend/t_fp12_bls12_377.nim", false),
-  ("tests/backend/t_fp12_bls12_381.nim", false),
-  ("tests/backend/t_fp12_exponentiation.nim", false),
-  ("tests/backend/t_fp12_anti_regression.nim", false),
+  ("tests/math/t_fp2.nim", false),
+  ("tests/math/t_fp2_sqrt.nim", false),
+  ("tests/math/t_fp4.nim", false),
+  ("tests/math/t_fp6_bn254_snarks.nim", false),
+  ("tests/math/t_fp6_bls12_377.nim", false),
+  ("tests/math/t_fp6_bls12_381.nim", false),
+  ("tests/math/t_fp6_bw6_761.nim", false),
+  ("tests/math/t_fp12_bn254_snarks.nim", false),
+  ("tests/math/t_fp12_bls12_377.nim", false),
+  ("tests/math/t_fp12_bls12_381.nim", false),
+  ("tests/math/t_fp12_exponentiation.nim", false),
+  ("tests/math/t_fp12_anti_regression.nim", false),
 
-  ("tests/backend/t_fp4_frobenius.nim", false),
-  ("tests/backend/t_fp6_frobenius.nim", false),
-  ("tests/backend/t_fp12_frobenius.nim", false),
+  ("tests/math/t_fp4_frobenius.nim", false),
+  ("tests/math/t_fp6_frobenius.nim", false),
+  ("tests/math/t_fp12_frobenius.nim", false),
 
   # Elliptic curve arithmetic 
   # ----------------------------------------------------------
-  ("tests/backend/t_ec_conversion.nim", false),
+  ("tests/math/t_ec_conversion.nim", false),
 
   # Elliptic curve arithmetic G1
   # ----------------------------------------------------------
-  # ("tests/backend/t_ec_shortw_prj_g1_add_double.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g1_mul_sanity.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g1_mul_distri.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g1_mul_vs_ref.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g1_mixed_add.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g1_add_double.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g1_mul_sanity.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g1_mul_distri.nim", false),
+  ("tests/math/t_ec_shortw_prj_g1_mul_vs_ref.nim", false),
+  ("tests/math/t_ec_shortw_prj_g1_mixed_add.nim", false),
 
-  # ("tests/backend/t_ec_shortw_jac_g1_add_double.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g1_mul_sanity.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g1_mul_distri.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g1_mul_vs_ref.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g1_mixed_add.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g1_add_double.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g1_mul_sanity.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g1_mul_distri.nim", false),
+  ("tests/math/t_ec_shortw_jac_g1_mul_vs_ref.nim", false),
+  ("tests/math/t_ec_shortw_jac_g1_mixed_add.nim", false),
 
-  ("tests/backend/t_ec_twedwards_prj_add_double", false),
-  ("tests/backend/t_ec_twedwards_prj_mul_sanity", false),
-  ("tests/backend/t_ec_twedwards_prj_mul_distri", false),
+  ("tests/math/t_ec_twedwards_prj_add_double", false),
+  ("tests/math/t_ec_twedwards_prj_mul_sanity", false),
+  ("tests/math/t_ec_twedwards_prj_mul_distri", false),
  
 
   # Elliptic curve arithmetic G2
   # ----------------------------------------------------------
-  # ("tests/backend/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim", false),
 
-  # ("tests/backend/t_ec_shortw_prj_g2_add_double_bls12_381.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_add_double_bls12_381.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim", false),
 
-  # ("tests/backend/t_ec_shortw_prj_g2_add_double_bls12_377.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_add_double_bls12_377.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim", false),
 
-  # ("tests/backend/t_ec_shortw_prj_g2_add_double_bw6_761.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim", false),
-  # ("tests/backend/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim", false),
-  ("tests/backend/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_add_double_bw6_761.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim", false),
+  # ("tests/math/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim", false),
+  ("tests/math/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim", false),
 
-  # ("tests/backend/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim", false),
 
-  # ("tests/backend/t_ec_shortw_jac_g2_add_double_bls12_381.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_add_double_bls12_381.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim", false),
 
-  # ("tests/backend/t_ec_shortw_jac_g2_add_double_bls12_377.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_add_double_bls12_377.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim", false),
 
-  # ("tests/backend/t_ec_shortw_jac_g2_add_double_bw6_761.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim", false),
-  # ("tests/backend/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim", false),
-  ("tests/backend/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_add_double_bw6_761.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim", false),
+  # ("tests/math/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim", false),
+  ("tests/math/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim", false),
 
   # Elliptic curve arithmetic vs Sagemath
   # ----------------------------------------------------------
-  ("tests/backend/t_ec_frobenius.nim", false),
-  ("tests/backend/t_ec_sage_bn254_nogami.nim", false),
-  ("tests/backend/t_ec_sage_bn254_snarks.nim", false),
-  ("tests/backend/t_ec_sage_bls12_377.nim", false),
-  ("tests/backend/t_ec_sage_bls12_381.nim", false),
+  ("tests/math/t_ec_frobenius.nim", false),
+  ("tests/math/t_ec_sage_bn254_nogami.nim", false),
+  ("tests/math/t_ec_sage_bn254_snarks.nim", false),
+  ("tests/math/t_ec_sage_bls12_377.nim", false),
+  ("tests/math/t_ec_sage_bls12_381.nim", false),
   # Edge cases highlighted by past bugs
   # ----------------------------------------------------------
-  ("tests/backend/t_ec_shortw_prj_edge_cases.nim", false),
+  ("tests/math/t_ec_shortw_prj_edge_cases.nim", false),
 
   # Subgroups and cofactors
   # ----------------------------------------------------------
-  ("tests/backend/t_ec_subgroups_bn254_nogami.nim", false),
-  ("tests/backend/t_ec_subgroups_bn254_snarks.nim", false),
-  ("tests/backend/t_ec_subgroups_bls12_377.nim", false),
-  ("tests/backend/t_ec_subgroups_bls12_381.nim", false),
+  ("tests/math/t_ec_subgroups_bn254_nogami.nim", false),
+  ("tests/math/t_ec_subgroups_bn254_snarks.nim", false),
+  ("tests/math/t_ec_subgroups_bls12_377.nim", false),
+  ("tests/math/t_ec_subgroups_bls12_381.nim", false),
 
-  ("tests/backend/t_pairing_bn254_nogami_gt_subgroup.nim", false),
-  ("tests/backend/t_pairing_bn254_snarks_gt_subgroup.nim", false),
-  ("tests/backend/t_pairing_bls12_377_gt_subgroup.nim", false),
-  ("tests/backend/t_pairing_bls12_381_gt_subgroup.nim", false),
-  ("tests/backend/t_pairing_bw6_761_gt_subgroup.nim", false),
+  ("tests/math/t_pairing_bn254_nogami_gt_subgroup.nim", false),
+  ("tests/math/t_pairing_bn254_snarks_gt_subgroup.nim", false),
+  ("tests/math/t_pairing_bls12_377_gt_subgroup.nim", false),
+  ("tests/math/t_pairing_bls12_381_gt_subgroup.nim", false),
+  ("tests/math/t_pairing_bw6_761_gt_subgroup.nim", false),
 
   # Pairing
   # ----------------------------------------------------------
-  # ("tests/backend/t_pairing_bls12_377_line_functions.nim", false),
-  # ("tests/backend/t_pairing_bls12_381_line_functions.nim", false),
-  ("tests/backend/t_pairing_mul_fp12_by_lines.nim", false),
-  ("tests/backend/t_pairing_cyclotomic_subgroup.nim", false),
-  ("tests/backend/t_pairing_bn254_nogami_optate.nim", false),
-  ("tests/backend/t_pairing_bn254_snarks_optate.nim", false),
-  ("tests/backend/t_pairing_bls12_377_optate.nim", false),
-  ("tests/backend/t_pairing_bls12_381_optate.nim", false),
-  ("tests/backend/t_pairing_bls12_381_multi.nim", false),
+  # ("tests/math/t_pairing_bls12_377_line_functions.nim", false),
+  # ("tests/math/t_pairing_bls12_381_line_functions.nim", false),
+  ("tests/math/t_pairing_mul_fp12_by_lines.nim", false),
+  ("tests/math/t_pairing_cyclotomic_subgroup.nim", false),
+  ("tests/math/t_pairing_bn254_nogami_optate.nim", false),
+  ("tests/math/t_pairing_bn254_snarks_optate.nim", false),
+  ("tests/math/t_pairing_bls12_377_optate.nim", false),
+  ("tests/math/t_pairing_bls12_381_optate.nim", false),
+  ("tests/math/t_pairing_bls12_381_multi.nim", false),
 
   # Hashing to elliptic curves
   # ----------------------------------------------------------
-  ("tests/backend/t_hash_to_field.nim", false),
-  ("tests/backend/t_hash_to_curve.nim", false),
+  ("tests/math/t_hash_to_field.nim", false),
+  ("tests/math/t_hash_to_curve.nim", false),
 
   # Prime order fields
   # ----------------------------------------------------------
-  ("tests/backend/t_fr.nim", false),
+  ("tests/math/t_fr.nim", false),
 
   # Hashing vs OpenSSL
   # ----------------------------------------------------------
@@ -196,20 +196,20 @@ const testDesc: seq[tuple[path: string, useGMP: bool]] = @[
 
 # For temporary (hopefully) investigation that can only be reproduced in CI
 const useDebug = [
-  "tests/backend/t_bigints.nim",
-  "tests/backend/t_hash_sha256_vs_openssl.nim",
+  "tests/math/t_bigints.nim",
+  "tests/math/t_hash_sha256_vs_openssl.nim",
 ]
 
 # Tests that uses sequences require Nim GC, stack scanning and nil pointer passed to openarray
 # In particular the tests that uses the json test vectors, don't sanitize them.
 # we do use gc:none to help
 const skipSanitizers = [
-  "tests/backend/t_ec_sage_bn254_nogami.nim",
-  "tests/backend/t_ec_sage_bn254_snarks.nim",
-  "tests/backend/t_ec_sage_bls12_377.nim",
-  "tests/backend/t_ec_sage_bls12_381.nim",
-  "tests/backend/t_hash_to_field.nim",
-  "tests/backend/t_hash_to_curve.nim"
+  "tests/math/t_ec_sage_bn254_nogami.nim",
+  "tests/math/t_ec_sage_bn254_snarks.nim",
+  "tests/math/t_ec_sage_bls12_377.nim",
+  "tests/math/t_ec_sage_bls12_381.nim",
+  "tests/math/t_hash_to_field.nim",
+  "tests/math/t_hash_to_curve.nim"
 ]
 
 when defined(windows):
diff --git a/constantine/backend/primitives/static_for.nim b/constantine/backend/primitives/static_for.nim
deleted file mode 100644
index af531ee..0000000
--- a/constantine/backend/primitives/static_for.nim
+++ /dev/null
@@ -1,36 +0,0 @@
-# Constantine
-# Copyright (c) 2018-2019    Status Research & Development GmbH
-# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
-# Licensed and distributed under either of
-#   * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
-#   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
-# at your option. This file may not be copied, modified, or distributed except according to those terms.
-
-import std/macros
-
-proc replaceNodes(ast: NimNode, what: NimNode, by: NimNode): NimNode =
-  # Replace "what" ident node by "by"
-  proc inspect(node: NimNode): NimNode =
-    case node.kind:
-    of {nnkIdent, nnkSym}:
-      if node.eqIdent(what):
-        return by
-      return node
-    of nnkEmpty:
-      return node
-    of nnkLiterals:
-      return node
-    else:
-      var rTree = node.kind.newTree()
-      for child in node:
-        rTree.add inspect(child)
-      return rTree
-  result = inspect(ast)
-
-macro staticFor*(idx: untyped{nkIdent}, start, stopEx: static int, body: untyped): untyped =
-  result = newStmtList()
-  for i in start ..< stopEx:
-    result.add nnkBlockStmt.newTree(
-      ident("unrolledIter_" & $idx & $i),
-      body.replaceNodes(idx, newLit i)
-    )
diff --git a/constantine/blssig_pop_on_bls12381_g2.nim b/constantine/blssig_pop_on_bls12381_g2.nim
index 5856b97..07074fe 100644
--- a/constantine/blssig_pop_on_bls12381_g2.nim
+++ b/constantine/blssig_pop_on_bls12381_g2.nim
@@ -7,24 +7,21 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-    ./backend/config/[
-      common, curves, type_bigint, type_ff
-    ],
-    ./backend/[
+    ./platforms/abstractions,
+    ./math/config/curves,
+    ./math/[
       ec_shortweierstrass,
-      hash_to_curve/hash_to_curve,
-      hashes,
-      towers,
+      extension_fields,
       arithmetic,
-      signatures/bls_signatures,
-      curves/zoo_subgroups,
-      primitives
+      curves/zoo_subgroups
     ],
-    ./backend/io/[io_bigints, io_fields]
+    ./math/io/[io_bigints, io_fields],
+    hashes,
+    signatures/bls_signatures
 
 export
   curves, # generic sandwich on matchingBigInt
-  towers, # generic sandwich on extension field access
+  extension_fields, # generic sandwich on extension field access
   hashes, # generic sandwich on sha256
   ec_shortweierstrass # generic sandwich on affine
 
diff --git a/constantine/ethereum_evm_precompiles.nim b/constantine/ethereum_evm_precompiles.nim
index d75f483..30d1772 100644
--- a/constantine/ethereum_evm_precompiles.nim
+++ b/constantine/ethereum_evm_precompiles.nim
@@ -7,13 +7,14 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ./backend/config/[common, curves],
-  ./backend/[arithmetic, towers],
-  ./backend/arithmetic/limbs_montgomery,
-  ./backend/ec_shortweierstrass,
-  ./backend/pairing/[pairing_bn, miller_loops, cyclotomic_subgroup],
-  ./backend/curves/zoo_subgroups,
-  ./backend/io/[io_bigints, io_fields]
+  ./platforms/abstractions,
+  ./math/config/curves,
+  ./math/[arithmetic, extension_fields],
+  ./math/arithmetic/limbs_montgomery,
+  ./math/ec_shortweierstrass,
+  ./math/pairing/[pairing_bn, miller_loops, cyclotomic_subgroup],
+  ./math/curves/zoo_subgroups,
+  ./math/io/[io_bigints, io_fields]
 
 # ############################################################
 #
diff --git a/constantine/backend/hash_to_curve/README.md b/constantine/hash_to_curve/README.md
similarity index 100%
rename from constantine/backend/hash_to_curve/README.md
rename to constantine/hash_to_curve/README.md
diff --git a/constantine/backend/hash_to_curve/h2c_hash_to_field.nim b/constantine/hash_to_curve/h2c_hash_to_field.nim
similarity index 97%
rename from constantine/backend/hash_to_curve/h2c_hash_to_field.nim
rename to constantine/hash_to_curve/h2c_hash_to_field.nim
index 1cfde96..0632f8c 100644
--- a/constantine/backend/hash_to_curve/h2c_hash_to_field.nim
+++ b/constantine/hash_to_curve/h2c_hash_to_field.nim
@@ -8,11 +8,12 @@
 
 import
   # Internals
+  ../platforms/[abstractions, endians],
   ../hashes,
-  ../io/[endians, io_bigints, io_fields],
-  ../config/[common, curves, type_bigint, type_ff],
-  ../arithmetic/limbs_montgomery,
-  ../tower_field_extensions/extension_fields
+  ../math/io/[io_bigints, io_fields],
+  ../math/config/curves,
+  ../math/arithmetic/limbs_montgomery,
+  ../math/extension_fields/towers
 
 # ############################################################
 #
diff --git a/constantine/backend/isogeny/h2c_isogeny_maps.nim b/constantine/hash_to_curve/h2c_isogeny_maps.nim
similarity index 97%
rename from constantine/backend/isogeny/h2c_isogeny_maps.nim
rename to constantine/hash_to_curve/h2c_isogeny_maps.nim
index 83c1522..46bf59a 100644
--- a/constantine/backend/isogeny/h2c_isogeny_maps.nim
+++ b/constantine/hash_to_curve/h2c_isogeny_maps.nim
@@ -8,9 +8,10 @@
 
 import
   # Internals
-  ../primitives, ../arithmetic, ../towers,
-  ../curves/zoo_hash_to_curve,
-  ../elliptic/[
+  ../platforms/abstractions,
+  ../math/[arithmetic, extension_fields],
+  ../math/curves/zoo_hash_to_curve,
+  ../math/elliptic/[
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian,
   ]
@@ -194,7 +195,7 @@ func h2c_isogeny_map*[F; G: static Subgroup](
   r.x.prod(rxn, ryd) # X = xn * yd
   r.x *= r.z         # X = xn * xd * yd²
   r.y.square(r.z)    # Y = xd² * yd²
-  r.y *= rdx         # Y = yd² * xd³
+  r.y *= rxd         # Y = yd² * xd³
   r.y *= ryn         # Y = yn * yd² * xd³
 
 func h2c_isogeny_map*[F; G: static Subgroup](
diff --git a/constantine/backend/hash_to_curve/h2c_map_to_isocurve_swu.nim b/constantine/hash_to_curve/h2c_map_to_isocurve_swu.nim
similarity index 98%
rename from constantine/backend/hash_to_curve/h2c_map_to_isocurve_swu.nim
rename to constantine/hash_to_curve/h2c_map_to_isocurve_swu.nim
index 9506242..931620d 100644
--- a/constantine/backend/hash_to_curve/h2c_map_to_isocurve_swu.nim
+++ b/constantine/hash_to_curve/h2c_map_to_isocurve_swu.nim
@@ -8,9 +8,10 @@
 
 import
   # Internals
-  ../config/[common, curves],
-  ../primitives, ../arithmetic, ../towers,
-  ../curves/zoo_hash_to_curve
+  ../platforms/abstractions,
+  ../math/config/curves,
+  ../math/[arithmetic, extension_fields],
+  ../math/curves/zoo_hash_to_curve
 
 # ############################################################
 #
diff --git a/constantine/backend/hash_to_curve/hash_to_curve.nim b/constantine/hash_to_curve/hash_to_curve.nim
similarity index 97%
rename from constantine/backend/hash_to_curve/hash_to_curve.nim
rename to constantine/hash_to_curve/hash_to_curve.nim
index f11e131..50698b4 100644
--- a/constantine/backend/hash_to_curve/hash_to_curve.nim
+++ b/constantine/hash_to_curve/hash_to_curve.nim
@@ -8,13 +8,14 @@
 
 import
   # Internals
-  ../config/[common, curves],
-  ../primitives, ../arithmetic, ../towers,
-  ../curves/[zoo_hash_to_curve, zoo_subgroups],
-  ../ec_shortweierstrass,
+  ../platforms/abstractions,
+  ../math/config/curves,
+  ../math/[arithmetic, extension_fields],
+  ../math/curves/[zoo_hash_to_curve, zoo_subgroups],
+  ../math/ec_shortweierstrass,
   ./h2c_hash_to_field,
   ./h2c_map_to_isocurve_swu,
-  ../isogeny/h2c_isogeny_maps,
+  ./h2c_isogeny_maps,
   ../hashes
 
 # ############################################################
diff --git a/constantine/backend/hashes.nim b/constantine/hashes.nim
similarity index 100%
rename from constantine/backend/hashes.nim
rename to constantine/hashes.nim
diff --git a/constantine/backend/hashes/h_sha256.nim b/constantine/hashes/h_sha256.nim
similarity index 99%
rename from constantine/backend/hashes/h_sha256.nim
rename to constantine/hashes/h_sha256.nim
index 873a4fd..76ea41d 100644
--- a/constantine/backend/hashes/h_sha256.nim
+++ b/constantine/hashes/h_sha256.nim
@@ -8,9 +8,7 @@
 
 import
   std/macros,
-  ../config/common,
-  ../io/endians,
-  ../primitives/static_for
+  ../platforms/[abstractions, endians]
 
 # SHA256, a hash function from the SHA2 family
 # --------------------------------------------------------------------------------
diff --git a/constantine/backend/arithmetic.nim b/constantine/math/arithmetic.nim
similarity index 100%
rename from constantine/backend/arithmetic.nim
rename to constantine/math/arithmetic.nim
diff --git a/constantine/backend/arithmetic/README.md b/constantine/math/arithmetic/README.md
similarity index 100%
rename from constantine/backend/arithmetic/README.md
rename to constantine/math/arithmetic/README.md
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_modular_dbl_prec_x86.nim b/constantine/math/arithmetic/assembly/limbs_asm_modular_dbl_prec_x86.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_modular_dbl_prec_x86.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_modular_dbl_prec_x86.nim
index c19d4e9..dff0d80 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_modular_dbl_prec_x86.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_modular_dbl_prec_x86.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #                                                            #
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_modular_x86.nim b/constantine/math/arithmetic/assembly/limbs_asm_modular_x86.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_modular_x86.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_modular_x86.nim
index 1cffb0d..a752ea6 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_modular_x86.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_modular_x86.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_mul_mont_x86.nim b/constantine/math/arithmetic/assembly/limbs_asm_mul_mont_x86.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_mul_mont_x86.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_mul_mont_x86.nim
index 46b8947..e290503 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_mul_mont_x86.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_mul_mont_x86.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives,
+  ../../../platforms/abstractions,
   ./limbs_asm_modular_x86,
   ./limbs_asm_redc_mont_x86,
   ./limbs_asm_mul_x86
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_mul_mont_x86_adx_bmi2.nim b/constantine/math/arithmetic/assembly/limbs_asm_mul_mont_x86_adx_bmi2.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_mul_mont_x86_adx_bmi2.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_mul_mont_x86_adx_bmi2.nim
index b845500..e72bea0 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_mul_mont_x86_adx_bmi2.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_mul_mont_x86_adx_bmi2.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/[macros, algorithm],
   # Internal
-  ../../config/common,
-  ../../primitives,
+  ../../../platforms/abstractions,
   ./limbs_asm_modular_x86,
   ./limbs_asm_redc_mont_x86_adx_bmi2,
   ./limbs_asm_mul_x86_adx_bmi2
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_mul_x86.nim b/constantine/math/arithmetic/assembly/limbs_asm_mul_x86.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_mul_x86.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_mul_x86.nim
index 28d3def..4a88557 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_mul_x86.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_mul_x86.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim b/constantine/math/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
index 6077684..9c8c693 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_mul_x86_adx_bmi2.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #
@@ -620,7 +619,8 @@ func square_asm_adx*[rLen, aLen: static int](r: var Limbs[rLen], a: Limbs[aLen])
 
 when isMainModule:
   import
-    ../../config/[type_bigint, common],
+    ../../../platforms/abstractions,
+    ../../config/type_bigint,
     ../../arithmetic/limbs
 
   type SW = SecretWord
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_redc_mont_x86.nim b/constantine/math/arithmetic/assembly/limbs_asm_redc_mont_x86.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_redc_mont_x86.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_redc_mont_x86.nim
index 866df62..3730e13 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_redc_mont_x86.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_redc_mont_x86.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives,
+  ../../../platforms/abstractions,
   ./limbs_asm_modular_x86
 
 # ############################################################
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_redc_mont_x86_adx_bmi2.nim b/constantine/math/arithmetic/assembly/limbs_asm_redc_mont_x86_adx_bmi2.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_redc_mont_x86_adx_bmi2.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_redc_mont_x86_adx_bmi2.nim
index 0be05af..c0628ef 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_redc_mont_x86_adx_bmi2.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_redc_mont_x86_adx_bmi2.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives,
+  ../../../platforms/abstractions,
   ./limbs_asm_modular_x86
 
 # ############################################################
diff --git a/constantine/backend/arithmetic/assembly/limbs_asm_x86.nim b/constantine/math/arithmetic/assembly/limbs_asm_x86.nim
similarity index 99%
rename from constantine/backend/arithmetic/assembly/limbs_asm_x86.nim
rename to constantine/math/arithmetic/assembly/limbs_asm_x86.nim
index 105bd2e..091cbb2 100644
--- a/constantine/backend/arithmetic/assembly/limbs_asm_x86.nim
+++ b/constantine/math/arithmetic/assembly/limbs_asm_x86.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #
diff --git a/constantine/backend/arithmetic/bigints.nim b/constantine/math/arithmetic/bigints.nim
similarity index 99%
rename from constantine/backend/arithmetic/bigints.nim
rename to constantine/math/arithmetic/bigints.nim
index 183e15d..0dae80c 100644
--- a/constantine/backend/arithmetic/bigints.nim
+++ b/constantine/math/arithmetic/bigints.nim
@@ -7,8 +7,8 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, type_bigint],
-  ../primitives,
+  ../../platforms/abstractions,
+  ../config/type_bigint,
   ./limbs,
   ./limbs_extmul,
   ./limbs_invmod,
diff --git a/constantine/backend/arithmetic/bigints_montgomery.nim b/constantine/math/arithmetic/bigints_montgomery.nim
similarity index 99%
rename from constantine/backend/arithmetic/bigints_montgomery.nim
rename to constantine/math/arithmetic/bigints_montgomery.nim
index 39abc21..31a316a 100644
--- a/constantine/backend/arithmetic/bigints_montgomery.nim
+++ b/constantine/math/arithmetic/bigints_montgomery.nim
@@ -7,8 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, type_bigint],
-  ../primitives,
+  ../../platforms/abstractions,
   ../io/io_bigints,
   ./limbs,
   ./limbs_montgomery,
diff --git a/constantine/backend/arithmetic/finite_fields.nim b/constantine/math/arithmetic/finite_fields.nim
similarity index 99%
rename from constantine/backend/arithmetic/finite_fields.nim
rename to constantine/math/arithmetic/finite_fields.nim
index fb3fac7..aea31d0 100644
--- a/constantine/backend/arithmetic/finite_fields.nim
+++ b/constantine/math/arithmetic/finite_fields.nim
@@ -27,8 +27,8 @@
 #     which requires a prime
 
 import
-  ../primitives,
-  ../config/[common, type_ff, curves_prop_field_core, curves_prop_field_derived],
+  ../../platforms/abstractions,
+  ../config/[type_ff, curves_prop_field_core, curves_prop_field_derived],
   ./bigints, ./bigints_montgomery
 
 when UseASM_X86_64:
@@ -100,7 +100,7 @@ func cswap*(a, b: var FF, ctl: CTBool) {.meter.} =
 #       Routines for special field modulus form:
 #       - Mersenne Prime (2ᵏ - 1),
 #       - Generalized Mersenne Prime (NIST Prime P256: 2^256 - 2^224 + 2^192 + 2^96 - 1)
-#       - Pseudo-Mersenne Prime (2^m - k for example Curve25519: 2^255 - 19)
+#       - Pseudo-Mersenne Prime (2^m - k for example Edwards25519: 2^255 - 19)
 #       - Golden Primes (φ^2 - φ - 1 with φ = 2ᵏ for example Ed448-Goldilocks: 2^448 - 2^224 - 1)
 #       exist and can be implemented with compile-time specialization.
 
diff --git a/constantine/backend/arithmetic/finite_fields_double_precision.nim b/constantine/math/arithmetic/finite_fields_double_precision.nim
similarity index 99%
rename from constantine/backend/arithmetic/finite_fields_double_precision.nim
rename to constantine/math/arithmetic/finite_fields_double_precision.nim
index f5cb81a..e41cfe3 100644
--- a/constantine/backend/arithmetic/finite_fields_double_precision.nim
+++ b/constantine/math/arithmetic/finite_fields_double_precision.nim
@@ -7,8 +7,8 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves, type_ff],
-  ../primitives,
+  ../../platforms/abstractions,
+  ../config/curves,
   ./bigints,
   ./finite_fields,
   ./limbs,
diff --git a/constantine/backend/arithmetic/finite_fields_square_root.nim b/constantine/math/arithmetic/finite_fields_square_root.nim
similarity index 99%
rename from constantine/backend/arithmetic/finite_fields_square_root.nim
rename to constantine/math/arithmetic/finite_fields_square_root.nim
index 5943a9a..9347f68 100644
--- a/constantine/backend/arithmetic/finite_fields_square_root.nim
+++ b/constantine/math/arithmetic/finite_fields_square_root.nim
@@ -7,8 +7,8 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, type_ff, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../curves/zoo_square_roots,
   ./bigints, ./finite_fields
 
diff --git a/constantine/backend/arithmetic/limbs.nim b/constantine/math/arithmetic/limbs.nim
similarity index 99%
rename from constantine/backend/arithmetic/limbs.nim
rename to constantine/math/arithmetic/limbs.nim
index a10cdf0..55fefce 100644
--- a/constantine/backend/arithmetic/limbs.nim
+++ b/constantine/math/arithmetic/limbs.nim
@@ -6,9 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import
-  ../config/common,
-  ../primitives
+import ../../platforms/abstractions
 
 when UseASM_X86_32:
   import ./assembly/limbs_asm_x86
diff --git a/constantine/backend/arithmetic/limbs_division.nim b/constantine/math/arithmetic/limbs_division.nim
similarity index 99%
rename from constantine/backend/arithmetic/limbs_division.nim
rename to constantine/math/arithmetic/limbs_division.nim
index 4e0e6ec..44240c0 100644
--- a/constantine/backend/arithmetic/limbs_division.nim
+++ b/constantine/math/arithmetic/limbs_division.nim
@@ -6,9 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import
-  ../config/common,
-  ../primitives
+import ../../platforms/abstractions
 
 # No exceptions allowed
 {.push raises: [].}
diff --git a/constantine/backend/arithmetic/limbs_extmul.nim b/constantine/math/arithmetic/limbs_extmul.nim
similarity index 99%
rename from constantine/backend/arithmetic/limbs_extmul.nim
rename to constantine/math/arithmetic/limbs_extmul.nim
index 49ec322..807d3a3 100644
--- a/constantine/backend/arithmetic/limbs_extmul.nim
+++ b/constantine/math/arithmetic/limbs_extmul.nim
@@ -7,8 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/common,
-  ../primitives,
+  ../../platforms/abstractions,
   ./limbs
 
 when UseASM_X86_64:
diff --git a/constantine/backend/arithmetic/limbs_invmod.nim b/constantine/math/arithmetic/limbs_invmod.nim
similarity index 99%
rename from constantine/backend/arithmetic/limbs_invmod.nim
rename to constantine/math/arithmetic/limbs_invmod.nim
index c128fb2..8fddcdc 100644
--- a/constantine/backend/arithmetic/limbs_invmod.nim
+++ b/constantine/math/arithmetic/limbs_invmod.nim
@@ -7,8 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/common,
-  ../primitives,
+  ../../platforms/abstractions,
   ./limbs, ./limbs_unsaturated
 
 # No exceptions allowed
diff --git a/constantine/backend/arithmetic/limbs_montgomery.nim b/constantine/math/arithmetic/limbs_montgomery.nim
similarity index 99%
rename from constantine/backend/arithmetic/limbs_montgomery.nim
rename to constantine/math/arithmetic/limbs_montgomery.nim
index b8d2018..9e2be6d 100644
--- a/constantine/backend/arithmetic/limbs_montgomery.nim
+++ b/constantine/math/arithmetic/limbs_montgomery.nim
@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../config/common,
-  ../primitives,
+  ../../platforms/abstractions,
   ./limbs, ./limbs_extmul
 
 when UseASM_X86_32:
diff --git a/constantine/backend/arithmetic/limbs_unsaturated.nim b/constantine/math/arithmetic/limbs_unsaturated.nim
similarity index 99%
rename from constantine/backend/arithmetic/limbs_unsaturated.nim
rename to constantine/math/arithmetic/limbs_unsaturated.nim
index 3920545..d2ff772 100644
--- a/constantine/backend/arithmetic/limbs_unsaturated.nim
+++ b/constantine/math/arithmetic/limbs_unsaturated.nim
@@ -6,9 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import
-  ../config/common,
-  ../primitives
+import  ../../platforms/abstractions
 
 type
   SignedSecretWord* = distinct SecretWord
diff --git a/constantine/backend/config/README.md b/constantine/math/config/README.md
similarity index 100%
rename from constantine/backend/config/README.md
rename to constantine/math/config/README.md
diff --git a/constantine/backend/config/curves.nim b/constantine/math/config/curves.nim
similarity index 100%
rename from constantine/backend/config/curves.nim
rename to constantine/math/config/curves.nim
diff --git a/constantine/backend/config/curves_declaration.nim b/constantine/math/config/curves_declaration.nim
similarity index 99%
rename from constantine/backend/config/curves_declaration.nim
rename to constantine/math/config/curves_declaration.nim
index 2b5be17..4836b5b 100644
--- a/constantine/backend/config/curves_declaration.nim
+++ b/constantine/math/config/curves_declaration.nim
@@ -152,7 +152,7 @@ declareCurves:
     coef_a: -5
     coef_d: "6389c12633c267cbc66e3bf86be3b6d8cb66677177e54f92b369f2f5188d58e7"
 
-  curve Curve25519: # Bernstein curve
+  curve Edwards25519: # Bernstein curve
     bitwidth: 255
     modulus: "0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffed"
 
diff --git a/constantine/backend/config/curves_derived.nim b/constantine/math/config/curves_derived.nim
similarity index 100%
rename from constantine/backend/config/curves_derived.nim
rename to constantine/math/config/curves_derived.nim
diff --git a/constantine/backend/config/curves_parser_curve.nim b/constantine/math/config/curves_parser_curve.nim
similarity index 100%
rename from constantine/backend/config/curves_parser_curve.nim
rename to constantine/math/config/curves_parser_curve.nim
diff --git a/constantine/backend/config/curves_parser_field.nim b/constantine/math/config/curves_parser_field.nim
similarity index 100%
rename from constantine/backend/config/curves_parser_field.nim
rename to constantine/math/config/curves_parser_field.nim
diff --git a/constantine/backend/config/curves_prop_curve.nim b/constantine/math/config/curves_prop_curve.nim
similarity index 100%
rename from constantine/backend/config/curves_prop_curve.nim
rename to constantine/math/config/curves_prop_curve.nim
diff --git a/constantine/backend/config/curves_prop_field_core.nim b/constantine/math/config/curves_prop_field_core.nim
similarity index 96%
rename from constantine/backend/config/curves_prop_field_core.nim
rename to constantine/math/config/curves_prop_field_core.nim
index 16cd86e..23155a4 100644
--- a/constantine/backend/config/curves_prop_field_core.nim
+++ b/constantine/math/config/curves_prop_field_core.nim
@@ -9,7 +9,8 @@ import
   # Standard library
   std/macros,
   # Internal
-  ./type_bigint, ./common,
+  ../../platforms/abstractions,
+  ./type_bigint,
   ./curves_declaration
 
 export Curve
diff --git a/constantine/backend/config/curves_prop_field_derived.nim b/constantine/math/config/curves_prop_field_derived.nim
similarity index 98%
rename from constantine/backend/config/curves_prop_field_derived.nim
rename to constantine/math/config/curves_prop_field_derived.nim
index dc41b54..dc7d5c8 100644
--- a/constantine/backend/config/curves_prop_field_derived.nim
+++ b/constantine/math/config/curves_prop_field_derived.nim
@@ -10,7 +10,8 @@ import
   # Standard library
   std/macros,
   # Internal
-  ./type_bigint, ./type_ff, ./common,
+  ../../platforms/abstractions,
+  ./type_bigint, ./type_ff,
   ./curves_declaration, ./curves_prop_field_core, ./curves_derived
 
 # ############################################################
diff --git a/constantine/backend/config/precompute.nim b/constantine/math/config/precompute.nim
similarity index 99%
rename from constantine/backend/config/precompute.nim
rename to constantine/math/config/precompute.nim
index 00d10aa..18b065e 100644
--- a/constantine/backend/config/precompute.nim
+++ b/constantine/math/config/precompute.nim
@@ -7,8 +7,8 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ./type_bigint, ./common,
-  ../primitives,
+  ../../platforms/abstractions,
+  ./type_bigint,
   ../io/io_bigints
 
 # Precomputed constants
diff --git a/constantine/backend/config/type_bigint.nim b/constantine/math/config/type_bigint.nim
similarity index 98%
rename from constantine/backend/config/type_bigint.nim
rename to constantine/math/config/type_bigint.nim
index 4579545..15de197 100644
--- a/constantine/backend/config/type_bigint.nim
+++ b/constantine/math/config/type_bigint.nim
@@ -6,7 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import ./common
+import ../../platforms/abstractions
 
 func wordsRequired*(bits: int): int {.compileTime.} =
   ## Compute the number of limbs required
diff --git a/constantine/backend/config/type_ff.nim b/constantine/math/config/type_ff.nim
similarity index 98%
rename from constantine/backend/config/type_ff.nim
rename to constantine/math/config/type_ff.nim
index 50a465d..d2d10a2 100644
--- a/constantine/backend/config/type_ff.nim
+++ b/constantine/math/config/type_ff.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ./common,
+  ../../platforms/abstractions,
   ./curves_declaration,
   ./curves_prop_field_core
 
diff --git a/constantine/backend/curves/README.md b/constantine/math/curves/README.md
similarity index 100%
rename from constantine/backend/curves/README.md
rename to constantine/math/curves/README.md
diff --git a/constantine/backend/curves/bandersnatch_sqrt.nim b/constantine/math/curves/bandersnatch_sqrt.nim
similarity index 95%
rename from constantine/backend/curves/bandersnatch_sqrt.nim
rename to constantine/math/curves/bandersnatch_sqrt.nim
index 92a1e25..1f7d406 100644
--- a/constantine/backend/curves/bandersnatch_sqrt.nim
+++ b/constantine/math/curves/bandersnatch_sqrt.nim
@@ -5,7 +5,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields],
   ../arithmetic/finite_fields
 
diff --git a/constantine/backend/curves/bls12_377_constants.nim b/constantine/math/curves/bls12_377_constants.nim
similarity index 97%
rename from constantine/backend/curves/bls12_377_constants.nim
rename to constantine/math/curves/bls12_377_constants.nim
index b30f016..9f95ea1 100644
--- a/constantine/backend/curves/bls12_377_constants.nim
+++ b/constantine/math/curves/bls12_377_constants.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_377_endomorphisms.nim b/constantine/math/curves/bls12_377_endomorphisms.nim
similarity index 98%
rename from constantine/backend/curves/bls12_377_endomorphisms.nim
rename to constantine/math/curves/bls12_377_endomorphisms.nim
index 0f55f69..d6b2582 100644
--- a/constantine/backend/curves/bls12_377_endomorphisms.nim
+++ b/constantine/math/curves/bls12_377_endomorphisms.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields]
 
 # BLS12_377 G1
diff --git a/constantine/backend/curves/bls12_377_frobenius.nim b/constantine/math/curves/bls12_377_frobenius.nim
similarity index 99%
rename from constantine/backend/curves/bls12_377_frobenius.nim
rename to constantine/math/curves/bls12_377_frobenius.nim
index fd039b1..408d66c 100644
--- a/constantine/backend/curves/bls12_377_frobenius.nim
+++ b/constantine/math/curves/bls12_377_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   ../config/curves,
-  ../towers,
-  ../io/io_towers
+  ../extension_fields,
+  ../io/io_extfields
 
 # Frobenius map - on extension fields
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_377_pairing.nim b/constantine/math/curves/bls12_377_pairing.nim
similarity index 98%
rename from constantine/backend/curves/bls12_377_pairing.nim
rename to constantine/math/curves/bls12_377_pairing.nim
index 0430619..d59b000 100644
--- a/constantine/backend/curves/bls12_377_pairing.nim
+++ b/constantine/math/curves/bls12_377_pairing.nim
@@ -7,12 +7,13 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves, type_bigint, type_ff],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../io/io_bigints,
-  ../towers,
+  ../extension_fields,
   ../elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective],
   ../pairing/[cyclotomic_subgroup, miller_loops],
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 # Slow generic implementation
 # ------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_377_sqrt.nim b/constantine/math/curves/bls12_377_sqrt.nim
similarity index 99%
rename from constantine/backend/curves/bls12_377_sqrt.nim
rename to constantine/math/curves/bls12_377_sqrt.nim
index 3af0f4b..d0fe528 100644
--- a/constantine/backend/curves/bls12_377_sqrt.nim
+++ b/constantine/math/curves/bls12_377_sqrt.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields],
   ../arithmetic/finite_fields
 
diff --git a/constantine/backend/curves/bls12_377_subgroups.nim b/constantine/math/curves/bls12_377_subgroups.nim
similarity index 98%
rename from constantine/backend/curves/bls12_377_subgroups.nim
rename to constantine/math/curves/bls12_377_subgroups.nim
index d543ff3..cf34c6c 100644
--- a/constantine/backend/curves/bls12_377_subgroups.nim
+++ b/constantine/math/curves/bls12_377_subgroups.nim
@@ -8,13 +8,13 @@
 
 import
   # Internals
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../primitives,
-  ../towers,
+  ../extension_fields,
   ../ec_shortweierstrass,
   ../io/io_bigints,
-  ../isogeny/frobenius,
+  ../isogenies/frobenius,
   ../curves/zoo_endomorphisms
 
 func pow_bls12_377_abs_x[ECP: ECP_ShortW[Fp[BLS12_377], G1] or
diff --git a/constantine/backend/curves/bls12_381_constants.nim b/constantine/math/curves/bls12_381_constants.nim
similarity index 97%
rename from constantine/backend/curves/bls12_381_constants.nim
rename to constantine/math/curves/bls12_381_constants.nim
index f8fb016..ab8ca64 100644
--- a/constantine/backend/curves/bls12_381_constants.nim
+++ b/constantine/math/curves/bls12_381_constants.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_381_endomorphisms.nim b/constantine/math/curves/bls12_381_endomorphisms.nim
similarity index 98%
rename from constantine/backend/curves/bls12_381_endomorphisms.nim
rename to constantine/math/curves/bls12_381_endomorphisms.nim
index 9085d95..bec9d39 100644
--- a/constantine/backend/curves/bls12_381_endomorphisms.nim
+++ b/constantine/math/curves/bls12_381_endomorphisms.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields]
 
 # BLS12_381 G1
diff --git a/constantine/backend/curves/bls12_381_frobenius.nim b/constantine/math/curves/bls12_381_frobenius.nim
similarity index 99%
rename from constantine/backend/curves/bls12_381_frobenius.nim
rename to constantine/math/curves/bls12_381_frobenius.nim
index 761ae96..ca1e5fb 100644
--- a/constantine/backend/curves/bls12_381_frobenius.nim
+++ b/constantine/math/curves/bls12_381_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   ../config/curves,
-  ../towers,
-  ../io/io_towers
+  ../extension_fields,
+  ../io/io_extfields
 
 # Frobenius map - on extension fields
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_381_g2_hash_to_curve.nim b/constantine/math/curves/bls12_381_g2_hash_to_curve.nim
similarity index 99%
rename from constantine/backend/curves/bls12_381_g2_hash_to_curve.nim
rename to constantine/math/curves/bls12_381_g2_hash_to_curve.nim
index 0ffec6c..ab10ad9 100644
--- a/constantine/backend/curves/bls12_381_g2_hash_to_curve.nim
+++ b/constantine/math/curves/bls12_381_g2_hash_to_curve.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/[io_fields, io_towers]
+  ../io/[io_fields, io_extfields]
 
 # Hash-to-Curve map to isogenous BLS12-381 E'2 constants
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_381_generators.nim b/constantine/math/curves/bls12_381_generators.nim
similarity index 96%
rename from constantine/backend/curves/bls12_381_generators.nim
rename to constantine/math/curves/bls12_381_generators.nim
index d1eb747..59051fa 100644
--- a/constantine/backend/curves/bls12_381_generators.nim
+++ b/constantine/math/curves/bls12_381_generators.nim
@@ -7,9 +7,9 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_ff],
+  ../config/curves,
   ../elliptic/ec_shortweierstrass_affine,
-  ../io/[io_fields, io_towers]
+  ../io/[io_fields, io_extfields]
 
 # Generators
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_381_pairing.nim b/constantine/math/curves/bls12_381_pairing.nim
similarity index 98%
rename from constantine/backend/curves/bls12_381_pairing.nim
rename to constantine/math/curves/bls12_381_pairing.nim
index 4f22cb5..0f02b43 100644
--- a/constantine/backend/curves/bls12_381_pairing.nim
+++ b/constantine/math/curves/bls12_381_pairing.nim
@@ -7,12 +7,13 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves, type_bigint, type_ff],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../io/io_bigints,
-  ../towers,
+  ../extension_fields,
   ../elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective],
   ../pairing/[cyclotomic_subgroup, miller_loops],
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 # Slow generic implementation
 # ------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_381_sqrt.nim b/constantine/math/curves/bls12_381_sqrt.nim
similarity index 100%
rename from constantine/backend/curves/bls12_381_sqrt.nim
rename to constantine/math/curves/bls12_381_sqrt.nim
diff --git a/constantine/backend/curves/bls12_381_sqrt_fp2.nim b/constantine/math/curves/bls12_381_sqrt_fp2.nim
similarity index 98%
rename from constantine/backend/curves/bls12_381_sqrt_fp2.nim
rename to constantine/math/curves/bls12_381_sqrt_fp2.nim
index ceb52ea..7dcdd7d 100644
--- a/constantine/backend/curves/bls12_381_sqrt_fp2.nim
+++ b/constantine/math/curves/bls12_381_sqrt_fp2.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Square Root Fp2 constants
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bls12_381_subgroups.nim b/constantine/math/curves/bls12_381_subgroups.nim
similarity index 98%
rename from constantine/backend/curves/bls12_381_subgroups.nim
rename to constantine/math/curves/bls12_381_subgroups.nim
index 7aeaf21..8216f53 100644
--- a/constantine/backend/curves/bls12_381_subgroups.nim
+++ b/constantine/math/curves/bls12_381_subgroups.nim
@@ -8,13 +8,13 @@
 
 import
   # Internals
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../primitives,
-  ../towers,
+  ../extension_fields,
   ../ec_shortweierstrass,
   ../io/io_bigints,
-  ../isogeny/frobenius,
+  ../isogenies/frobenius,
   ../curves/zoo_endomorphisms
 
 func pow_bls12_381_abs_x[ECP: ECP_ShortW[Fp[BLS12_381], G1] or
diff --git a/constantine/backend/curves/bn254_nogami_constants.nim b/constantine/math/curves/bn254_nogami_constants.nim
similarity index 97%
rename from constantine/backend/curves/bn254_nogami_constants.nim
rename to constantine/math/curves/bn254_nogami_constants.nim
index 948933c..8c2ba96 100644
--- a/constantine/backend/curves/bn254_nogami_constants.nim
+++ b/constantine/math/curves/bn254_nogami_constants.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_nogami_endomorphisms.nim b/constantine/math/curves/bn254_nogami_endomorphisms.nim
similarity index 98%
rename from constantine/backend/curves/bn254_nogami_endomorphisms.nim
rename to constantine/math/curves/bn254_nogami_endomorphisms.nim
index 302fa63..00fc212 100644
--- a/constantine/backend/curves/bn254_nogami_endomorphisms.nim
+++ b/constantine/math/curves/bn254_nogami_endomorphisms.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields]
 
 # BN254_Nogami G1
diff --git a/constantine/backend/curves/bn254_nogami_frobenius.nim b/constantine/math/curves/bn254_nogami_frobenius.nim
similarity index 99%
rename from constantine/backend/curves/bn254_nogami_frobenius.nim
rename to constantine/math/curves/bn254_nogami_frobenius.nim
index 69535c9..2adfac8 100644
--- a/constantine/backend/curves/bn254_nogami_frobenius.nim
+++ b/constantine/math/curves/bn254_nogami_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   ../config/curves,
-  ../towers,
-  ../io/io_towers
+  ../extension_fields,
+  ../io/io_extfields
 
 # Frobenius map - on extension fields
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_nogami_pairing.nim b/constantine/math/curves/bn254_nogami_pairing.nim
similarity index 97%
rename from constantine/backend/curves/bn254_nogami_pairing.nim
rename to constantine/math/curves/bn254_nogami_pairing.nim
index ae21841..986de67 100644
--- a/constantine/backend/curves/bn254_nogami_pairing.nim
+++ b/constantine/math/curves/bn254_nogami_pairing.nim
@@ -7,12 +7,13 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves, type_bigint, type_ff],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../io/io_bigints,
-  ../towers,
+  ../extension_fields,
   ../elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective],
   ../pairing/[cyclotomic_subgroup, miller_loops],
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 # Slow generic implementation
 # ------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_nogami_sqrt.nim b/constantine/math/curves/bn254_nogami_sqrt.nim
similarity index 100%
rename from constantine/backend/curves/bn254_nogami_sqrt.nim
rename to constantine/math/curves/bn254_nogami_sqrt.nim
diff --git a/constantine/backend/curves/bn254_nogami_sqrt_fp2.nim b/constantine/math/curves/bn254_nogami_sqrt_fp2.nim
similarity index 98%
rename from constantine/backend/curves/bn254_nogami_sqrt_fp2.nim
rename to constantine/math/curves/bn254_nogami_sqrt_fp2.nim
index 37e995d..c976bd5 100644
--- a/constantine/backend/curves/bn254_nogami_sqrt_fp2.nim
+++ b/constantine/math/curves/bn254_nogami_sqrt_fp2.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Square Root Fp2 constants
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_nogami_subgroups.nim b/constantine/math/curves/bn254_nogami_subgroups.nim
similarity index 98%
rename from constantine/backend/curves/bn254_nogami_subgroups.nim
rename to constantine/math/curves/bn254_nogami_subgroups.nim
index d724e91..346c291 100644
--- a/constantine/backend/curves/bn254_nogami_subgroups.nim
+++ b/constantine/math/curves/bn254_nogami_subgroups.nim
@@ -8,13 +8,13 @@
 
 import
   # Internals
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../primitives,
-  ../towers,
+  ../extension_fields,
   ../ec_shortweierstrass,
   ../io/io_bigints,
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 func pow_BN254_Nogami_abs_u*[ECP: ECP_ShortW[Fp[BN254_Nogami], G1] or
        ECP_ShortW[Fp2[BN254_Nogami], G2]](
diff --git a/constantine/backend/curves/bn254_snarks_constants.nim b/constantine/math/curves/bn254_snarks_constants.nim
similarity index 97%
rename from constantine/backend/curves/bn254_snarks_constants.nim
rename to constantine/math/curves/bn254_snarks_constants.nim
index c49bcac..0f53b95 100644
--- a/constantine/backend/curves/bn254_snarks_constants.nim
+++ b/constantine/math/curves/bn254_snarks_constants.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_snarks_endomorphisms.nim b/constantine/math/curves/bn254_snarks_endomorphisms.nim
similarity index 98%
rename from constantine/backend/curves/bn254_snarks_endomorphisms.nim
rename to constantine/math/curves/bn254_snarks_endomorphisms.nim
index 5955d85..6243e7a 100644
--- a/constantine/backend/curves/bn254_snarks_endomorphisms.nim
+++ b/constantine/math/curves/bn254_snarks_endomorphisms.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields]
 
 # BN254_Snarks G1
diff --git a/constantine/backend/curves/bn254_snarks_frobenius.nim b/constantine/math/curves/bn254_snarks_frobenius.nim
similarity index 99%
rename from constantine/backend/curves/bn254_snarks_frobenius.nim
rename to constantine/math/curves/bn254_snarks_frobenius.nim
index 0dd6c91..b70ded7 100644
--- a/constantine/backend/curves/bn254_snarks_frobenius.nim
+++ b/constantine/math/curves/bn254_snarks_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   ../config/curves,
-  ../towers,
-  ../io/io_towers
+  ../extension_fields,
+  ../io/io_extfields
 
 # Frobenius map - on extension fields
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_snarks_pairing.nim b/constantine/math/curves/bn254_snarks_pairing.nim
similarity index 97%
rename from constantine/backend/curves/bn254_snarks_pairing.nim
rename to constantine/math/curves/bn254_snarks_pairing.nim
index 3f99510..34807c1 100644
--- a/constantine/backend/curves/bn254_snarks_pairing.nim
+++ b/constantine/math/curves/bn254_snarks_pairing.nim
@@ -7,12 +7,13 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves, type_bigint, type_ff],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../io/io_bigints,
-  ../towers,
+  ../extension_fields,
   ../elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective],
   ../pairing/[cyclotomic_subgroup, miller_loops],
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 # Slow generic implementation
 # ------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_snarks_sqrt.nim b/constantine/math/curves/bn254_snarks_sqrt.nim
similarity index 100%
rename from constantine/backend/curves/bn254_snarks_sqrt.nim
rename to constantine/math/curves/bn254_snarks_sqrt.nim
diff --git a/constantine/backend/curves/bn254_snarks_sqrt_fp2.nim b/constantine/math/curves/bn254_snarks_sqrt_fp2.nim
similarity index 98%
rename from constantine/backend/curves/bn254_snarks_sqrt_fp2.nim
rename to constantine/math/curves/bn254_snarks_sqrt_fp2.nim
index 70e0c21..c03101c 100644
--- a/constantine/backend/curves/bn254_snarks_sqrt_fp2.nim
+++ b/constantine/math/curves/bn254_snarks_sqrt_fp2.nim
@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Square Root Fp2 constants
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bn254_snarks_subgroups.nim b/constantine/math/curves/bn254_snarks_subgroups.nim
similarity index 98%
rename from constantine/backend/curves/bn254_snarks_subgroups.nim
rename to constantine/math/curves/bn254_snarks_subgroups.nim
index fcff531..60fdd4c 100644
--- a/constantine/backend/curves/bn254_snarks_subgroups.nim
+++ b/constantine/math/curves/bn254_snarks_subgroups.nim
@@ -8,13 +8,13 @@
 
 import
   # Internals
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../primitives,
-  ../towers,
+  ../extension_fields,
   ../ec_shortweierstrass,
   ../io/io_bigints,
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 func pow_bn254_snarks_abs_u*[ECP: ECP_ShortW[Fp[BN254_Snarks], G1] or
        ECP_ShortW[Fp2[BN254_Snarks], G2]](
diff --git a/constantine/backend/curves/bw6_761_constants.nim b/constantine/math/curves/bw6_761_constants.nim
similarity index 100%
rename from constantine/backend/curves/bw6_761_constants.nim
rename to constantine/math/curves/bw6_761_constants.nim
diff --git a/constantine/backend/curves/bw6_761_endomorphisms.nim b/constantine/math/curves/bw6_761_endomorphisms.nim
similarity index 98%
rename from constantine/backend/curves/bw6_761_endomorphisms.nim
rename to constantine/math/curves/bw6_761_endomorphisms.nim
index 344c2c7..0887a93 100644
--- a/constantine/backend/curves/bw6_761_endomorphisms.nim
+++ b/constantine/math/curves/bw6_761_endomorphisms.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields]
 
 # BW6_761 G1
diff --git a/constantine/backend/curves/bw6_761_frobenius.nim b/constantine/math/curves/bw6_761_frobenius.nim
similarity index 98%
rename from constantine/backend/curves/bw6_761_frobenius.nim
rename to constantine/math/curves/bw6_761_frobenius.nim
index 19b7cc0..1d542ec 100644
--- a/constantine/backend/curves/bw6_761_frobenius.nim
+++ b/constantine/math/curves/bw6_761_frobenius.nim
@@ -7,9 +7,9 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_ff],
-  ../towers,
-  ../io/[io_fields, io_towers]
+  ../config/curves,
+  ../extension_fields,
+  ../io/[io_fields, io_extfields]
 
 # Frobenius map - on extension fields
 # -----------------------------------------------------------------
diff --git a/constantine/backend/curves/bw6_761_pairing.nim b/constantine/math/curves/bw6_761_pairing.nim
similarity index 98%
rename from constantine/backend/curves/bw6_761_pairing.nim
rename to constantine/math/curves/bw6_761_pairing.nim
index 989ecba..03824fb 100644
--- a/constantine/backend/curves/bw6_761_pairing.nim
+++ b/constantine/math/curves/bw6_761_pairing.nim
@@ -7,11 +7,12 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves, type_bigint],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../io/io_bigints,
-  ../towers,
+  ../extension_fields,
   ../pairing/cyclotomic_subgroup,
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 # Slow generic implementation
 # ------------------------------------------------------------
diff --git a/constantine/backend/curves/bw6_761_sqrt.nim b/constantine/math/curves/bw6_761_sqrt.nim
similarity index 100%
rename from constantine/backend/curves/bw6_761_sqrt.nim
rename to constantine/math/curves/bw6_761_sqrt.nim
diff --git a/constantine/backend/curves/bw6_761_subgroups.nim b/constantine/math/curves/bw6_761_subgroups.nim
similarity index 94%
rename from constantine/backend/curves/bw6_761_subgroups.nim
rename to constantine/math/curves/bw6_761_subgroups.nim
index baa72c3..7271c57 100644
--- a/constantine/backend/curves/bw6_761_subgroups.nim
+++ b/constantine/math/curves/bw6_761_subgroups.nim
@@ -8,13 +8,13 @@
 
 import
   # Internals
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../primitives,
-  ../towers,
+  ../extension_fields,
   ../ec_shortweierstrass,
   ../io/io_bigints,
-  ../isogeny/frobenius
+  ../isogenies/frobenius
 
 # ############################################################
 #
diff --git a/constantine/backend/curves/curve25519_sqrt.nim b/constantine/math/curves/curve25519_sqrt.nim
similarity index 89%
rename from constantine/backend/curves/curve25519_sqrt.nim
rename to constantine/math/curves/curve25519_sqrt.nim
index 322eb4a..eb4419b 100644
--- a/constantine/backend/curves/curve25519_sqrt.nim
+++ b/constantine/math/curves/curve25519_sqrt.nim
@@ -7,13 +7,13 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_ff],
+  ../config/curves,
   ../arithmetic/finite_fields
 
-func invsqrt_addchain_pminus5over8*(r: var Fp[Curve25519], a: Fp[Curve25519]) =
+func invsqrt_addchain_pminus5over8*(r: var Fp[Edwards25519], a: Fp[Edwards25519]) =
   ## Returns a^((p-5)/8) = 2²⁵²-3 for inverse square root computation
   
-  var t{.noInit.}, u{.noInit.}, v{.noinit.}: Fp[Curve25519]
+  var t{.noInit.}, u{.noInit.}, v{.noinit.}: Fp[Edwards25519]
   u.square(a)               # 2
   v.square_repeated(u, 2)   # 8
   v *= a                    # 9
diff --git a/constantine/backend/curves/jubjub_sqrt.nim b/constantine/math/curves/jubjub_sqrt.nim
similarity index 95%
rename from constantine/backend/curves/jubjub_sqrt.nim
rename to constantine/math/curves/jubjub_sqrt.nim
index 066a709..523fcd7 100644
--- a/constantine/backend/curves/jubjub_sqrt.nim
+++ b/constantine/math/curves/jubjub_sqrt.nim
@@ -5,7 +5,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_bigint, type_ff],
+  ../config/curves,
   ../io/[io_bigints, io_fields],
   ../arithmetic/finite_fields
 
diff --git a/constantine/backend/curves/zoo_constants.nim b/constantine/math/curves/zoo_constants.nim
similarity index 100%
rename from constantine/backend/curves/zoo_constants.nim
rename to constantine/math/curves/zoo_constants.nim
diff --git a/constantine/backend/curves/zoo_endomorphisms.nim b/constantine/math/curves/zoo_endomorphisms.nim
similarity index 97%
rename from constantine/backend/curves/zoo_endomorphisms.nim
rename to constantine/math/curves/zoo_endomorphisms.nim
index c9dd5a3..4c0179c 100644
--- a/constantine/backend/curves/zoo_endomorphisms.nim
+++ b/constantine/math/curves/zoo_endomorphisms.nim
@@ -8,8 +8,8 @@
 
 import
   std/macros,
-  ../config/[curves, type_ff],
-  ../towers,
+  ../config/curves,
+  ../extension_fields,
   ./bls12_377_endomorphisms,
   ./bls12_381_endomorphisms,
   ./bn254_nogami_endomorphisms,
diff --git a/constantine/backend/curves/zoo_frobenius.nim b/constantine/math/curves/zoo_frobenius.nim
similarity index 100%
rename from constantine/backend/curves/zoo_frobenius.nim
rename to constantine/math/curves/zoo_frobenius.nim
diff --git a/constantine/backend/curves/zoo_generators.nim b/constantine/math/curves/zoo_generators.nim
similarity index 100%
rename from constantine/backend/curves/zoo_generators.nim
rename to constantine/math/curves/zoo_generators.nim
diff --git a/constantine/backend/curves/zoo_hash_to_curve.nim b/constantine/math/curves/zoo_hash_to_curve.nim
similarity index 100%
rename from constantine/backend/curves/zoo_hash_to_curve.nim
rename to constantine/math/curves/zoo_hash_to_curve.nim
diff --git a/constantine/backend/curves/zoo_pairings.nim b/constantine/math/curves/zoo_pairings.nim
similarity index 100%
rename from constantine/backend/curves/zoo_pairings.nim
rename to constantine/math/curves/zoo_pairings.nim
diff --git a/constantine/backend/curves/zoo_square_roots.nim b/constantine/math/curves/zoo_square_roots.nim
similarity index 91%
rename from constantine/backend/curves/zoo_square_roots.nim
rename to constantine/math/curves/zoo_square_roots.nim
index 9683dbb..286206a 100644
--- a/constantine/backend/curves/zoo_square_roots.nim
+++ b/constantine/math/curves/zoo_square_roots.nim
@@ -8,7 +8,7 @@
 
 import
   std/macros,
-  ../config/[curves, type_ff],
+  ../config/curves,
   ./bls12_377_sqrt,
   ./bls12_381_sqrt,
   ./bn254_nogami_sqrt,
@@ -27,7 +27,7 @@ export
   curve25519_sqrt
 
 func hasSqrtAddchain*(C: static Curve): static bool =
-  when C in {BLS12_381, BN254_Nogami, BN254_Snarks, BW6_761, Curve25519}:
+  when C in {BLS12_381, BN254_Nogami, BN254_Snarks, BW6_761, Edwards25519}:
     true
   else:
     false
diff --git a/constantine/backend/curves/zoo_square_roots_fp2.nim b/constantine/math/curves/zoo_square_roots_fp2.nim
similarity index 100%
rename from constantine/backend/curves/zoo_square_roots_fp2.nim
rename to constantine/math/curves/zoo_square_roots_fp2.nim
diff --git a/constantine/backend/curves/zoo_subgroups.nim b/constantine/math/curves/zoo_subgroups.nim
similarity index 100%
rename from constantine/backend/curves/zoo_subgroups.nim
rename to constantine/math/curves/zoo_subgroups.nim
diff --git a/constantine/backend/ec_shortweierstrass.nim b/constantine/math/ec_shortweierstrass.nim
similarity index 100%
rename from constantine/backend/ec_shortweierstrass.nim
rename to constantine/math/ec_shortweierstrass.nim
diff --git a/constantine/backend/elliptic/README.md b/constantine/math/elliptic/README.md
similarity index 100%
rename from constantine/backend/elliptic/README.md
rename to constantine/math/elliptic/README.md
diff --git a/constantine/backend/elliptic/ec_endomorphism_accel.nim b/constantine/math/elliptic/ec_endomorphism_accel.nim
similarity index 99%
rename from constantine/backend/elliptic/ec_endomorphism_accel.nim
rename to constantine/math/elliptic/ec_endomorphism_accel.nim
index fe3523c..170c191 100644
--- a/constantine/backend/elliptic/ec_endomorphism_accel.nim
+++ b/constantine/math/elliptic/ec_endomorphism_accel.nim
@@ -10,12 +10,12 @@ import
   # Standard Library
   std/typetraits,
   # Internal
-  ../primitives,
-  ../config/[common, curves, type_bigint],
+  ../../platforms/abstractions,
+  ../config/[curves, type_bigint],
   ../curves/zoo_endomorphisms,
   ../arithmetic,
-  ../towers,
-  ../isogeny/frobenius,
+  ../extension_fields,
+  ../isogenies/frobenius,
   ./ec_shortweierstrass_affine
 
 # ############################################################
diff --git a/constantine/backend/elliptic/ec_scalar_mul.nim b/constantine/math/elliptic/ec_scalar_mul.nim
similarity index 99%
rename from constantine/backend/elliptic/ec_scalar_mul.nim
rename to constantine/math/elliptic/ec_scalar_mul.nim
index 0b900f2..260b7f4 100644
--- a/constantine/backend/elliptic/ec_scalar_mul.nim
+++ b/constantine/math/elliptic/ec_scalar_mul.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../towers,
+  ../extension_fields,
   ../io/io_bigints,
   ../curves/zoo_endomorphisms,
   ./ec_endomorphism_accel
diff --git a/constantine/backend/elliptic/ec_shortweierstrass_affine.nim b/constantine/math/elliptic/ec_shortweierstrass_affine.nim
similarity index 97%
rename from constantine/backend/elliptic/ec_shortweierstrass_affine.nim
rename to constantine/math/elliptic/ec_shortweierstrass_affine.nim
index b968003..155498c 100644
--- a/constantine/backend/elliptic/ec_shortweierstrass_affine.nim
+++ b/constantine/math/elliptic/ec_shortweierstrass_affine.nim
@@ -7,11 +7,11 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../towers,
-  ../io/[io_fields, io_towers],
+  ../extension_fields,
+  ../io/[io_fields, io_extfields],
   ../curves/zoo_constants
 
 # ############################################################
diff --git a/constantine/backend/elliptic/ec_shortweierstrass_jacobian.nim b/constantine/math/elliptic/ec_shortweierstrass_jacobian.nim
similarity index 99%
rename from constantine/backend/elliptic/ec_shortweierstrass_jacobian.nim
rename to constantine/math/elliptic/ec_shortweierstrass_jacobian.nim
index 682163f..71694a8 100644
--- a/constantine/backend/elliptic/ec_shortweierstrass_jacobian.nim
+++ b/constantine/math/elliptic/ec_shortweierstrass_jacobian.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../towers,
+  ../extension_fields,
   ./ec_shortweierstrass_affine
 
 export Subgroup
diff --git a/constantine/backend/elliptic/ec_shortweierstrass_projective.nim b/constantine/math/elliptic/ec_shortweierstrass_projective.nim
similarity index 99%
rename from constantine/backend/elliptic/ec_shortweierstrass_projective.nim
rename to constantine/math/elliptic/ec_shortweierstrass_projective.nim
index 5980fc4..7a20006 100644
--- a/constantine/backend/elliptic/ec_shortweierstrass_projective.nim
+++ b/constantine/math/elliptic/ec_shortweierstrass_projective.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../towers,
+  ../extension_fields,
   ./ec_shortweierstrass_affine
 
 export Subgroup
diff --git a/constantine/backend/elliptic/ec_twistededwards_affine.nim b/constantine/math/elliptic/ec_twistededwards_affine.nim
similarity index 97%
rename from constantine/backend/elliptic/ec_twistededwards_affine.nim
rename to constantine/math/elliptic/ec_twistededwards_affine.nim
index 139b816..4644915 100644
--- a/constantine/backend/elliptic/ec_twistededwards_affine.nim
+++ b/constantine/math/elliptic/ec_twistededwards_affine.nim
@@ -7,11 +7,11 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../towers,
-  ../io/[io_fields, io_towers]
+  ../extension_fields,
+  ../io/[io_fields, io_extfields]
 
 # ############################################################
 #
diff --git a/constantine/backend/elliptic/ec_twistededwards_projective.nim b/constantine/math/elliptic/ec_twistededwards_projective.nim
similarity index 99%
rename from constantine/backend/elliptic/ec_twistededwards_projective.nim
rename to constantine/math/elliptic/ec_twistededwards_projective.nim
index 45f6b4f..1398948 100644
--- a/constantine/backend/elliptic/ec_twistededwards_projective.nim
+++ b/constantine/math/elliptic/ec_twistededwards_projective.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../towers,
+  ../extension_fields,
   ./ec_twistededwards_affine
 
 # ############################################################
diff --git a/constantine/backend/towers.nim b/constantine/math/extension_fields.nim
similarity index 83%
rename from constantine/backend/towers.nim
rename to constantine/math/extension_fields.nim
index f07ff89..4d6a572 100644
--- a/constantine/backend/towers.nim
+++ b/constantine/math/extension_fields.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  tower_field_extensions/[
+  extension_fields/[
     square_root_fp2,
     exponentiations,
-    extension_fields
+    towers
   ]
 
-export extension_fields, square_root_fp2, exponentiations
+export towers, square_root_fp2, exponentiations
diff --git a/constantine/backend/tower_field_extensions/README.md b/constantine/math/extension_fields/README.md
similarity index 100%
rename from constantine/backend/tower_field_extensions/README.md
rename to constantine/math/extension_fields/README.md
diff --git a/constantine/backend/tower_field_extensions/assembly/fp2_asm_x86_adx_bmi2.nim b/constantine/math/extension_fields/assembly/fp2_asm_x86_adx_bmi2.nim
similarity index 98%
rename from constantine/backend/tower_field_extensions/assembly/fp2_asm_x86_adx_bmi2.nim
rename to constantine/math/extension_fields/assembly/fp2_asm_x86_adx_bmi2.nim
index 9965b71..04f5811 100644
--- a/constantine/backend/tower_field_extensions/assembly/fp2_asm_x86_adx_bmi2.nim
+++ b/constantine/math/extension_fields/assembly/fp2_asm_x86_adx_bmi2.nim
@@ -8,8 +8,8 @@
 
 import
   # Internal
-  ../../config/[common, curves],
-  ../../primitives,
+  ../../../platforms/abstractions,
+  ../../config/curves,
   ../../arithmetic,
   ../../arithmetic/assembly/[
     limbs_asm_mul_x86_adx_bmi2,
diff --git a/constantine/backend/tower_field_extensions/exponentiations.nim b/constantine/math/extension_fields/exponentiations.nim
similarity index 99%
rename from constantine/backend/tower_field_extensions/exponentiations.nim
rename to constantine/math/extension_fields/exponentiations.nim
index 8a60d5c..46d7539 100644
--- a/constantine/backend/tower_field_extensions/exponentiations.nim
+++ b/constantine/math/extension_fields/exponentiations.nim
@@ -8,11 +8,10 @@
 
 
 import
+  ../../platforms/abstractions,
   ../arithmetic,
-  ../config/common,
-  ../primitives,
   ../io/io_bigints,
-  ./extension_fields
+  ./towers
 
 # ############################################################
 #
diff --git a/constantine/backend/tower_field_extensions/square_root_fp2.nim b/constantine/math/extension_fields/square_root_fp2.nim
similarity index 98%
rename from constantine/backend/tower_field_extensions/square_root_fp2.nim
rename to constantine/math/extension_fields/square_root_fp2.nim
index d67c35d..88e1984 100644
--- a/constantine/backend/tower_field_extensions/square_root_fp2.nim
+++ b/constantine/math/extension_fields/square_root_fp2.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ./extension_fields,
+  ../../platforms/abstractions,
+  ./towers,
   ../arithmetic,
-  ../primitives,
-  ../config/[common, curves],
+  ../config/curves,
   ../curves/zoo_square_roots_fp2
 
 # Square root
diff --git a/constantine/backend/tower_field_extensions/extension_fields.nim b/constantine/math/extension_fields/towers.nim
similarity index 99%
rename from constantine/backend/tower_field_extensions/extension_fields.nim
rename to constantine/math/extension_fields/towers.nim
index a68502f..8c4ac22 100644
--- a/constantine/backend/tower_field_extensions/extension_fields.nim
+++ b/constantine/math/extension_fields/towers.nim
@@ -7,11 +7,13 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves],
-  ../primitives,
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
   ../io/io_fields
 
+export Fp
+
 when UseASM_X86_64:
   import
     ./assembly/fp2_asm_x86_adx_bmi2
diff --git a/constantine/backend/io/README.md b/constantine/math/io/README.md
similarity index 100%
rename from constantine/backend/io/README.md
rename to constantine/math/io/README.md
diff --git a/constantine/backend/io/io_bigints.nim b/constantine/math/io/io_bigints.nim
similarity index 99%
rename from constantine/backend/io/io_bigints.nim
rename to constantine/math/io/io_bigints.nim
index d6b59df..66b1140 100644
--- a/constantine/backend/io/io_bigints.nim
+++ b/constantine/math/io/io_bigints.nim
@@ -11,10 +11,11 @@
 #   - Burning memory to ensure secrets are not left after dealloc.
 
 import
-  ../primitives,
+  ../../platforms/[abstractions, endians],
   ../arithmetic/bigints,
-  ../config/[common, type_bigint],
-  ./endians
+  ../config/type_bigint
+
+export BigInt, wordsRequired
 
 # ############################################################
 #
diff --git a/constantine/backend/io/io_ec.nim b/constantine/math/io/io_ec.nim
similarity index 97%
rename from constantine/backend/io/io_ec.nim
rename to constantine/math/io/io_ec.nim
index 8203056..e247a9d 100644
--- a/constantine/backend/io/io_ec.nim
+++ b/constantine/math/io/io_ec.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ./io_bigints, ./io_fields, ./io_towers,
+  ../../platforms/primitives,
+  ./io_bigints, ./io_fields, ./io_extfields,
   ../arithmetic,
-  ../towers,
-  ../primitives,
+  ../extension_fields,
   ../elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
diff --git a/constantine/backend/io/io_towers.nim b/constantine/math/io/io_extfields.nim
similarity index 98%
rename from constantine/backend/io/io_towers.nim
rename to constantine/math/io/io_extfields.nim
index 280f1d0..c02b309 100644
--- a/constantine/backend/io/io_towers.nim
+++ b/constantine/math/io/io_extfields.nim
@@ -12,11 +12,11 @@ import
   std/typetraits,
   # Internal
   ./io_bigints, ./io_fields,
-  ../primitives,
+  ../../platforms/primitives,
   ../arithmetic/finite_fields,
-  ../tower_field_extensions/extension_fields
+  ../extension_fields/towers
 
-export extension_fields
+export towers
 
 # No exceptions allowed
 {.push raises: [].}
diff --git a/constantine/backend/io/io_fields.nim b/constantine/math/io/io_fields.nim
similarity index 98%
rename from constantine/backend/io/io_fields.nim
rename to constantine/math/io/io_fields.nim
index 69bcb5f..16147a2 100644
--- a/constantine/backend/io/io_fields.nim
+++ b/constantine/math/io/io_fields.nim
@@ -8,9 +8,8 @@
 
 import
   ./io_bigints,
-  ../config/[common, type_ff],
-  ../arithmetic/finite_fields,
-  ../primitives
+  ../../platforms/abstractions,
+  ../arithmetic/finite_fields
 
 export Fp
 
diff --git a/constantine/backend/isogeny/README.md b/constantine/math/isogenies/README.md
similarity index 100%
rename from constantine/backend/isogeny/README.md
rename to constantine/math/isogenies/README.md
diff --git a/constantine/backend/isogeny/frobenius.nim b/constantine/math/isogenies/frobenius.nim
similarity index 98%
rename from constantine/backend/isogeny/frobenius.nim
rename to constantine/math/isogenies/frobenius.nim
index 5b5cb7e..6b932f6 100644
--- a/constantine/backend/isogeny/frobenius.nim
+++ b/constantine/math/isogenies/frobenius.nim
@@ -8,9 +8,9 @@
 
 import
   std/macros,
+  ../../platforms/primitives,
   ../arithmetic,
-  ../towers,
-  ../primitives,
+  ../extension_fields,
   ../curves/zoo_frobenius
 
 # Frobenius Map
diff --git a/constantine/backend/pairing/README.md b/constantine/math/pairing/README.md
similarity index 100%
rename from constantine/backend/pairing/README.md
rename to constantine/math/pairing/README.md
diff --git a/constantine/backend/pairing/cyclotomic_subgroup.nim b/constantine/math/pairing/cyclotomic_subgroup.nim
similarity index 99%
rename from constantine/backend/pairing/cyclotomic_subgroup.nim
rename to constantine/math/pairing/cyclotomic_subgroup.nim
index fed9b05..dd2f310 100644
--- a/constantine/backend/pairing/cyclotomic_subgroup.nim
+++ b/constantine/math/pairing/cyclotomic_subgroup.nim
@@ -7,11 +7,11 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../primitives,
-  ../config/[common, curves],
+  ../../platforms/abstractions,
+  ../config/curves,
   ../arithmetic,
-  ../towers,
-  ../isogeny/frobenius
+  ../extension_fields,
+  ../isogenies/frobenius
 
 # No exceptions allowed
 {.push raises: [].}
diff --git a/constantine/backend/pairing/lines_eval.nim b/constantine/math/pairing/lines_eval.nim
similarity index 99%
rename from constantine/backend/pairing/lines_eval.nim
rename to constantine/math/pairing/lines_eval.nim
index 243b9e3..f81a4d1 100644
--- a/constantine/backend/pairing/lines_eval.nim
+++ b/constantine/math/pairing/lines_eval.nim
@@ -9,14 +9,14 @@
 import
   std/typetraits,
   ../config/curves,
-  ../primitives,
+  ../../platforms/primitives,
   ../arithmetic,
-  ../towers,
+  ../extension_fields,
   ../elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective
   ],
-  ../io/io_towers
+  ../io/io_extfields
 
 # No exceptions allowed
 {.push raises: [].}
diff --git a/constantine/backend/pairing/miller_loops.nim b/constantine/math/pairing/miller_loops.nim
similarity index 99%
rename from constantine/backend/pairing/miller_loops.nim
rename to constantine/math/pairing/miller_loops.nim
index 0d2cef0..12a4306 100644
--- a/constantine/backend/pairing/miller_loops.nim
+++ b/constantine/math/pairing/miller_loops.nim
@@ -11,7 +11,7 @@ import
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective
   ],
-  ../isogeny/frobenius,
+  ../isogenies/frobenius,
   ./lines_eval
 
 # No exceptions allowed
diff --git a/constantine/backend/pairing/multi_pairing.md b/constantine/math/pairing/multi_pairing.md
similarity index 100%
rename from constantine/backend/pairing/multi_pairing.md
rename to constantine/math/pairing/multi_pairing.md
diff --git a/constantine/backend/pairing/pairing_bls12.nim b/constantine/math/pairing/pairing_bls12.nim
similarity index 98%
rename from constantine/backend/pairing/pairing_bls12.nim
rename to constantine/math/pairing/pairing_bls12.nim
index fc09f18..63e903a 100644
--- a/constantine/backend/pairing/pairing_bls12.nim
+++ b/constantine/math/pairing/pairing_bls12.nim
@@ -7,13 +7,14 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[common, curves, type_ff],
-  ../towers,
+  ../../platforms/abstractions,
+  ../config/curves,
+  ../extension_fields,
   ../elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective
   ],
-  ../isogeny/frobenius,
+  ../isogenies/frobenius,
   ../curves/zoo_pairings,
   ../arithmetic,
   ./cyclotomic_subgroup,
diff --git a/constantine/backend/pairing/pairing_bn.nim b/constantine/math/pairing/pairing_bn.nim
similarity index 98%
rename from constantine/backend/pairing/pairing_bn.nim
rename to constantine/math/pairing/pairing_bn.nim
index 4e65779..f64c325 100644
--- a/constantine/backend/pairing/pairing_bn.nim
+++ b/constantine/math/pairing/pairing_bn.nim
@@ -7,13 +7,13 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_ff],
-  ../towers,
+  ../config/curves,
+  ../extension_fields,
   ../elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective
   ],
-  ../isogeny/frobenius,
+  ../isogenies/frobenius,
   ../curves/zoo_pairings,
   ./lines_eval,
   ./cyclotomic_subgroup,
diff --git a/constantine/backend/pairing/pairing_bw6_761.nim b/constantine/math/pairing/pairing_bw6_761.nim
similarity index 98%
rename from constantine/backend/pairing/pairing_bw6_761.nim
rename to constantine/math/pairing/pairing_bw6_761.nim
index 47a6c1d..d5b1a05 100644
--- a/constantine/backend/pairing/pairing_bw6_761.nim
+++ b/constantine/math/pairing/pairing_bw6_761.nim
@@ -7,14 +7,14 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../config/[curves, type_ff],
+  ../config/curves,
   ../arithmetic,
-  ../towers,
+  ../extension_fields,
   ../elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective
   ],
-  ../isogeny/frobenius,
+  ../isogenies/frobenius,
   ../curves/zoo_pairings,
   ./lines_eval,
   ./miller_loops
diff --git a/constantine/backend/pairings.nim b/constantine/math/pairings.nim
similarity index 97%
rename from constantine/backend/pairings.nim
rename to constantine/math/pairings.nim
index 1633d0d..e143fd1 100644
--- a/constantine/backend/pairings.nim
+++ b/constantine/math/pairings.nim
@@ -9,7 +9,7 @@
 import
   ./config/curves,
   ./pairing/[pairing_bn, pairing_bls12],
-  ./towers
+  ./extension_fields
 
 template pairing*[C](gt: var Fp12[C], P, Q: typed) =
   when family(C) == BarretoNaehrig:
diff --git a/constantine/backend/primitives/README.md b/constantine/platforms/README.md
similarity index 100%
rename from constantine/backend/primitives/README.md
rename to constantine/platforms/README.md
diff --git a/constantine/backend/config/common.nim b/constantine/platforms/abstractions.nim
similarity index 94%
rename from constantine/backend/config/common.nim
rename to constantine/platforms/abstractions.nim
index a7b46b2..c5a9c50 100644
--- a/constantine/backend/config/common.nim
+++ b/constantine/platforms/abstractions.nim
@@ -8,14 +8,14 @@
 
 # ############################################################
 #
-#                Common configuration
+#                Platforms abstractions
 #
 # ############################################################
 
-import ../primitives
-import ../../../metering/tracer
+import ./primitives
+import ../../metering/tracer
 
-export tracer
+export primitives, tracer
 
 when sizeof(int) == 8 and not defined(Constantine32):
   type
diff --git a/constantine/backend/primitives/bithacks.nim b/constantine/platforms/bithacks.nim
similarity index 100%
rename from constantine/backend/primitives/bithacks.nim
rename to constantine/platforms/bithacks.nim
diff --git a/constantine/backend/primitives/addcarry_subborrow.nim b/constantine/platforms/compilers/addcarry_subborrow.nim
similarity index 99%
rename from constantine/backend/primitives/addcarry_subborrow.nim
rename to constantine/platforms/compilers/addcarry_subborrow.nim
index 03bec55..01b6ea9 100644
--- a/constantine/backend/primitives/addcarry_subborrow.nim
+++ b/constantine/platforms/compilers/addcarry_subborrow.nim
@@ -6,7 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import ./constant_time_types
+import ../constant_time/ct_types
 
 # ############################################################
 #
diff --git a/constantine/backend/primitives/extended_precision.nim b/constantine/platforms/compilers/extended_precision.nim
similarity index 99%
rename from constantine/backend/primitives/extended_precision.nim
rename to constantine/platforms/compilers/extended_precision.nim
index b81e6cd..f3eb103 100644
--- a/constantine/backend/primitives/extended_precision.nim
+++ b/constantine/platforms/compilers/extended_precision.nim
@@ -13,9 +13,9 @@
 # ############################################################
 
 import
-  ./constant_time_types,
   ./addcarry_subborrow,
-  ./constant_time
+  ../constant_time/ct_types,
+  ../constant_time/ct_routines
 
 # ############################################################
 #
diff --git a/constantine/backend/primitives/extended_precision_64bit_uint128.nim b/constantine/platforms/compilers/extended_precision_64bit_uint128.nim
similarity index 99%
rename from constantine/backend/primitives/extended_precision_64bit_uint128.nim
rename to constantine/platforms/compilers/extended_precision_64bit_uint128.nim
index 045df87..1eceb13 100644
--- a/constantine/backend/primitives/extended_precision_64bit_uint128.nim
+++ b/constantine/platforms/compilers/extended_precision_64bit_uint128.nim
@@ -6,7 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import ./constant_time_types
+import ../constant_time/ct_types
 
 # ############################################################
 #
diff --git a/constantine/backend/primitives/extended_precision_x86_64_gcc.nim b/constantine/platforms/compilers/extended_precision_x86_64_gcc.nim
similarity index 98%
rename from constantine/backend/primitives/extended_precision_x86_64_gcc.nim
rename to constantine/platforms/compilers/extended_precision_x86_64_gcc.nim
index 3a4ec61..3fb1d7e 100644
--- a/constantine/backend/primitives/extended_precision_x86_64_gcc.nim
+++ b/constantine/platforms/compilers/extended_precision_x86_64_gcc.nim
@@ -6,7 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import ./constant_time_types
+import ../constant_time/ct_types
 
 # ############################################################
 #
diff --git a/constantine/backend/primitives/extended_precision_x86_64_msvc.nim b/constantine/platforms/compilers/extended_precision_x86_64_msvc.nim
similarity index 99%
rename from constantine/backend/primitives/extended_precision_x86_64_msvc.nim
rename to constantine/platforms/compilers/extended_precision_x86_64_msvc.nim
index 774cd05..960dc14 100644
--- a/constantine/backend/primitives/extended_precision_x86_64_msvc.nim
+++ b/constantine/platforms/compilers/extended_precision_x86_64_msvc.nim
@@ -7,7 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ./constant_time_types,
+  ./ct_types,
   ./addcarry_subborrow
 
 # ############################################################
diff --git a/constantine/backend/primitives/constant_time.nim b/constantine/platforms/constant_time/ct_routines.nim
similarity index 99%
rename from constantine/backend/primitives/constant_time.nim
rename to constantine/platforms/constant_time/ct_routines.nim
index b542cff..93bbb4c 100644
--- a/constantine/backend/primitives/constant_time.nim
+++ b/constantine/platforms/constant_time/ct_routines.nim
@@ -6,7 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import ./constant_time_types
+import ./ct_types
 
 # ############################################################
 #
diff --git a/constantine/backend/primitives/constant_time_types.nim b/constantine/platforms/constant_time/ct_types.nim
similarity index 100%
rename from constantine/backend/primitives/constant_time_types.nim
rename to constantine/platforms/constant_time/ct_types.nim
diff --git a/constantine/backend/primitives/multiplexers.nim b/constantine/platforms/constant_time/multiplexers.nim
similarity index 99%
rename from constantine/backend/primitives/multiplexers.nim
rename to constantine/platforms/constant_time/multiplexers.nim
index 955482d..2fed158 100644
--- a/constantine/backend/primitives/multiplexers.nim
+++ b/constantine/platforms/constant_time/multiplexers.nim
@@ -6,7 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import ./constant_time_types
+import ./ct_types
 
 # ############################################################
 #
diff --git a/constantine/backend/io/endians.nim b/constantine/platforms/endians.nim
similarity index 99%
rename from constantine/backend/io/endians.nim
rename to constantine/platforms/endians.nim
index beedd40..44ff953 100644
--- a/constantine/backend/io/endians.nim
+++ b/constantine/platforms/endians.nim
@@ -6,7 +6,7 @@
 #   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
-import ../config/common
+import ./abstractions
 
 # perf critical we don't want bound checks here
 # So no checks and we avoid signed int to ensur eno exceptions.
diff --git a/constantine/backend/primitives/cpuinfo_x86.nim b/constantine/platforms/isa/cpuinfo_x86.nim
similarity index 100%
rename from constantine/backend/primitives/cpuinfo_x86.nim
rename to constantine/platforms/isa/cpuinfo_x86.nim
diff --git a/constantine/backend/primitives/macro_assembler_x86.nim b/constantine/platforms/isa/macro_assembler_x86.nim
similarity index 100%
rename from constantine/backend/primitives/macro_assembler_x86.nim
rename to constantine/platforms/isa/macro_assembler_x86.nim
diff --git a/constantine/backend/primitives.nim b/constantine/platforms/primitives.nim
similarity index 69%
rename from constantine/backend/primitives.nim
rename to constantine/platforms/primitives.nim
index 7bea2a9..7ec6c50 100644
--- a/constantine/backend/primitives.nim
+++ b/constantine/platforms/primitives.nim
@@ -7,17 +7,21 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  primitives/constant_time_types,
-  primitives/constant_time,
-  primitives/multiplexers,
-  primitives/addcarry_subborrow,
-  primitives/extended_precision,
-  primitives/bithacks,
-  primitives/static_for
+  constant_time/[
+    ct_types,
+    ct_routines,
+    multiplexers
+  ],
+  compilers/[
+    addcarry_subborrow,
+    extended_precision
+  ],
+  ./bithacks,
+  ../../helpers/static_for
 
 export
-  constant_time_types,
-  constant_time,
+  ct_types,
+  ct_routines,
   multiplexers,
   addcarry_subborrow,
   extended_precision,
@@ -25,5 +29,5 @@ export
   staticFor
 
 when X86 and GCC_Compatible:
-  import primitives/[cpuinfo_x86, macro_assembler_x86]
+  import isa/[cpuinfo_x86, macro_assembler_x86]
   export cpuinfo_x86, macro_assembler_x86
diff --git a/constantine/backend/signatures/README.md b/constantine/signatures/README.md
similarity index 100%
rename from constantine/backend/signatures/README.md
rename to constantine/signatures/README.md
diff --git a/constantine/backend/signatures/bls_signatures.nim b/constantine/signatures/bls_signatures.nim
similarity index 98%
rename from constantine/backend/signatures/bls_signatures.nim
rename to constantine/signatures/bls_signatures.nim
index 87ba27b..3db0061 100644
--- a/constantine/backend/signatures/bls_signatures.nim
+++ b/constantine/signatures/bls_signatures.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-    ../ec_shortweierstrass,
+    ../math/[ec_shortweierstrass, pairings],
+    ../math/curves/zoo_generators,
     ../hash_to_curve/hash_to_curve,
-    ../hashes, ../pairings,
-    ../curves/zoo_generators
+    ../hashes
 
 # ############################################################
 #
diff --git a/docs/optimizations.md b/docs/optimizations.md
index 1ce4fcc..48af6f2 100644
--- a/docs/optimizations.md
+++ b/docs/optimizations.md
@@ -40,7 +40,7 @@ The optimizations can be of algebraic, algorithmic or "implementation details" n
   - [x] Unsaturated Representation
     - [ ] Mersenne Prime (2ᵏ - 1),
     - [ ] Generalized Mersenne Prime (NIST Prime P256: 2^256 - 2^224 + 2^192 + 2^96 - 1)
-    - [ ] Pseudo-Mersenne Prime (2^m - k for example Curve25519: 2^255 - 19)
+    - [ ] Pseudo-Mersenne Prime (2^m - k for example Edwards25519: 2^255 - 19)
     - [ ] Golden Primes (φ^2 - φ - 1 with φ = 2ᵏ for example Ed448-Goldilocks: 2^448 - 2^224 - 1)
     - [ ] any prime modulus (lazy carry)
 
diff --git a/helpers/prng_unsafe.nim b/helpers/prng_unsafe.nim
index d1999a7..025b555 100644
--- a/helpers/prng_unsafe.nim
+++ b/helpers/prng_unsafe.nim
@@ -7,17 +7,17 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../constantine/backend/arithmetic,
-  ../constantine/backend/primitives,
-  ../constantine/backend/config/[common, curves, type_ff],
-  ../constantine/backend/elliptic/[
+  ../constantine/platforms/abstractions,
+  ../constantine/math/arithmetic,
+  ../constantine/math/config/curves,
+  ../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian,
     ec_twistededwards_affine,
     ec_twistededwards_projective],
-  ../constantine/backend/io/io_bigints,
-  ../constantine/backend/tower_field_extensions/extension_fields
+  ../constantine/math/io/io_bigints,
+  ../constantine/math/extension_fields/towers
 
 # ############################################################
 #
diff --git a/helpers/static_for.nim b/helpers/static_for.nim
index f78305b..ab988a0 100644
--- a/helpers/static_for.nim
+++ b/helpers/static_for.nim
@@ -1,3 +1,11 @@
+# Constantine
+# Copyright (c) 2018-2019    Status Research & Development GmbH
+# Copyright (c) 2020-Present Mamy André-Ratsimbazafy
+# Licensed and distributed under either of
+#   * MIT license (license terms in the root directory or at http://opensource.org/licenses/MIT).
+#   * Apache v2 license (license terms in the root directory or at http://www.apache.org/licenses/LICENSE-2.0).
+# at your option. This file may not be copied, modified, or distributed except according to those terms.
+
 import std/macros
 
 proc replaceNodes(ast: NimNode, what: NimNode, by: NimNode): NimNode =
diff --git a/metering/m_pairings.nim b/metering/m_pairings.nim
index 15fa6c1..86c1a7c 100644
--- a/metering/m_pairings.nim
+++ b/metering/m_pairings.nim
@@ -9,11 +9,11 @@
 import
   std/times,
   ./reports, ./tracer,
-  ../constantine/backend/config/[common, curves],
-  ../constantine/backend/[arithmetic, towers],
-  ../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../constantine/backend/curves/zoo_subgroups,
-  ../constantine/backend/pairing/pairing_bls12,
+  ../constantine/math/config/[common, curves],
+  ../constantine/math/[arithmetic, extension_fields],
+  ../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../constantine/math/curves/zoo_subgroups,
+  ../constantine/math/pairing/pairing_bls12,
   # Helpers
   ../helpers/prng_unsafe
 
diff --git a/research/kzg_poly_commit/fft_fr.nim b/research/kzg_poly_commit/fft_fr.nim
index bac5a5b..6ceffee 100644
--- a/research/kzg_poly_commit/fft_fr.nim
+++ b/research/kzg_poly_commit/fft_fr.nim
@@ -7,9 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/io/io_fields,
+  ../../constantine/platforms/primitives,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/io_fields,
   # Research
   ./strided_views,
   ./fft_lut
@@ -24,7 +25,7 @@ import
 #
 # Other readable FFTs includes:
 # - https://github.com/kwantam/fffft
-# - https://github.com/ConsenSys/gnark/blob/master/internal/backend/bls381/fft/fft.go
+# - https://github.com/ConsenSys/gnark/blob/master/internal/math/bls381/fft/fft.go
 # - https://github.com/poanetwork/threshold_crypto/blob/8820c11/src/poly_vals.rs#L332-L370
 # - https://github.com/zkcrypto/bellman/blob/10c5010/src/domain.rs#L272-L315
 # - Modern Computer Arithmetic, Brent and Zimmermann, p53 algorithm 2.2
diff --git a/research/kzg_poly_commit/fft_g1.nim b/research/kzg_poly_commit/fft_g1.nim
index e4c7843..50b0788 100644
--- a/research/kzg_poly_commit/fft_g1.nim
+++ b/research/kzg_poly_commit/fft_g1.nim
@@ -7,15 +7,16 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/elliptic/[
+  ../../constantine/platforms/primitives,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/elliptic/[
     ec_scalar_mul,
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian,
   ],
-  ../../constantine/backend/io/[io_fields, io_ec],
+  ../../constantine/math/io/[io_fields, io_ec],
   # Research
   ./strided_views,
   ./fft_lut
@@ -30,7 +31,7 @@ import
 #
 # Other readable FFTs includes:
 # - https://github.com/kwantam/fffft
-# - https://github.com/ConsenSys/gnark/blob/master/internal/backend/bls381/fft/fft.go
+# - https://github.com/ConsenSys/gnark/blob/master/internal/math/bls381/fft/fft.go
 # - https://github.com/poanetwork/threshold_crypto/blob/8820c11/src/poly_vals.rs#L332-L370
 # - https://github.com/zkcrypto/bellman/blob/10c5010/src/domain.rs#L272-L315
 # - Modern Computer Arithmetic, Brent and Zimmermann, p53 algorithm 2.2
diff --git a/research/kzg_poly_commit/fft_lut.nim b/research/kzg_poly_commit/fft_lut.nim
index d3f2b4a..f3af753 100644
--- a/research/kzg_poly_commit/fft_lut.nim
+++ b/research/kzg_poly_commit/fft_lut.nim
@@ -8,9 +8,10 @@
 
 import
   std/macros,
-  ../../constantine/backend/config/[curves, common],
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/io/io_fields
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/io_fields
 
 # TODO automate this
 # we can precompute everything in Sage
diff --git a/research/kzg_poly_commit/kzg_single_proofs.nim b/research/kzg_poly_commit/kzg_single_proofs.nim
index 1fe37fd..287e2d3 100644
--- a/research/kzg_poly_commit/kzg_single_proofs.nim
+++ b/research/kzg_poly_commit/kzg_single_proofs.nim
@@ -1,15 +1,15 @@
 # https://github.com/ethereum/research/blob/master/kzg_data_availability/kzg_proofs.py
 
 import
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/[arithmetic, primitives, towers],
-  ../../constantine/backend/elliptic/[
+  ../../constantine/math/config/curves,
+  ../../constantine/math/[arithmetic, primitives, extension_fields],
+  ../../constantine/math/elliptic/[
     ec_scalar_mul,
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
   ],
-  ../../constantine/backend/io/[io_fields, io_ec],
-  ../../constantine/backend/pairing/[
+  ../../constantine/math/io/[io_fields, io_ec],
+  ../../constantine/math/pairing/[
     pairing_bls12,
     miller_loops
   ],
diff --git a/research/kzg_poly_commit/polynomials.nim b/research/kzg_poly_commit/polynomials.nim
index 0a623f8..214dfc3 100644
--- a/research/kzg_poly_commit/polynomials.nim
+++ b/research/kzg_poly_commit/polynomials.nim
@@ -1,13 +1,14 @@
 import
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/[arithmetic, primitives, towers],
-  ../../constantine/backend/elliptic/[
+  ../../constantine/platforms/primitives,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/[arithmetic, extension_fields],
+  ../../constantine/math/elliptic/[
     ec_scalar_mul,
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
   ],
-  ../../constantine/backend/io/[io_fields, io_ec],
-  ../../constantine/backend/pairing/[
+  ../../constantine/math/io/[io_fields, io_ec],
+  ../../constantine/math/pairing/[
     pairing_bls12,
     miller_loops,
     cyclotomic_subgroup
diff --git a/sage/derive_endomorphisms.sage b/sage/derive_endomorphisms.sage
index 27032e1..a230fbe 100644
--- a/sage/derive_endomorphisms.sage
+++ b/sage/derive_endomorphisms.sage
@@ -266,7 +266,7 @@ if __name__ == "__main__":
       f.write('\n\n')
       f.write(inspect.cleandoc(f"""
         import
-          ../config/[curves, type_bigint, type_ff],
+          ../config/curves,,
           ../io/[io_bigints, io_fields]
 
         # {curve} G1
diff --git a/sage/derive_frobenius.sage b/sage/derive_frobenius.sage
index 9ad614f..96ed47a 100644
--- a/sage/derive_frobenius.sage
+++ b/sage/derive_frobenius.sage
@@ -279,15 +279,15 @@ if __name__ == "__main__":
         f.write(inspect.cleandoc("""
           import
             ../config/curves,
-            ../towers,
-            ../io/io_towers
+            ../extension_fields,
+            ../io/io_extfields
         """))
       else:
         f.write(inspect.cleandoc("""
           import
-            ../config/[curves, type_ff],
-            ../towers,
-            ../io/[io_fields, io_towers]
+            ../config/curves,
+            ../extension_fields,
+            ../io/[io_fields, io_extfields]
         """))
       f.write('\n\n')
       f.write(FrobMap)
diff --git a/sage/derive_hash_to_curve.sage b/sage/derive_hash_to_curve.sage
index 1a11a07..0567386 100644
--- a/sage/derive_hash_to_curve.sage
+++ b/sage/derive_hash_to_curve.sage
@@ -315,7 +315,7 @@ if __name__ == "__main__":
       f.write(inspect.cleandoc("""
           import
             ../config/curves,
-            ../io/[io_fields, io_towers]
+            ../io/[io_fields, io_extfields]
       """))
 
       f.write('\n\n')
diff --git a/sage/derive_pairing.sage b/sage/derive_pairing.sage
index e4ddf9b..538be69 100644
--- a/sage/derive_pairing.sage
+++ b/sage/derive_pairing.sage
@@ -239,7 +239,7 @@ if __name__ == "__main__":
       f.write('\n\n')
       f.write(inspect.cleandoc("""
         import
-          ../config/[curves, type_bigint],
+          ../config/curves,
           ../io/io_bigints
 
         # Slow generic implementation
diff --git a/sage/derive_square_root.sage b/sage/derive_square_root.sage
index 4c33f08..3ea7256 100644
--- a/sage/derive_square_root.sage
+++ b/sage/derive_square_root.sage
@@ -139,7 +139,7 @@ if __name__ == "__main__":
       f.write(inspect.cleandoc("""
           import
             ../config/curves,
-            ../io/io_towers
+            ../io/io_extfields
       """))
 
       f.write('\n\n')
diff --git a/sage/g2_params.sage b/sage/g2_params.sage
index 158a9d6..63f4201 100644
--- a/sage/g2_params.sage
+++ b/sage/g2_params.sage
@@ -163,7 +163,7 @@ if __name__ == "__main__":
       f.write(inspect.cleandoc("""
           import
             ../config/curves,
-            ../io/io_towers
+            ../io/io_extfields
       """))
 
       f.write('\n\n')
diff --git a/tests/backend/support/canaries.nim b/tests/math/support/canaries.nim
similarity index 80%
rename from tests/backend/support/canaries.nim
rename to tests/math/support/canaries.nim
index a907b1f..1702032 100644
--- a/tests/backend/support/canaries.nim
+++ b/tests/math/support/canaries.nim
@@ -7,9 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../../constantine/backend/arithmetic/bigints,
-  ../../../constantine/backend/config/[common, curves],
-  ../../../constantine/backend/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective]
+  ../../../constantine/platforms/abstractions,
+  ../../../constantine/math/arithmetic/bigints,
+  ../../../constantine/math/config/curves,
+  ../../../constantine/math/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective]
 
 # Canaries
 # --------------------------------------------------------------
diff --git a/tests/backend/support/ec_reference_scalar_mult.nim b/tests/math/support/ec_reference_scalar_mult.nim
similarity index 95%
rename from tests/backend/support/ec_reference_scalar_mult.nim
rename to tests/math/support/ec_reference_scalar_mult.nim
index 2df089e..82148ca 100644
--- a/tests/backend/support/ec_reference_scalar_mult.nim
+++ b/tests/math/support/ec_reference_scalar_mult.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../../constantine/backend/arithmetic,
-  ../../../constantine/backend/io/io_bigints
+  ../../../constantine/math/arithmetic,
+  ../../../constantine/math/io/io_bigints
 
 # Support files for testing Elliptic Curve arithmetic
 # ------------------------------------------------------------------------------
diff --git a/tests/backend/t_bigints.nim b/tests/math/t_bigints.nim
similarity index 99%
rename from tests/backend/t_bigints.nim
rename to tests/math/t_bigints.nim
index 6d667b9..c0364a6 100644
--- a/tests/backend/t_bigints.nim
+++ b/tests/math/t_bigints.nim
@@ -10,10 +10,9 @@ import
   # Standard library
   std/unittest,
   # Internal
-  ../../constantine/backend/io/io_bigints,
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/config/[common, type_bigint],
-  ../../constantine/backend/primitives,
+  ../../constantine/math/io/io_bigints,
+  ../../constantine/math/arithmetic,
+  ../../constantine/platforms/abstractions,
   # Test utilities,
   support/canaries
 
diff --git a/tests/backend/t_bigints_mod_vs_gmp.nim b/tests/math/t_bigints_mod_vs_gmp.nim
similarity index 97%
rename from tests/backend/t_bigints_mod_vs_gmp.nim
rename to tests/math/t_bigints_mod_vs_gmp.nim
index b90029a..62ab73c 100644
--- a/tests/backend/t_bigints_mod_vs_gmp.nim
+++ b/tests/math/t_bigints_mod_vs_gmp.nim
@@ -12,9 +12,9 @@ import
   # Third-party
   gmp, stew/byteutils,
   # Internal
-  ../../constantine/backend/io/io_bigints,
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/primitives
+  ../../constantine/math/io/io_bigints,
+  ../../constantine/math/arithmetic,
+  ../../constantine/platforms/primitives
 
 echo "\n------------------------------------------------------\n"
 # We test up to 1024-bit, more is really slow
@@ -28,7 +28,7 @@ const CryptoModSizes = [
   1024,
   2048,
   3072,
-  # secp256k1, Curve25519
+  # secp256k1, Edwards25519
   256,
   # Barreto-Naehrig
   254, # BN254
diff --git a/tests/backend/t_bigints_mul_high_words_vs_gmp.nim b/tests/math/t_bigints_mul_high_words_vs_gmp.nim
similarity index 97%
rename from tests/backend/t_bigints_mul_high_words_vs_gmp.nim
rename to tests/math/t_bigints_mul_high_words_vs_gmp.nim
index 13afc30..e513221 100644
--- a/tests/backend/t_bigints_mul_high_words_vs_gmp.nim
+++ b/tests/math/t_bigints_mul_high_words_vs_gmp.nim
@@ -12,10 +12,9 @@ import
   # Third-party
   gmp, stew/byteutils,
   # Internal
-  ../../constantine/backend/io/io_bigints,
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/primitives,
-  ../../constantine/backend/config/[common, type_bigint]
+  ../../constantine/math/io/io_bigints,
+  ../../constantine/math/arithmetic,
+  ../../constantine/platforms/abstractions
 
 echo "\n------------------------------------------------------\n"
 # We test up to 1024-bit, more is really slow
diff --git a/tests/backend/t_bigints_mul_vs_gmp.nim b/tests/math/t_bigints_mul_vs_gmp.nim
similarity index 96%
rename from tests/backend/t_bigints_mul_vs_gmp.nim
rename to tests/math/t_bigints_mul_vs_gmp.nim
index 855964b..79985e9 100644
--- a/tests/backend/t_bigints_mul_vs_gmp.nim
+++ b/tests/math/t_bigints_mul_vs_gmp.nim
@@ -12,10 +12,9 @@ import
   # Third-party
   gmp, stew/byteutils,
   # Internal
-  ../../constantine/backend/io/io_bigints,
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/primitives,
-  ../../constantine/backend/config/[common, type_bigint]
+  ../../constantine/math/io/io_bigints,
+  ../../constantine/math/arithmetic,
+  ../../constantine/platforms/abstractions
 
 echo "\n------------------------------------------------------\n"
 # We test up to 1024-bit, more is really slow
diff --git a/tests/backend/t_bigints_multimod.nim b/tests/math/t_bigints_multimod.nim
similarity index 98%
rename from tests/backend/t_bigints_multimod.nim
rename to tests/math/t_bigints_multimod.nim
index e7981d6..c4915f8 100644
--- a/tests/backend/t_bigints_multimod.nim
+++ b/tests/math/t_bigints_multimod.nim
@@ -10,10 +10,9 @@ import
   # Standard library
   std/unittest,
   # Third-party
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/io/io_bigints,
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/primitives
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/io/io_bigints,
+  ../../constantine/math/arithmetic
 
 echo "\n------------------------------------------------------\n"
 
diff --git a/tests/backend/t_ec_conversion.nim b/tests/math/t_ec_conversion.nim
similarity index 91%
rename from tests/backend/t_ec_conversion.nim
rename to tests/math/t_ec_conversion.nim
index 141c115..0e9dcf0 100644
--- a/tests/backend/t_ec_conversion.nim
+++ b/tests/math/t_ec_conversion.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/[ec_shortweierstrass_jacobian, ec_shortweierstrass_projective],
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/[ec_shortweierstrass_jacobian, ec_shortweierstrass_projective],
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_frobenius.nim b/tests/math/t_ec_frobenius.nim
similarity index 98%
rename from tests/backend/t_ec_frobenius.nim
rename to tests/math/t_ec_frobenius.nim
index 08cf6cc..7ddae52 100644
--- a/tests/backend/t_ec_frobenius.nim
+++ b/tests/math/t_ec_frobenius.nim
@@ -11,11 +11,12 @@ import
   # Standard library
   std/[times, unittest],
   # Internals
-  ../../constantine/backend/config/[common, curves],
-  ../../constantine/backend/[arithmetic, towers],
-  ../../constantine/backend/io/[io_bigints, io_ec],
-  ../../constantine/backend/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective, ec_scalar_mul],
-  ../../constantine/backend/isogeny/frobenius,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/[arithmetic, extension_fields],
+  ../../constantine/math/io/[io_bigints, io_ec],
+  ../../constantine/math/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective, ec_scalar_mul],
+  ../../constantine/math/isogenies/frobenius,
   # Tests
   ../../helpers/prng_unsafe,
   ./t_ec_template
diff --git a/tests/backend/t_ec_sage_bls12_377.nim b/tests/math/t_ec_sage_bls12_377.nim
similarity index 81%
rename from tests/backend/t_ec_sage_bls12_377.nim
rename to tests/math/t_ec_sage_bls12_377.nim
index 40ed9e3..af502a0 100644
--- a/tests/backend/t_ec_sage_bls12_377.nim
+++ b/tests/math/t_ec_sage_bls12_377.nim
@@ -8,10 +8,10 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_sage_template
 
diff --git a/tests/backend/t_ec_sage_bls12_381.nim b/tests/math/t_ec_sage_bls12_381.nim
similarity index 81%
rename from tests/backend/t_ec_sage_bls12_381.nim
rename to tests/math/t_ec_sage_bls12_381.nim
index 096fc3c..ecd5326 100644
--- a/tests/backend/t_ec_sage_bls12_381.nim
+++ b/tests/math/t_ec_sage_bls12_381.nim
@@ -8,10 +8,10 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_sage_template
 
diff --git a/tests/backend/t_ec_sage_bn254_nogami.nim b/tests/math/t_ec_sage_bn254_nogami.nim
similarity index 81%
rename from tests/backend/t_ec_sage_bn254_nogami.nim
rename to tests/math/t_ec_sage_bn254_nogami.nim
index 324e55a..f4c4330 100644
--- a/tests/backend/t_ec_sage_bn254_nogami.nim
+++ b/tests/math/t_ec_sage_bn254_nogami.nim
@@ -8,10 +8,10 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_sage_template
 
diff --git a/tests/backend/t_ec_sage_bn254_snarks.nim b/tests/math/t_ec_sage_bn254_snarks.nim
similarity index 81%
rename from tests/backend/t_ec_sage_bn254_snarks.nim
rename to tests/math/t_ec_sage_bn254_snarks.nim
index a6f8944..e6be63e 100644
--- a/tests/backend/t_ec_sage_bn254_snarks.nim
+++ b/tests/math/t_ec_sage_bn254_snarks.nim
@@ -8,10 +8,10 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_sage_template
 
diff --git a/tests/backend/t_ec_sage_bw6_761_g1.nim b/tests/math/t_ec_sage_bw6_761_g1.nim
similarity index 86%
rename from tests/backend/t_ec_sage_bw6_761_g1.nim
rename to tests/math/t_ec_sage_bw6_761_g1.nim
index 7eed998..4864bbc 100644
--- a/tests/backend/t_ec_sage_bw6_761_g1.nim
+++ b/tests/math/t_ec_sage_bw6_761_g1.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_sage_template
 
diff --git a/tests/backend/t_ec_sage_bw6_761_g2.nim b/tests/math/t_ec_sage_bw6_761_g2.nim
similarity index 86%
rename from tests/backend/t_ec_sage_bw6_761_g2.nim
rename to tests/math/t_ec_sage_bw6_761_g2.nim
index 661166e..e0c37e9 100644
--- a/tests/backend/t_ec_sage_bw6_761_g2.nim
+++ b/tests/math/t_ec_sage_bw6_761_g2.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_sage_template
 
diff --git a/tests/backend/t_ec_sage_template.nim b/tests/math/t_ec_sage_template.nim
similarity index 96%
rename from tests/backend/t_ec_sage_template.nim
rename to tests/math/t_ec_sage_template.nim
index b3ccda8..27690f7 100644
--- a/tests/backend/t_ec_sage_template.nim
+++ b/tests/math/t_ec_sage_template.nim
@@ -10,12 +10,13 @@ import
   # Standard library
   std/[unittest, times, os, strutils, macros],
   # 3rd party
-  jsony,
+  pkg/jsony,
   # Internals
-  ../../constantine/backend/config/[common, curves, type_bigint, type_ff],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/io/[io_bigints, io_ec],
-  ../../constantine/backend/elliptic/[
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/io/[io_bigints, io_ec],
+  ../../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
     ec_shortweierstrass_jacobian,
@@ -24,6 +25,8 @@ import
   # Test utilities
   ./support/ec_reference_scalar_mult
 
+export unittest # Generic sandwich
+
 # Serialization
 # --------------------------------------------------------------------------
 
diff --git a/tests/backend/t_ec_shortw_jac_g1_add_double.nim b/tests/math/t_ec_shortw_jac_g1_add_double.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_jac_g1_add_double.nim
rename to tests/math/t_ec_shortw_jac_g1_add_double.nim
index ccf4d22..8e93350 100644
--- a/tests/backend/t_ec_shortw_jac_g1_add_double.nim
+++ b/tests/math/t_ec_shortw_jac_g1_add_double.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g1_mixed_add.nim b/tests/math/t_ec_shortw_jac_g1_mixed_add.nim
similarity index 89%
rename from tests/backend/t_ec_shortw_jac_g1_mixed_add.nim
rename to tests/math/t_ec_shortw_jac_g1_mixed_add.nim
index f5d3be9..05e6c82 100644
--- a/tests/backend/t_ec_shortw_jac_g1_mixed_add.nim
+++ b/tests/math/t_ec_shortw_jac_g1_mixed_add.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/arithmetic,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/arithmetic,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g1_mul_distri.nim b/tests/math/t_ec_shortw_jac_g1_mul_distri.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_jac_g1_mul_distri.nim
rename to tests/math/t_ec_shortw_jac_g1_mul_distri.nim
index 762f148..8674a13 100644
--- a/tests/backend/t_ec_shortw_jac_g1_mul_distri.nim
+++ b/tests/math/t_ec_shortw_jac_g1_mul_distri.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g1_mul_sanity.nim b/tests/math/t_ec_shortw_jac_g1_mul_sanity.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_jac_g1_mul_sanity.nim
rename to tests/math/t_ec_shortw_jac_g1_mul_sanity.nim
index 5b5f325..8147d9f 100644
--- a/tests/backend/t_ec_shortw_jac_g1_mul_sanity.nim
+++ b/tests/math/t_ec_shortw_jac_g1_mul_sanity.nim
@@ -10,10 +10,10 @@ import
   # Standard library
   std/[unittest, times],
   # Internals
-  ../../constantine/backend/config/[common, curves],
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/io/[io_bigints, io_fields, io_ec],
-  ../../constantine/backend/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_jacobian, ec_scalar_mul],
+  ../../constantine/math/config/[common, curves],
+  ../../constantine/math/[arithmetic, primitives],
+  ../../constantine/math/io/[io_bigints, io_fields, io_ec],
+  ../../constantine/math/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_jacobian, ec_scalar_mul],
   # Test utilities
   ../../helpers/prng_unsafe,
   ./support/ec_reference_scalar_mult,
diff --git a/tests/backend/t_ec_shortw_jac_g1_mul_vs_ref.nim b/tests/math/t_ec_shortw_jac_g1_mul_vs_ref.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_jac_g1_mul_vs_ref.nim
rename to tests/math/t_ec_shortw_jac_g1_mul_vs_ref.nim
index cf4a8d6..1a39096 100644
--- a/tests/backend/t_ec_shortw_jac_g1_mul_vs_ref.nim
+++ b/tests/math/t_ec_shortw_jac_g1_mul_vs_ref.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_add_double_bls12_377.nim b/tests/math/t_ec_shortw_jac_g2_add_double_bls12_377.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_jac_g2_add_double_bls12_377.nim
rename to tests/math/t_ec_shortw_jac_g2_add_double_bls12_377.nim
index 13c431e..3c25bb4 100644
--- a/tests/backend/t_ec_shortw_jac_g2_add_double_bls12_377.nim
+++ b/tests/math/t_ec_shortw_jac_g2_add_double_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_add_double_bls12_381.nim b/tests/math/t_ec_shortw_jac_g2_add_double_bls12_381.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_jac_g2_add_double_bls12_381.nim
rename to tests/math/t_ec_shortw_jac_g2_add_double_bls12_381.nim
index 00f79ac..fe6c0c8 100644
--- a/tests/backend/t_ec_shortw_jac_g2_add_double_bls12_381.nim
+++ b/tests/math/t_ec_shortw_jac_g2_add_double_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim b/tests/math/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim
rename to tests/math/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim
index 1960486..e7bef55 100644
--- a/tests/backend/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_jac_g2_add_double_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_add_double_bw6_761.nim b/tests/math/t_ec_shortw_jac_g2_add_double_bw6_761.nim
similarity index 85%
rename from tests/backend/t_ec_shortw_jac_g2_add_double_bw6_761.nim
rename to tests/math/t_ec_shortw_jac_g2_add_double_bw6_761.nim
index 3e5a7ea..50c1b2b 100644
--- a/tests/backend/t_ec_shortw_jac_g2_add_double_bw6_761.nim
+++ b/tests/math/t_ec_shortw_jac_g2_add_double_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim b/tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim
rename to tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim
index c750bb5..16939c0 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim b/tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim
rename to tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim
index d4f5415..5d83867 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mixed_add_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim b/tests/math/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim
rename to tests/math/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim
index 8b2efaf..19a5f5c 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mixed_add_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim b/tests/math/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim
similarity index 85%
rename from tests/backend/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim
rename to tests/math/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim
index 7b4cc49..37e5a32 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mixed_add_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim b/tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim
index 7904d9e..f14ac8c 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim b/tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim
index 2ec7dc3..e00fc76 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_distri_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim b/tests/math/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim
index fd7194f..a655cbd 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_distri_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim b/tests/math/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim
similarity index 86%
rename from tests/backend/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim
index f7ba124..d5c44fe 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_distri_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim
similarity index 92%
rename from tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim
index 0a9c50b..f66d60b 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim
similarity index 92%
rename from tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim
index b4433f0..2a124b2 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim
similarity index 92%
rename from tests/backend/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim
index 2079411..0e9289c 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim
similarity index 86%
rename from tests/backend/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim
index e082582..e8bced9 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_sanity_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim
index 1a1e1e8..3079d26 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim
index 9a3e944..7ae2b5f 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim
index b5364c4..5bebf66 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim
similarity index 86%
rename from tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim
rename to tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim
index a089384..c18e582 100644
--- a/tests/backend/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim
+++ b/tests/math/t_ec_shortw_jac_g2_mul_vs_ref_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_jacobian,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_jacobian,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_edge_cases.nim b/tests/math/t_ec_shortw_prj_edge_cases.nim
similarity index 95%
rename from tests/backend/t_ec_shortw_prj_edge_cases.nim
rename to tests/math/t_ec_shortw_prj_edge_cases.nim
index 50452bf..7cfedf8 100644
--- a/tests/backend/t_ec_shortw_prj_edge_cases.nim
+++ b/tests/math/t_ec_shortw_prj_edge_cases.nim
@@ -16,11 +16,12 @@ import
   # Standard library
   std/[unittest, times],
   # Internals
-  ../../constantine/backend/config/[common, curves],
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/towers,
-  ../../constantine/backend/io/[io_bigints, io_fields, io_towers, io_ec],
-  ../../constantine/backend/elliptic/[ec_shortweierstrass_projective, ec_scalar_mul],
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/io/[io_bigints, io_fields, io_extfields, io_ec],
+  ../../constantine/math/elliptic/[ec_shortweierstrass_projective, ec_scalar_mul],
   # Test utilities
   ../../helpers/prng_unsafe,
   ./support/ec_reference_scalar_mult
diff --git a/tests/backend/t_ec_shortw_prj_g1_add_double.nim b/tests/math/t_ec_shortw_prj_g1_add_double.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_prj_g1_add_double.nim
rename to tests/math/t_ec_shortw_prj_g1_add_double.nim
index 0e3960a..7a91251 100644
--- a/tests/backend/t_ec_shortw_prj_g1_add_double.nim
+++ b/tests/math/t_ec_shortw_prj_g1_add_double.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g1_mixed_add.nim b/tests/math/t_ec_shortw_prj_g1_mixed_add.nim
similarity index 89%
rename from tests/backend/t_ec_shortw_prj_g1_mixed_add.nim
rename to tests/math/t_ec_shortw_prj_g1_mixed_add.nim
index 76d1a12..e948c1c 100644
--- a/tests/backend/t_ec_shortw_prj_g1_mixed_add.nim
+++ b/tests/math/t_ec_shortw_prj_g1_mixed_add.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/arithmetic,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/arithmetic,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g1_mul_distri.nim b/tests/math/t_ec_shortw_prj_g1_mul_distri.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_prj_g1_mul_distri.nim
rename to tests/math/t_ec_shortw_prj_g1_mul_distri.nim
index 043c827..1add539 100644
--- a/tests/backend/t_ec_shortw_prj_g1_mul_distri.nim
+++ b/tests/math/t_ec_shortw_prj_g1_mul_distri.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g1_mul_sanity.nim b/tests/math/t_ec_shortw_prj_g1_mul_sanity.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_prj_g1_mul_sanity.nim
rename to tests/math/t_ec_shortw_prj_g1_mul_sanity.nim
index c9ec332..621fcff 100644
--- a/tests/backend/t_ec_shortw_prj_g1_mul_sanity.nim
+++ b/tests/math/t_ec_shortw_prj_g1_mul_sanity.nim
@@ -10,10 +10,10 @@ import
   # Standard library
   std/[unittest, times],
   # Internals
-  ../../constantine/backend/config/[common, curves],
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/io/[io_bigints, io_fields, io_ec],
-  ../../constantine/backend/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective, ec_scalar_mul],
+  ../../constantine/math/config/[common, curves],
+  ../../constantine/math/[arithmetic, primitives],
+  ../../constantine/math/io/[io_bigints, io_fields, io_ec],
+  ../../constantine/math/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective, ec_scalar_mul],
   # Test utilities
   ../../helpers/prng_unsafe,
   ./support/ec_reference_scalar_mult,
diff --git a/tests/backend/t_ec_shortw_prj_g1_mul_vs_ref.nim b/tests/math/t_ec_shortw_prj_g1_mul_vs_ref.nim
similarity index 91%
rename from tests/backend/t_ec_shortw_prj_g1_mul_vs_ref.nim
rename to tests/math/t_ec_shortw_prj_g1_mul_vs_ref.nim
index 3199eaf..85caf97 100644
--- a/tests/backend/t_ec_shortw_prj_g1_mul_vs_ref.nim
+++ b/tests/math/t_ec_shortw_prj_g1_mul_vs_ref.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_add_double_bls12_377.nim b/tests/math/t_ec_shortw_prj_g2_add_double_bls12_377.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_add_double_bls12_377.nim
rename to tests/math/t_ec_shortw_prj_g2_add_double_bls12_377.nim
index c95d73d..7f8b682 100644
--- a/tests/backend/t_ec_shortw_prj_g2_add_double_bls12_377.nim
+++ b/tests/math/t_ec_shortw_prj_g2_add_double_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_add_double_bls12_381.nim b/tests/math/t_ec_shortw_prj_g2_add_double_bls12_381.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_add_double_bls12_381.nim
rename to tests/math/t_ec_shortw_prj_g2_add_double_bls12_381.nim
index 78e84fb..7c614d4 100644
--- a/tests/backend/t_ec_shortw_prj_g2_add_double_bls12_381.nim
+++ b/tests/math/t_ec_shortw_prj_g2_add_double_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim b/tests/math/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim
rename to tests/math/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim
index 0523d1b..e0954b2 100644
--- a/tests/backend/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_prj_g2_add_double_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_add_double_bw6_761.nim b/tests/math/t_ec_shortw_prj_g2_add_double_bw6_761.nim
similarity index 85%
rename from tests/backend/t_ec_shortw_prj_g2_add_double_bw6_761.nim
rename to tests/math/t_ec_shortw_prj_g2_add_double_bw6_761.nim
index 0504872..190b569 100644
--- a/tests/backend/t_ec_shortw_prj_g2_add_double_bw6_761.nim
+++ b/tests/math/t_ec_shortw_prj_g2_add_double_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim b/tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim
rename to tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim
index 7d9c3de..5e8e1d2 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim b/tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim
rename to tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim
index b60b03d..119115d 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mixed_add_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim b/tests/math/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim
rename to tests/math/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim
index 82a6f1a..d135037 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mixed_add_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim b/tests/math/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim
similarity index 85%
rename from tests/backend/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim
rename to tests/math/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim
index d3f236a..d8f6b9c 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mixed_add_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim b/tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim
index 314da9b..b8d45a7 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim b/tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim
index 89748b9..9254fe5 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_distri_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim b/tests/math/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim
similarity index 84%
rename from tests/backend/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim
index 1dc6164..8926789 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_distri_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim b/tests/math/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim
similarity index 86%
rename from tests/backend/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim
index 1c2afe7..336c65b 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_distri_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim
similarity index 92%
rename from tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim
index 39a2147..2bed3d0 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim
similarity index 92%
rename from tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim
index d1d1a8e..3af1726 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim
similarity index 92%
rename from tests/backend/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim
index a23cf85..f5d00dd 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim
similarity index 86%
rename from tests/backend/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim
index 91b0bb0..50630e7 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_sanity_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim
index d1258af..42eb130 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim
index 105d396..200a939 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim
similarity index 83%
rename from tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim
index 312bdc1..bfc4221 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim
similarity index 86%
rename from tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim
rename to tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim
index 8111d35..c48f683 100644
--- a/tests/backend/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim
+++ b/tests/math/t_ec_shortw_prj_g2_mul_vs_ref_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_subgroups_bls12_377.nim b/tests/math/t_ec_subgroups_bls12_377.nim
similarity index 85%
rename from tests/backend/t_ec_subgroups_bls12_377.nim
rename to tests/math/t_ec_subgroups_bls12_377.nim
index 6599a35..72d9ca7 100644
--- a/tests/backend/t_ec_subgroups_bls12_377.nim
+++ b/tests/math/t_ec_subgroups_bls12_377.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_subgroups_bls12_381.nim b/tests/math/t_ec_subgroups_bls12_381.nim
similarity index 85%
rename from tests/backend/t_ec_subgroups_bls12_381.nim
rename to tests/math/t_ec_subgroups_bls12_381.nim
index 3da853b..34c51b9 100644
--- a/tests/backend/t_ec_subgroups_bls12_381.nim
+++ b/tests/math/t_ec_subgroups_bls12_381.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_subgroups_bn254_nogami.nim b/tests/math/t_ec_subgroups_bn254_nogami.nim
similarity index 85%
rename from tests/backend/t_ec_subgroups_bn254_nogami.nim
rename to tests/math/t_ec_subgroups_bn254_nogami.nim
index 951ee00..ac4291f 100644
--- a/tests/backend/t_ec_subgroups_bn254_nogami.nim
+++ b/tests/math/t_ec_subgroups_bn254_nogami.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_subgroups_bn254_snarks.nim b/tests/math/t_ec_subgroups_bn254_snarks.nim
similarity index 85%
rename from tests/backend/t_ec_subgroups_bn254_snarks.nim
rename to tests/math/t_ec_subgroups_bn254_snarks.nim
index 564f5b8..aa3c33b 100644
--- a/tests/backend/t_ec_subgroups_bn254_snarks.nim
+++ b/tests/math/t_ec_subgroups_bn254_snarks.nim
@@ -8,9 +8,9 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_shortweierstrass_projective,
-  ../../constantine/backend/towers,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/ec_shortweierstrass_projective,
+  ../../constantine/math/extension_fields,
   # Test utilities
   ./t_ec_template
 
diff --git a/tests/backend/t_ec_template.nim b/tests/math/t_ec_template.nim
similarity index 98%
rename from tests/backend/t_ec_template.nim
rename to tests/math/t_ec_template.nim
index e3d4755..6b59c62 100644
--- a/tests/backend/t_ec_template.nim
+++ b/tests/math/t_ec_template.nim
@@ -16,22 +16,25 @@ import
   # Standard library
   std/[unittest, times],
   # Internals
-  ../../constantine/backend/config/[common, curves],
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/towers,
-  ../../constantine/backend/elliptic/[
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_jacobian,
     ec_shortweierstrass_projective,
     ec_twistededwards_affine,
     ec_twistededwards_projective,
     ec_scalar_mul],
-  ../../constantine/backend/io/[io_bigints, io_fields, io_ec],
-  ../../constantine/backend/curves/zoo_subgroups,
+  ../../constantine/math/io/[io_bigints, io_fields, io_ec],
+  ../../constantine/math/curves/zoo_subgroups,
   # Test utilities
   ../../helpers/prng_unsafe,
   ./support/ec_reference_scalar_mult
 
+export unittest # Generic sandwich
+
 type
   RandomGen* = enum
     Uniform
diff --git a/tests/backend/t_ec_twedwards_prj_add_double.nim b/tests/math/t_ec_twedwards_prj_add_double.nim
similarity index 84%
rename from tests/backend/t_ec_twedwards_prj_add_double.nim
rename to tests/math/t_ec_twedwards_prj_add_double.nim
index e9ed936..4da74e1 100644
--- a/tests/backend/t_ec_twedwards_prj_add_double.nim
+++ b/tests/math/t_ec_twedwards_prj_add_double.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_twistededwards_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_twistededwards_projective,
   # Test utilities
   ./t_ec_template
 
@@ -17,9 +17,9 @@ const
   Iters = 8
 
 run_EC_addition_tests(
-    ec = ECP_TwEdwards_Prj[Fp[Curve25519]],
+    ec = ECP_TwEdwards_Prj[Fp[Edwards25519]],
     Iters = Iters,
-    moduleName = "test_ec_twistededwards_projective_add_double_" & $Curve25519
+    moduleName = "test_ec_twistededwards_projective_add_double_" & $Edwards25519
   )
 
 run_EC_addition_tests(
diff --git a/tests/backend/t_ec_twedwards_prj_mul_distri.nim b/tests/math/t_ec_twedwards_prj_mul_distri.nim
similarity index 85%
rename from tests/backend/t_ec_twedwards_prj_mul_distri.nim
rename to tests/math/t_ec_twedwards_prj_mul_distri.nim
index 4845145..92161c2 100644
--- a/tests/backend/t_ec_twedwards_prj_mul_distri.nim
+++ b/tests/math/t_ec_twedwards_prj_mul_distri.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_twistededwards_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_twistededwards_projective,
   # Test utilities
   ./t_ec_template
 
@@ -18,9 +18,9 @@ const
   ItersMul = Iters div 4
 
 run_EC_mul_distributive_tests(
-    ec = ECP_TwEdwards_Prj[Fp[Curve25519]],
+    ec = ECP_TwEdwards_Prj[Fp[Edwards25519]],
     ItersMul = ItersMul,
-    moduleName = "test_ec_twistededwards_projective_mul_distributive_" & $Curve25519
+    moduleName = "test_ec_twistededwards_projective_mul_distributive_" & $Edwards25519
   )
 
 run_EC_mul_distributive_tests(
diff --git a/tests/backend/t_ec_twedwards_prj_mul_sanity.nim b/tests/math/t_ec_twedwards_prj_mul_sanity.nim
similarity index 85%
rename from tests/backend/t_ec_twedwards_prj_mul_sanity.nim
rename to tests/math/t_ec_twedwards_prj_mul_sanity.nim
index 2f742ab..be52778 100644
--- a/tests/backend/t_ec_twedwards_prj_mul_sanity.nim
+++ b/tests/math/t_ec_twedwards_prj_mul_sanity.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_twistededwards_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_twistededwards_projective,
   # Test utilities
   ./t_ec_template
   
@@ -18,9 +18,9 @@ const
   ItersMul = Iters div 4
 
 run_EC_mul_sanity_tests(
-    ec = ECP_TwEdwards_Prj[Fp[Curve25519]],
+    ec = ECP_TwEdwards_Prj[Fp[Edwards25519]],
     ItersMul = ItersMul,
-    moduleName = "test_ec_twistededwards_projective_mul_sanity_" & $Curve25519
+    moduleName = "test_ec_twistededwards_projective_mul_sanity_" & $Edwards25519
   )
 
 run_EC_mul_sanity_tests(
diff --git a/tests/backend/t_ec_twedwards_prj_mul_vs_ref.nim b/tests/math/t_ec_twedwards_prj_mul_vs_ref.nim
similarity index 85%
rename from tests/backend/t_ec_twedwards_prj_mul_vs_ref.nim
rename to tests/math/t_ec_twedwards_prj_mul_vs_ref.nim
index 5260963..b8c50c4 100644
--- a/tests/backend/t_ec_twedwards_prj_mul_vs_ref.nim
+++ b/tests/math/t_ec_twedwards_prj_mul_vs_ref.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/config/[type_ff, curves],
-  ../../constantine/backend/elliptic/ec_twistededwards_projective,
+  ../../constantine/math/config/[type_ff, curves],
+  ../../constantine/math/elliptic/ec_twistededwards_projective,
   # Test utilities
   ./t_ec_template
 
@@ -18,9 +18,9 @@ const
   ItersMul = Iters div 4
 
 run_EC_mul_vs_ref_impl(
-    ec = ECP_TwEdwards_Prj[Fp[Curve25519]],
+    ec = ECP_TwEdwards_Prj[Fp[Edwards25519]],
     ItersMul = ItersMul,
-    moduleName = "test_ec_twistededwards_projective_mul_vs_ref_" & $Curve25519
+    moduleName = "test_ec_twistededwards_projective_mul_vs_ref_" & $Edwards25519
   )
 
 run_EC_mul_vs_ref_impl(
diff --git a/tests/backend/t_finite_fields.nim b/tests/math/t_finite_fields.nim
similarity index 95%
rename from tests/backend/t_finite_fields.nim
rename to tests/math/t_finite_fields.nim
index 6dbe88f..5e64e36 100644
--- a/tests/backend/t_finite_fields.nim
+++ b/tests/math/t_finite_fields.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import  std/unittest,
-        ../../constantine/backend/arithmetic,
-        ../../constantine/backend/arithmetic/limbs_montgomery,
-        ../../constantine/backend/io/[io_bigints, io_fields],
-        ../../constantine/backend/config/curves
+        ../../constantine/math/arithmetic,
+        ../../constantine/math/arithmetic/limbs_montgomery,
+        ../../constantine/math/io/[io_bigints, io_fields],
+        ../../constantine/math/config/curves
 
 static: doAssert defined(testingCurves), "This modules requires the -d:testingCurves compile option"
 
@@ -345,8 +345,8 @@ proc largeField() =
 
     test "fromMont doesn't need a final substraction with 255-bit prime (1 spare bit)":
       block:
-        var a: Fp[Curve25519]
-        a.mres = Fp[Curve25519].getMontyPrimeMinus1()
+        var a: Fp[Edwards25519]
+        a.mres = Fp[Edwards25519].getMontyPrimeMinus1()
         let expected = BigInt[255].fromHex"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec"
 
         var r: BigInt[255]
@@ -354,8 +354,8 @@ proc largeField() =
 
         check: bool(r == expected)
       block:
-        var a: Fp[Curve25519]
-        var d: FpDbl[Curve25519]
+        var a: Fp[Edwards25519]
+        var d: FpDbl[Edwards25519]
 
         # Set Montgomery repr to the largest field element in Montgomery Residue form
         a.mres    = BigInt[255].fromHex"0x7fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffec"
@@ -364,7 +364,7 @@ proc largeField() =
         var r, expected: BigInt[255]
 
         r.fromField(a)
-        expected.limbs.redc2xMont(d.limbs2x, Curve25519.Mod().limbs, Fp[Curve25519].getNegInvModWord(), Fp[Curve25519].getSpareBits())
+        expected.limbs.redc2xMont(d.limbs2x, Edwards25519.Mod().limbs, Fp[Edwards25519].getNegInvModWord(), Fp[Edwards25519].getSpareBits())
  
         check: bool(r == expected)
 
diff --git a/tests/backend/t_finite_fields.nim.cfg b/tests/math/t_finite_fields.nim.cfg
similarity index 100%
rename from tests/backend/t_finite_fields.nim.cfg
rename to tests/math/t_finite_fields.nim.cfg
diff --git a/tests/backend/t_finite_fields_conditional_arithmetic.nim b/tests/math/t_finite_fields_conditional_arithmetic.nim
similarity index 87%
rename from tests/backend/t_finite_fields_conditional_arithmetic.nim
rename to tests/math/t_finite_fields_conditional_arithmetic.nim
index 0534cb6..9f4b553 100644
--- a/tests/backend/t_finite_fields_conditional_arithmetic.nim
+++ b/tests/math/t_finite_fields_conditional_arithmetic.nim
@@ -7,9 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import  std/unittest,
-        ../../constantine/backend/arithmetic,
-        ../../constantine/backend/io/io_fields,
-        ../../constantine/backend/config/[common, curves]
+        ../../constantine/platforms/abstractions,
+        ../../constantine/math/arithmetic,
+        ../../constantine/math/io/io_fields,
+        ../../constantine/math/config/curves
 
 echo "\n------------------------------------------------------\n"
 
diff --git a/tests/backend/t_finite_fields_double_precision.nim b/tests/math/t_finite_fields_double_precision.nim
similarity index 92%
rename from tests/backend/t_finite_fields_double_precision.nim
rename to tests/math/t_finite_fields_double_precision.nim
index 89df19c..4515663 100644
--- a/tests/backend/t_finite_fields_double_precision.nim
+++ b/tests/math/t_finite_fields_double_precision.nim
@@ -10,9 +10,10 @@ import
   # Standard library
   std/[unittest, times],
   # Internal
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/io/[io_bigints, io_fields],
-  ../../constantine/backend/config/[curves, common, type_bigint],
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/[io_bigints, io_fields],
+  ../../constantine/math/config/[curves, type_bigint],
   # Test utilities
   ../../helpers/prng_unsafe
 
@@ -157,13 +158,13 @@ suite "Field Addition/Substraction/Negation via double-precision field elements"
     for _ in 0 ..< Iters:
       addsubneg_random_long01Seq(BLS12_381)
 
-  test "With Curve25519 field modulus":
+  test "With Edwards25519 field modulus":
     for _ in 0 ..< Iters:
-      addsubneg_random_unsafe(Curve25519)
+      addsubneg_random_unsafe(Edwards25519)
     for _ in 0 ..< Iters:
-      addsubneg_randomHighHammingWeight(Curve25519)
+      addsubneg_randomHighHammingWeight(Edwards25519)
     for _ in 0 ..< Iters:
-      addsubneg_random_long01Seq(Curve25519)
+      addsubneg_random_long01Seq(Edwards25519)
 
   test "With Bandersnatch field modulus":
     for _ in 0 ..< Iters:
@@ -213,13 +214,13 @@ suite "Field Multiplication via double-precision field elements is consistent wi
     for _ in 0 ..< Iters:
       mul_random_long01Seq(BLS12_381)
 
-  test "With Curve25519 field modulus":
+  test "With Edwards25519 field modulus":
     for _ in 0 ..< Iters:
-      mul_random_unsafe(Curve25519)
+      mul_random_unsafe(Edwards25519)
     for _ in 0 ..< Iters:
-      mul_randomHighHammingWeight(Curve25519)
+      mul_randomHighHammingWeight(Edwards25519)
     for _ in 0 ..< Iters:
-      mul_random_long01Seq(Curve25519)
+      mul_random_long01Seq(Edwards25519)
 
   test "With Bandersnatch field modulus":
     for _ in 0 ..< Iters:
@@ -262,13 +263,13 @@ suite "Field Squaring via double-precision field elements is consistent with sin
     for _ in 0 ..< Iters:
       sqr_random_long01Seq(BLS12_381)
 
-  test "With Curve25519 field modulus":
+  test "With Edwards25519 field modulus":
     for _ in 0 ..< Iters:
-      sqr_random_unsafe(Curve25519)
+      sqr_random_unsafe(Edwards25519)
     for _ in 0 ..< Iters:
-      sqr_randomHighHammingWeight(Curve25519)
+      sqr_randomHighHammingWeight(Edwards25519)
     for _ in 0 ..< Iters:
-      sqr_random_long01Seq(Curve25519)
+      sqr_random_long01Seq(Edwards25519)
 
   test "With Bandersnatch field modulus":
     for _ in 0 ..< Iters:
diff --git a/tests/backend/t_finite_fields_double_precision.nim.cfg b/tests/math/t_finite_fields_double_precision.nim.cfg
similarity index 100%
rename from tests/backend/t_finite_fields_double_precision.nim.cfg
rename to tests/math/t_finite_fields_double_precision.nim.cfg
diff --git a/tests/backend/t_finite_fields_mulsquare.nim b/tests/math/t_finite_fields_mulsquare.nim
similarity index 94%
rename from tests/backend/t_finite_fields_mulsquare.nim
rename to tests/math/t_finite_fields_mulsquare.nim
index 0dedafb..f8d958c 100644
--- a/tests/backend/t_finite_fields_mulsquare.nim
+++ b/tests/math/t_finite_fields_mulsquare.nim
@@ -10,9 +10,10 @@ import
   # Standard library
   std/[unittest, times],
   # Internal
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/io/[io_bigints, io_fields],
-  ../../constantine/backend/config/[curves, common, type_bigint],
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/[io_bigints, io_fields],
+  ../../constantine/math/config/[curves, type_bigint],
   # Test utilities
   ../../helpers/prng_unsafe
 
@@ -85,7 +86,7 @@ proc mainSanity() =
     sanity P256
     sanity Secp256k1
     sanity BLS12_381
-    sanity Curve25519
+    sanity Edwards25519
     sanity Bandersnatch
 
 mainSanity()
@@ -171,13 +172,13 @@ suite "Random Modular Squaring is consistent with Modular Multiplication" & " ["
     for _ in 0 ..< Iters:
       random_long01Seq(BLS12_381)
 
-  test "Random squaring mod Curve25519 [FastSquaring = " & $(Fp[Curve25519].getSpareBits() >= 2) & "]":
+  test "Random squaring mod Edwards25519 [FastSquaring = " & $(Fp[Edwards25519].getSpareBits() >= 2) & "]":
     for _ in 0 ..< Iters:
-      randomCurve(Curve25519)
+      randomCurve(Edwards25519)
     for _ in 0 ..< Iters:
-      randomHighHammingWeight(Curve25519)
+      randomHighHammingWeight(Edwards25519)
     for _ in 0 ..< Iters:
-      random_long01Seq(Curve25519)
+      random_long01Seq(Edwards25519)
 
   test "Random squaring mod Bandersnatch [FastSquaring = " & $(Fp[Bandersnatch].getSpareBits() >= 2) & "]":
     for _ in 0 ..< Iters:
diff --git a/tests/backend/t_finite_fields_mulsquare.nim.cfg b/tests/math/t_finite_fields_mulsquare.nim.cfg
similarity index 100%
rename from tests/backend/t_finite_fields_mulsquare.nim.cfg
rename to tests/math/t_finite_fields_mulsquare.nim.cfg
diff --git a/tests/backend/t_finite_fields_powinv.nim b/tests/math/t_finite_fields_powinv.nim
similarity index 97%
rename from tests/backend/t_finite_fields_powinv.nim
rename to tests/math/t_finite_fields_powinv.nim
index 20ad12d..096c706 100644
--- a/tests/backend/t_finite_fields_powinv.nim
+++ b/tests/math/t_finite_fields_powinv.nim
@@ -10,10 +10,10 @@ import
   # Standard library
   std/[unittest, times],
   # Internal
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/io/[io_bigints, io_fields],
-  ../../constantine/backend/config/curves,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/[io_bigints, io_fields],
+  ../../constantine/math/config/curves,
   # Test utilities
   ../../helpers/prng_unsafe
 
@@ -193,7 +193,7 @@ proc main() =
     testRandomDiv2 P224
     testRandomDiv2 BN254_Nogami
     testRandomDiv2 BN254_Snarks
-    testRandomDiv2 Curve25519
+    testRandomDiv2 Edwards25519
     testRandomDiv2 P256
     testRandomDiv2 Secp256k1
     testRandomDiv2 BLS12_377
@@ -281,7 +281,7 @@ proc main() =
     testRandomInv P224
     testRandomInv BN254_Nogami
     testRandomInv BN254_Snarks
-    testRandomInv Curve25519
+    testRandomInv Edwards25519
     testRandomInv P256
     testRandomInv Secp256k1
     testRandomInv BLS12_377
diff --git a/tests/backend/t_finite_fields_powinv.nim.cfg b/tests/math/t_finite_fields_powinv.nim.cfg
similarity index 100%
rename from tests/backend/t_finite_fields_powinv.nim.cfg
rename to tests/math/t_finite_fields_powinv.nim.cfg
diff --git a/tests/backend/t_finite_fields_sqrt.nim b/tests/math/t_finite_fields_sqrt.nim
similarity index 96%
rename from tests/backend/t_finite_fields_sqrt.nim
rename to tests/math/t_finite_fields_sqrt.nim
index 21a2dc7..ab22451 100644
--- a/tests/backend/t_finite_fields_sqrt.nim
+++ b/tests/math/t_finite_fields_sqrt.nim
@@ -10,9 +10,10 @@ import
   # Standard library
   std/[tables, unittest, times],
   # Internal
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/io/[io_fields],
-  ../../constantine/backend/config/[curves, common],
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/io_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ../../helpers/prng_unsafe
 
@@ -154,12 +155,12 @@ proc main() =
     randomSqrtCheck BLS12_377 # p ≢ 3 (mod 4)
     randomSqrtCheck BLS12_381
     randomSqrtCheck BW6_761
-    randomSqrtCheck Curve25519
+    randomSqrtCheck Edwards25519
     randomSqrtCheck Jubjub
     randomSqrtCheck Bandersnatch
   
   suite "Modular sqrt(u/v)" & " [" & $WordBitwidth & "-bit mode]":
-    randomSqrtRatioCheck Curve25519
+    randomSqrtRatioCheck Edwards25519
     randomSqrtRatioCheck Jubjub
     randomSqrtRatioCheck Bandersnatch
 
diff --git a/tests/backend/t_finite_fields_sqrt.nim.cfg b/tests/math/t_finite_fields_sqrt.nim.cfg
similarity index 100%
rename from tests/backend/t_finite_fields_sqrt.nim.cfg
rename to tests/math/t_finite_fields_sqrt.nim.cfg
diff --git a/tests/backend/t_finite_fields_vs_gmp.nim b/tests/math/t_finite_fields_vs_gmp.nim
similarity index 97%
rename from tests/backend/t_finite_fields_vs_gmp.nim
rename to tests/math/t_finite_fields_vs_gmp.nim
index fd1f475..522f0e1 100644
--- a/tests/backend/t_finite_fields_vs_gmp.nim
+++ b/tests/math/t_finite_fields_vs_gmp.nim
@@ -12,10 +12,10 @@ import
   # Third-party
   gmp, stew/byteutils,
   # Internal
-  ../../constantine/backend/io/[io_bigints, io_fields],
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/primitives,
-  ../../constantine/backend/config/curves
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/io/[io_bigints, io_fields],
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/config/curves
 
 echo "\n------------------------------------------------------\n"
 
@@ -24,7 +24,7 @@ var RNG {.compileTime.} = initRand(1234)
 const AvailableCurves = [
   P224,
   BN254_Nogami, BN254_Snarks,
-  P256, Secp256k1, Curve25519, Bandersnatch,
+  P256, Secp256k1, Edwards25519, Bandersnatch,
   BLS12_377, BLS12_381, BW6_761
 ]
 
diff --git a/tests/backend/t_fp12_anti_regression.nim b/tests/math/t_fp12_anti_regression.nim
similarity index 97%
rename from tests/backend/t_fp12_anti_regression.nim
rename to tests/math/t_fp12_anti_regression.nim
index 3879783..43cf722 100644
--- a/tests/backend/t_fp12_anti_regression.nim
+++ b/tests/math/t_fp12_anti_regression.nim
@@ -10,11 +10,11 @@ import
   # stdlib
   std/unittest,
   # Internals
-  ../../constantine/backend/config/[common, type_ff],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/io/io_towers,
-  ../../constantine/backend/towers
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/io/io_extfields,
+  ../../constantine/math/extension_fields
 
 # ###############################################################
 #
diff --git a/tests/backend/t_fp12_bls12_377.nim b/tests/math/t_fp12_bls12_377.nim
similarity index 90%
rename from tests/backend/t_fp12_bls12_377.nim
rename to tests/math/t_fp12_bls12_377.nim
index 8fba73c..31cca84 100644
--- a/tests/backend/t_fp12_bls12_377.nim
+++ b/tests/math/t_fp12_bls12_377.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp12_bls12_381.nim b/tests/math/t_fp12_bls12_381.nim
similarity index 90%
rename from tests/backend/t_fp12_bls12_381.nim
rename to tests/math/t_fp12_bls12_381.nim
index dbca253..d015b56 100644
--- a/tests/backend/t_fp12_bls12_381.nim
+++ b/tests/math/t_fp12_bls12_381.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp12_bn254_snarks.nim b/tests/math/t_fp12_bn254_snarks.nim
similarity index 90%
rename from tests/backend/t_fp12_bn254_snarks.nim
rename to tests/math/t_fp12_bn254_snarks.nim
index e9b441d..9ee54ff 100644
--- a/tests/backend/t_fp12_bn254_snarks.nim
+++ b/tests/math/t_fp12_bn254_snarks.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp12_exponentiation.nim b/tests/math/t_fp12_exponentiation.nim
similarity index 96%
rename from tests/backend/t_fp12_exponentiation.nim
rename to tests/math/t_fp12_exponentiation.nim
index 34d7299..1152d1e 100644
--- a/tests/backend/t_fp12_exponentiation.nim
+++ b/tests/math/t_fp12_exponentiation.nim
@@ -10,11 +10,11 @@ import
   # Standard library
   std/[tables, unittest, times],
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/io/io_towers,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/io/io_extfields,
   # Test utilities
   ../../helpers/[prng_unsafe, static_for]
 
diff --git a/tests/backend/t_fp12_frobenius.nim b/tests/math/t_fp12_frobenius.nim
similarity index 89%
rename from tests/backend/t_fp12_frobenius.nim
rename to tests/math/t_fp12_frobenius.nim
index 7ab4360..3e994e3 100644
--- a/tests/backend/t_fp12_frobenius.nim
+++ b/tests/math/t_fp12_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_frobenius_template
 
@@ -22,7 +22,7 @@ const TestCurves = [
 
 runFrobeniusTowerTests(
   ExtDegree = 12,
-  Iters = 8,
+  Iters = 2,
   TestCurves = TestCurves,
   moduleName = "test_fp12_frobenius",
   testSuiteDesc = "𝔽p12 Frobenius map: Frobenius(a, k) = a^(pᵏ) (mod p^12)"
diff --git a/tests/backend/t_fp2.nim b/tests/math/t_fp2.nim
similarity index 92%
rename from tests/backend/t_fp2.nim
rename to tests/math/t_fp2.nim
index d966177..3fe42d6 100644
--- a/tests/backend/t_fp2.nim
+++ b/tests/math/t_fp2.nim
@@ -8,8 +8,7 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp2_frobenius.nim b/tests/math/t_fp2_frobenius.nim
similarity index 89%
rename from tests/backend/t_fp2_frobenius.nim
rename to tests/math/t_fp2_frobenius.nim
index 23ee39c..f7383c3 100644
--- a/tests/backend/t_fp2_frobenius.nim
+++ b/tests/math/t_fp2_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_frobenius_template
 
@@ -23,7 +23,7 @@ const TestCurves = [
 
 runFrobeniusTowerTests(
   ExtDegree = 2,
-  Iters = 8,
+  Iters = 2,
   TestCurves = TestCurves,
   moduleName = "test_fp2_frobenius",
   testSuiteDesc = "𝔽p2 Frobenius map: Frobenius(a, k) = a^(pᵏ) (mod p²)"
diff --git a/tests/backend/t_fp2_sqrt.nim b/tests/math/t_fp2_sqrt.nim
similarity index 94%
rename from tests/backend/t_fp2_sqrt.nim
rename to tests/math/t_fp2_sqrt.nim
index 8dca496..3ff3acb 100644
--- a/tests/backend/t_fp2_sqrt.nim
+++ b/tests/math/t_fp2_sqrt.nim
@@ -10,11 +10,11 @@ import
   # Standard library
   std/[tables, unittest, times],
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/io/io_towers,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/io/io_extfields,
   # Test utilities
   ../../helpers/[prng_unsafe, static_for]
 
diff --git a/tests/backend/t_fp4.nim b/tests/math/t_fp4.nim
similarity index 95%
rename from tests/backend/t_fp4.nim
rename to tests/math/t_fp4.nim
index d518274..ecfed51 100644
--- a/tests/backend/t_fp4.nim
+++ b/tests/math/t_fp4.nim
@@ -7,11 +7,9 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  std/unittest,
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/io/io_towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/io/io_extfields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp4_frobenius.nim b/tests/math/t_fp4_frobenius.nim
similarity index 89%
rename from tests/backend/t_fp4_frobenius.nim
rename to tests/math/t_fp4_frobenius.nim
index fef3980..b1d6f74 100644
--- a/tests/backend/t_fp4_frobenius.nim
+++ b/tests/math/t_fp4_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_frobenius_template
 
@@ -22,7 +22,7 @@ const TestCurves = [
 
 runFrobeniusTowerTests(
   ExtDegree = 4,
-  Iters = 8,
+  Iters = 2,
   TestCurves = TestCurves,
   moduleName = "test_fp4_frobenius",
   testSuiteDesc = "𝔽p4 Frobenius map: Frobenius(a, k) = a^(pᵏ) (mod p⁴)"
diff --git a/tests/backend/t_fp6_bls12_377.nim b/tests/math/t_fp6_bls12_377.nim
similarity index 90%
rename from tests/backend/t_fp6_bls12_377.nim
rename to tests/math/t_fp6_bls12_377.nim
index 50981f6..ae58683 100644
--- a/tests/backend/t_fp6_bls12_377.nim
+++ b/tests/math/t_fp6_bls12_377.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp6_bls12_381.nim b/tests/math/t_fp6_bls12_381.nim
similarity index 90%
rename from tests/backend/t_fp6_bls12_381.nim
rename to tests/math/t_fp6_bls12_381.nim
index 8c7b57d..d1e82fe 100644
--- a/tests/backend/t_fp6_bls12_381.nim
+++ b/tests/math/t_fp6_bls12_381.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp6_bn254_snarks.nim b/tests/math/t_fp6_bn254_snarks.nim
similarity index 90%
rename from tests/backend/t_fp6_bn254_snarks.nim
rename to tests/math/t_fp6_bn254_snarks.nim
index 642a68e..1344509 100644
--- a/tests/backend/t_fp6_bn254_snarks.nim
+++ b/tests/math/t_fp6_bn254_snarks.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp6_bw6_761.nim b/tests/math/t_fp6_bw6_761.nim
similarity index 90%
rename from tests/backend/t_fp6_bw6_761.nim
rename to tests/math/t_fp6_bw6_761.nim
index 0a4b0c5..c540ab6 100644
--- a/tests/backend/t_fp6_bw6_761.nim
+++ b/tests/math/t_fp6_bw6_761.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_template
 
diff --git a/tests/backend/t_fp6_frobenius.nim b/tests/math/t_fp6_frobenius.nim
similarity index 89%
rename from tests/backend/t_fp6_frobenius.nim
rename to tests/math/t_fp6_frobenius.nim
index 87a697f..21f09f2 100644
--- a/tests/backend/t_fp6_frobenius.nim
+++ b/tests/math/t_fp6_frobenius.nim
@@ -8,8 +8,8 @@
 
 import
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
   # Test utilities
   ./t_fp_tower_frobenius_template
 
@@ -23,7 +23,7 @@ const TestCurves = [
 
 runFrobeniusTowerTests(
   ExtDegree = 6,
-  Iters = 8,
+  Iters = 2,
   TestCurves = TestCurves,
   moduleName = "test_fp6_frobenius",
   testSuiteDesc = "𝔽p6 Frobenius map: Frobenius(a, k) = a^(pᵏ) (mod p⁶)"
diff --git a/tests/backend/t_fp_cubic_root.nim b/tests/math/t_fp_cubic_root.nim
similarity index 83%
rename from tests/backend/t_fp_cubic_root.nim
rename to tests/math/t_fp_cubic_root.nim
index 8e4f6cb..7d20e43 100644
--- a/tests/backend/t_fp_cubic_root.nim
+++ b/tests/math/t_fp_cubic_root.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import  std/unittest,
-        ../../constantine/backend/config/common,
-        ../../constantine/backend/arithmetic,
-        ../../constantine/backend/config/curves,
-        ../../constantine/backend/curves/zoo_endomorphisms
+        ../../constantine/platforms/abstractions,
+        ../../constantine/math/arithmetic,
+        ../../constantine/math/config/curves,
+        ../../constantine/math/curves/zoo_endomorphisms
 
 echo "\n------------------------------------------------------\n"
 
diff --git a/tests/backend/t_fp_tower_frobenius_template.nim b/tests/math/t_fp_tower_frobenius_template.nim
similarity index 94%
rename from tests/backend/t_fp_tower_frobenius_template.nim
rename to tests/math/t_fp_tower_frobenius_template.nim
index 0971c17..9447635 100644
--- a/tests/backend/t_fp_tower_frobenius_template.nim
+++ b/tests/math/t_fp_tower_frobenius_template.nim
@@ -17,13 +17,16 @@ import
   # Standard library
   std/[unittest, times],
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/[common, curves],
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/isogeny/frobenius,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/isogenies/frobenius,
   # Test utilities
   ../../helpers/[prng_unsafe, static_for]
 
+export unittest # Generic sandwich
+
 echo "\n------------------------------------------------------\n"
 
 template ExtField(degree: static int, curve: static Curve): untyped =
diff --git a/tests/backend/t_fp_tower_template.nim b/tests/math/t_fp_tower_template.nim
similarity index 98%
rename from tests/backend/t_fp_tower_template.nim
rename to tests/math/t_fp_tower_template.nim
index cd73757..1cf48c3 100644
--- a/tests/backend/t_fp_tower_template.nim
+++ b/tests/math/t_fp_tower_template.nim
@@ -17,13 +17,16 @@ import
   # Standard library
   std/[unittest, times],
   # Internals
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/[common, curves],
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/io/io_towers,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/io_extfields,
   # Test utilities
   ../../helpers/[prng_unsafe, static_for]
 
+export unittest # Generic sandwich
+
 echo "\n------------------------------------------------------\n"
 
 template ExtField(degree: static int, curve: static Curve): untyped =
diff --git a/tests/backend/t_fr.nim b/tests/math/t_fr.nim
similarity index 95%
rename from tests/backend/t_fr.nim
rename to tests/math/t_fr.nim
index 2b6a900..bc6b83b 100644
--- a/tests/backend/t_fr.nim
+++ b/tests/math/t_fr.nim
@@ -10,9 +10,10 @@ import
   # Standard library
   std/[unittest, times],
   # Internal
-  ../../constantine/backend/arithmetic,
-  ../../constantine/backend/io/[io_bigints, io_fields],
-  ../../constantine/backend/config/[curves, common, type_bigint],
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/io/[io_bigints, io_fields],
+  ../../constantine/math/config/curves,
   # Test utilities
   ../../helpers/prng_unsafe
 
diff --git a/tests/backend/t_hash_to_curve.nim b/tests/math/t_hash_to_curve.nim
similarity index 93%
rename from tests/backend/t_hash_to_curve.nim
rename to tests/math/t_hash_to_curve.nim
index 149d255..1313249 100644
--- a/tests/backend/t_hash_to_curve.nim
+++ b/tests/math/t_hash_to_curve.nim
@@ -10,15 +10,17 @@ import
   # Standard library
   std/[unittest, times, os, strutils, macros],
   # 3rd party
-  jsony,
+  pkg/jsony,
   # Internals
-  ../../constantine/backend/config/[common, curves, type_bigint, type_ff],
-  ../../constantine/backend/[towers, hashes],
-  ../../constantine/backend/io/[io_bigints, io_ec],
-  ../../constantine/backend/elliptic/[
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/io/[io_bigints, io_ec],
+  ../../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective],
-  ../../constantine/backend/hash_to_curve/hash_to_curve
+  ../../constantine/hash_to_curve/hash_to_curve,
+  ../../constantine/hashes
 
 # Serialization
 # --------------------------------------------------------------------------
diff --git a/tests/backend/t_hash_to_field.nim b/tests/math/t_hash_to_field.nim
similarity index 96%
rename from tests/backend/t_hash_to_field.nim
rename to tests/math/t_hash_to_field.nim
index 68a11f5..7ca7367 100644
--- a/tests/backend/t_hash_to_field.nim
+++ b/tests/math/t_hash_to_field.nim
@@ -7,12 +7,12 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/hashes,
-  ../../constantine/backend/hash_to_curve/h2c_hash_to_field,
-  ../../constantine/backend/config/[curves_declaration, type_ff],
-  ../../constantine/backend/tower_field_extensions/extension_fields,
+  ../../constantine/hashes,
+  ../../constantine/hash_to_curve/h2c_hash_to_field,
+  ../../constantine/math/config/[curves_declaration, type_ff],
+  ../../constantine/math/extension_fields/towers,
 
-  ../../constantine/backend/io/[io_fields, io_towers],
+  ../../constantine/math/io/[io_fields, io_extfields],
 
   # Third-party
   stew/byteutils
diff --git a/tests/backend/t_io_bigints.nim b/tests/math/t_io_bigints.nim
similarity index 97%
rename from tests/backend/t_io_bigints.nim
rename to tests/math/t_io_bigints.nim
index aa6b405..700ae42 100644
--- a/tests/backend/t_io_bigints.nim
+++ b/tests/math/t_io_bigints.nim
@@ -7,9 +7,9 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import  std/[unittest,times],
-        ../../constantine/backend/io/io_bigints,
-        ../../constantine/backend/config/common,
-        ../../constantine/backend/arithmetic,
+        ../../constantine/math/io/io_bigints,
+        ../../constantine/platforms/abstractions,
+        ../../constantine/math/arithmetic,
         ../../helpers/prng_unsafe
 
 # Random seed for reproducibility
diff --git a/tests/backend/t_io_fields.nim b/tests/math/t_io_fields.nim
similarity index 96%
rename from tests/backend/t_io_fields.nim
rename to tests/math/t_io_fields.nim
index 68cc5b3..39180a3 100644
--- a/tests/backend/t_io_fields.nim
+++ b/tests/math/t_io_fields.nim
@@ -7,10 +7,10 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import  std/[unittest, times],
-        ../../constantine/backend/io/[io_bigints, io_fields],
-        ../../constantine/backend/config/curves,
-        ../../constantine/backend/config/common,
-        ../../constantine/backend/arithmetic,
+        ../../constantine/math/io/[io_bigints, io_fields],
+        ../../constantine/math/config/curves,
+        ../../constantine/platforms/abstractions,
+        ../../constantine/math/arithmetic,
         ../../helpers/prng_unsafe
 
 # Random seed for reproducibility
diff --git a/tests/backend/t_io_fields.nim.cfg b/tests/math/t_io_fields.nim.cfg
similarity index 100%
rename from tests/backend/t_io_fields.nim.cfg
rename to tests/math/t_io_fields.nim.cfg
diff --git a/tests/backend/t_io_unsaturated.nim b/tests/math/t_io_unsaturated.nim
similarity index 86%
rename from tests/backend/t_io_unsaturated.nim
rename to tests/math/t_io_unsaturated.nim
index 520c012..a0d6f3f 100644
--- a/tests/backend/t_io_unsaturated.nim
+++ b/tests/math/t_io_unsaturated.nim
@@ -7,10 +7,11 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import  std/[unittest,times],
-        ../../constantine/backend/config/[common, curves],
-        ../../constantine/backend/arithmetic,
-        ../../constantine/backend/arithmetic/limbs_unsaturated,
-        ../../constantine/backend/io/io_bigints,
+        ../../constantine/platforms/abstractions,
+        ../../constantine/math/config/curves,
+        ../../constantine/math/arithmetic,
+        ../../constantine/math/arithmetic/limbs_unsaturated,
+        ../../constantine/math/io/io_bigints,
         ../../helpers/prng_unsafe
 
 # Random seed for reproducibility
@@ -64,13 +65,13 @@ proc main() =
         testRoundtrip(BN254_Snarks, HighHammingWeight)
       for _ in 0 ..< Iters:
         testRoundtrip(BN254_Snarks, Long01Sequence)
-    test "Curve25519":
+    test "Edwards25519":
       for _ in 0 ..< Iters:
-        testRoundtrip(Curve25519, Uniform)
+        testRoundtrip(Edwards25519, Uniform)
       for _ in 0 ..< Iters:
-        testRoundtrip(Curve25519, HighHammingWeight)
+        testRoundtrip(Edwards25519, HighHammingWeight)
       for _ in 0 ..< Iters:
-        testRoundtrip(Curve25519, Long01Sequence)
+        testRoundtrip(Edwards25519, Long01Sequence)
     test "secp256k1":
       for _ in 0 ..< Iters:
         testRoundtrip(Secp256k1, Uniform)
diff --git a/tests/backend/t_pairing_bls12_377_gt_subgroup.nim b/tests/math/t_pairing_bls12_377_gt_subgroup.nim
similarity index 81%
rename from tests/backend/t_pairing_bls12_377_gt_subgroup.nim
rename to tests/math/t_pairing_bls12_377_gt_subgroup.nim
index abc481b..3e456c9 100644
--- a/tests/backend/t_pairing_bls12_377_gt_subgroup.nim
+++ b/tests/math/t_pairing_bls12_377_gt_subgroup.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bls12,
+  ../../constantine/math/pairing/pairing_bls12,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bls12_377_line_functions.nim b/tests/math/t_pairing_bls12_377_line_functions.nim
similarity index 92%
rename from tests/backend/t_pairing_bls12_377_line_functions.nim
rename to tests/math/t_pairing_bls12_377_line_functions.nim
index 613d13b..0dd9131 100644
--- a/tests/backend/t_pairing_bls12_377_line_functions.nim
+++ b/tests/math/t_pairing_bls12_377_line_functions.nim
@@ -10,16 +10,16 @@ import
   # Standard library
   std/[tables, unittest, times],
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/io/io_towers,
-  ../../constantine/backend/elliptic/[
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/io/io_extfields,
+  ../../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
     ec_scalar_mul],
-  ../../constantine/backend/pairing/lines_eval,
+  ../../constantine/math/pairing/lines_eval,
   # Test utilities
   ../helpers/[prng_unsafe, static_for]
 
diff --git a/tests/backend/t_pairing_bls12_377_optate.nim b/tests/math/t_pairing_bls12_377_optate.nim
similarity index 83%
rename from tests/backend/t_pairing_bls12_377_optate.nim
rename to tests/math/t_pairing_bls12_377_optate.nim
index edc1b5a..fb9bb8a 100644
--- a/tests/backend/t_pairing_bls12_377_optate.nim
+++ b/tests/math/t_pairing_bls12_377_optate.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bls12,
+  ../../constantine/math/pairing/pairing_bls12,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bls12_381_gt_subgroup.nim b/tests/math/t_pairing_bls12_381_gt_subgroup.nim
similarity index 81%
rename from tests/backend/t_pairing_bls12_381_gt_subgroup.nim
rename to tests/math/t_pairing_bls12_381_gt_subgroup.nim
index bffae46..f1a39b8 100644
--- a/tests/backend/t_pairing_bls12_381_gt_subgroup.nim
+++ b/tests/math/t_pairing_bls12_381_gt_subgroup.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bls12,
+  ../../constantine/math/pairing/pairing_bls12,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bls12_381_line_functions.nim b/tests/math/t_pairing_bls12_381_line_functions.nim
similarity index 92%
rename from tests/backend/t_pairing_bls12_381_line_functions.nim
rename to tests/math/t_pairing_bls12_381_line_functions.nim
index 2e752e4..a5efa8e 100644
--- a/tests/backend/t_pairing_bls12_381_line_functions.nim
+++ b/tests/math/t_pairing_bls12_381_line_functions.nim
@@ -10,16 +10,16 @@ import
   # Standard library
   std/[tables, unittest, times],
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/io/io_towers,
-  ../../constantine/backend/elliptic/[
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/io/io_extfields,
+  ../../constantine/math/elliptic/[
     ec_shortweierstrass_affine,
     ec_shortweierstrass_projective,
     ec_scalar_mul],
-  ../../constantine/backend/pairing/lines_eval,
+  ../../constantine/math/pairing/lines_eval,
   # Test utilities
   ../helpers/[prng_unsafe, static_for]
 
diff --git a/tests/backend/t_pairing_bls12_381_multi.nim b/tests/math/t_pairing_bls12_381_multi.nim
similarity index 87%
rename from tests/backend/t_pairing_bls12_381_multi.nim
rename to tests/math/t_pairing_bls12_381_multi.nim
index b806d77..39868de 100644
--- a/tests/backend/t_pairing_bls12_381_multi.nim
+++ b/tests/math/t_pairing_bls12_381_multi.nim
@@ -10,14 +10,11 @@ import
   # Standard library
   std/[os, times, strformat],
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[
-    arithmetic, primitives,
-    towers, ec_shortweierstrass
-  ],
-  ../../constantine/backend/io/io_towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bls12,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/[arithmetic, extension_fields, ec_shortweierstrass],
+  ../../constantine/math/io/io_extfields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/pairing/pairing_bls12,
   # Test utilities
   ../../helpers/prng_unsafe
 
diff --git a/tests/backend/t_pairing_bls12_381_optate.nim b/tests/math/t_pairing_bls12_381_optate.nim
similarity index 83%
rename from tests/backend/t_pairing_bls12_381_optate.nim
rename to tests/math/t_pairing_bls12_381_optate.nim
index 0831b0f..4cf4d41 100644
--- a/tests/backend/t_pairing_bls12_381_optate.nim
+++ b/tests/math/t_pairing_bls12_381_optate.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bls12,
+  ../../constantine/math/pairing/pairing_bls12,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bn254_nogami_gt_subgroup.nim b/tests/math/t_pairing_bn254_nogami_gt_subgroup.nim
similarity index 82%
rename from tests/backend/t_pairing_bn254_nogami_gt_subgroup.nim
rename to tests/math/t_pairing_bn254_nogami_gt_subgroup.nim
index 58e90ed..641df01 100644
--- a/tests/backend/t_pairing_bn254_nogami_gt_subgroup.nim
+++ b/tests/math/t_pairing_bn254_nogami_gt_subgroup.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bn,
+  ../../constantine/math/pairing/pairing_bn,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bn254_nogami_optate.nim b/tests/math/t_pairing_bn254_nogami_optate.nim
similarity index 84%
rename from tests/backend/t_pairing_bn254_nogami_optate.nim
rename to tests/math/t_pairing_bn254_nogami_optate.nim
index 339b2e7..d89b750 100644
--- a/tests/backend/t_pairing_bn254_nogami_optate.nim
+++ b/tests/math/t_pairing_bn254_nogami_optate.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bn,
+  ../../constantine/math/pairing/pairing_bn,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bn254_snarks_gt_subgroup.nim b/tests/math/t_pairing_bn254_snarks_gt_subgroup.nim
similarity index 82%
rename from tests/backend/t_pairing_bn254_snarks_gt_subgroup.nim
rename to tests/math/t_pairing_bn254_snarks_gt_subgroup.nim
index 02a64e6..84e33df 100644
--- a/tests/backend/t_pairing_bn254_snarks_gt_subgroup.nim
+++ b/tests/math/t_pairing_bn254_snarks_gt_subgroup.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bn,
+  ../../constantine/math/pairing/pairing_bn,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bn254_snarks_optate.nim b/tests/math/t_pairing_bn254_snarks_optate.nim
similarity index 84%
rename from tests/backend/t_pairing_bn254_snarks_optate.nim
rename to tests/math/t_pairing_bn254_snarks_optate.nim
index 0c8303f..764fd62 100644
--- a/tests/backend/t_pairing_bn254_snarks_optate.nim
+++ b/tests/math/t_pairing_bn254_snarks_optate.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bn,
+  ../../constantine/math/pairing/pairing_bn,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bw6_761_gt_subgroup.nim b/tests/math/t_pairing_bw6_761_gt_subgroup.nim
similarity index 81%
rename from tests/backend/t_pairing_bw6_761_gt_subgroup.nim
rename to tests/math/t_pairing_bw6_761_gt_subgroup.nim
index 1ea80dd..18cfdf6 100644
--- a/tests/backend/t_pairing_bw6_761_gt_subgroup.nim
+++ b/tests/math/t_pairing_bw6_761_gt_subgroup.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bw6_761,
+  ../../constantine/math/pairing/pairing_bw6_761,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_bw6_761_optate.nim b/tests/math/t_pairing_bw6_761_optate.nim
similarity index 83%
rename from tests/backend/t_pairing_bw6_761_optate.nim
rename to tests/math/t_pairing_bw6_761_optate.nim
index 8c0d06a..435abab 100644
--- a/tests/backend/t_pairing_bw6_761_optate.nim
+++ b/tests/math/t_pairing_bw6_761_optate.nim
@@ -7,9 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/pairing/pairing_bw6_761,
+  ../../constantine/math/pairing/pairing_bw6_761,
   # Test utilities
   ./t_pairing_template
 
diff --git a/tests/backend/t_pairing_cyclotomic_subgroup.nim b/tests/math/t_pairing_cyclotomic_subgroup.nim
similarity index 93%
rename from tests/backend/t_pairing_cyclotomic_subgroup.nim
rename to tests/math/t_pairing_cyclotomic_subgroup.nim
index 35d749c..fc26e42 100644
--- a/tests/backend/t_pairing_cyclotomic_subgroup.nim
+++ b/tests/math/t_pairing_cyclotomic_subgroup.nim
@@ -10,13 +10,13 @@ import
   # Standard library
   std/[tables, unittest, times],
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/io/[io_bigints, io_towers],
-  ../../constantine/backend/pairing/cyclotomic_subgroup,
-  ../../constantine/backend/isogeny/frobenius,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/io/[io_bigints, io_extfields],
+  ../../constantine/math/pairing/cyclotomic_subgroup,
+  ../../constantine/math/isogenies/frobenius,
   # Test utilities
   ../../helpers/[prng_unsafe, static_for]
 
diff --git a/tests/backend/t_pairing_mul_fp12_by_lines.nim b/tests/math/t_pairing_mul_fp12_by_lines.nim
similarity index 97%
rename from tests/backend/t_pairing_mul_fp12_by_lines.nim
rename to tests/math/t_pairing_mul_fp12_by_lines.nim
index c3b3900..7d2e142 100644
--- a/tests/backend/t_pairing_mul_fp12_by_lines.nim
+++ b/tests/math/t_pairing_mul_fp12_by_lines.nim
@@ -10,12 +10,12 @@ import
   # Standard library
   std/[tables, unittest, times],
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/io/io_towers,
-  ../../constantine/backend/pairing/lines_eval,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/io/io_extfields,
+  ../../constantine/math/pairing/lines_eval,
   # Test utilities
   ../../helpers/[prng_unsafe, static_for]
 
diff --git a/tests/backend/t_pairing_template.nim b/tests/math/t_pairing_template.nim
similarity index 89%
rename from tests/backend/t_pairing_template.nim
rename to tests/math/t_pairing_template.nim
index 5f318ab..2ca9848 100644
--- a/tests/backend/t_pairing_template.nim
+++ b/tests/math/t_pairing_template.nim
@@ -10,14 +10,14 @@ import
   # Standard library
   std/unittest, times,
   # Internals
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/[arithmetic, primitives],
-  ../../constantine/backend/towers,
-  ../../constantine/backend/config/curves,
-  ../../constantine/backend/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective],
-  ../../constantine/backend/curves/[zoo_subgroups, zoo_pairings],
-  ../../constantine/backend/pairing/cyclotomic_subgroup,
-  ../../constantine/backend/io/io_towers,
+  ../../constantine/platforms/abstractions,
+  ../../constantine/math/arithmetic,
+  ../../constantine/math/extension_fields,
+  ../../constantine/math/config/curves,
+  ../../constantine/math/elliptic/[ec_shortweierstrass_affine, ec_shortweierstrass_projective],
+  ../../constantine/math/curves/[zoo_subgroups, zoo_pairings],
+  ../../constantine/math/pairing/cyclotomic_subgroup,
+  ../../constantine/math/io/io_extfields,
 
   # Test utilities
   ../../helpers/prng_unsafe
@@ -25,9 +25,10 @@ import
 export
   prng_unsafe, times, unittest,
   ec_shortweierstrass_affine, ec_shortweierstrass_projective,
-  arithmetic, towers,
-  primitives, io_towers,
-  cyclotomic_subgroup
+  arithmetic, extension_fields,
+  io_extfields,
+  cyclotomic_subgroup,
+  abstractions, curves
 
 type
   RandomGen* = enum
diff --git a/tests/backend/t_primitives.nim b/tests/math/t_primitives.nim
similarity index 98%
rename from tests/backend/t_primitives.nim
rename to tests/math/t_primitives.nim
index eecfb38..e1a86a4 100644
--- a/tests/backend/t_primitives.nim
+++ b/tests/math/t_primitives.nim
@@ -7,8 +7,7 @@
 # at your option. This file may not be copied, modified, or distributed except according to those terms.
 
 import  std/[unittest, times, math],
-        ../../constantine/backend/config/common,
-        ../../constantine/backend/primitives,
+        ../../constantine/platforms/abstractions,
         ../../helpers/prng_unsafe
 
 # Random seed for reproducibility
diff --git a/tests/backend/t_primitives_extended_precision.nim b/tests/math/t_primitives_extended_precision.nim
similarity index 95%
rename from tests/backend/t_primitives_extended_precision.nim
rename to tests/math/t_primitives_extended_precision.nim
index c127dce..5dc5c88 100644
--- a/tests/backend/t_primitives_extended_precision.nim
+++ b/tests/math/t_primitives_extended_precision.nim
@@ -9,8 +9,7 @@
 
 import
   std/[unittest, times, math],
-  ../../constantine/backend/config/common,
-  ../../constantine/backend/primitives,
+  ../../constantine/platforms/abstractions,
   ../../helpers/prng_unsafe
 
 suite "Extended precision bugs":
diff --git a/tests/backend/vectors/tv_BLS12_377_scalar_mul_G1.json b/tests/math/vectors/tv_BLS12_377_scalar_mul_G1.json
similarity index 100%
rename from tests/backend/vectors/tv_BLS12_377_scalar_mul_G1.json
rename to tests/math/vectors/tv_BLS12_377_scalar_mul_G1.json
diff --git a/tests/backend/vectors/tv_BLS12_377_scalar_mul_G2.json b/tests/math/vectors/tv_BLS12_377_scalar_mul_G2.json
similarity index 100%
rename from tests/backend/vectors/tv_BLS12_377_scalar_mul_G2.json
rename to tests/math/vectors/tv_BLS12_377_scalar_mul_G2.json
diff --git a/tests/backend/vectors/tv_BLS12_381_scalar_mul_G1.json b/tests/math/vectors/tv_BLS12_381_scalar_mul_G1.json
similarity index 100%
rename from tests/backend/vectors/tv_BLS12_381_scalar_mul_G1.json
rename to tests/math/vectors/tv_BLS12_381_scalar_mul_G1.json
diff --git a/tests/backend/vectors/tv_BLS12_381_scalar_mul_G2.json b/tests/math/vectors/tv_BLS12_381_scalar_mul_G2.json
similarity index 100%
rename from tests/backend/vectors/tv_BLS12_381_scalar_mul_G2.json
rename to tests/math/vectors/tv_BLS12_381_scalar_mul_G2.json
diff --git a/tests/backend/vectors/tv_BN254_Nogami_scalar_mul_G1.json b/tests/math/vectors/tv_BN254_Nogami_scalar_mul_G1.json
similarity index 100%
rename from tests/backend/vectors/tv_BN254_Nogami_scalar_mul_G1.json
rename to tests/math/vectors/tv_BN254_Nogami_scalar_mul_G1.json
diff --git a/tests/backend/vectors/tv_BN254_Nogami_scalar_mul_G2.json b/tests/math/vectors/tv_BN254_Nogami_scalar_mul_G2.json
similarity index 100%
rename from tests/backend/vectors/tv_BN254_Nogami_scalar_mul_G2.json
rename to tests/math/vectors/tv_BN254_Nogami_scalar_mul_G2.json
diff --git a/tests/backend/vectors/tv_BN254_Snarks_scalar_mul_G1.json b/tests/math/vectors/tv_BN254_Snarks_scalar_mul_G1.json
similarity index 100%
rename from tests/backend/vectors/tv_BN254_Snarks_scalar_mul_G1.json
rename to tests/math/vectors/tv_BN254_Snarks_scalar_mul_G1.json
diff --git a/tests/backend/vectors/tv_BN254_Snarks_scalar_mul_G2.json b/tests/math/vectors/tv_BN254_Snarks_scalar_mul_G2.json
similarity index 100%
rename from tests/backend/vectors/tv_BN254_Snarks_scalar_mul_G2.json
rename to tests/math/vectors/tv_BN254_Snarks_scalar_mul_G2.json
diff --git a/tests/backend/vectors/tv_BW6_761_scalar_mul_G1.json b/tests/math/vectors/tv_BW6_761_scalar_mul_G1.json
similarity index 100%
rename from tests/backend/vectors/tv_BW6_761_scalar_mul_G1.json
rename to tests/math/vectors/tv_BW6_761_scalar_mul_G1.json
diff --git a/tests/backend/vectors/tv_BW6_761_scalar_mul_G2.json b/tests/math/vectors/tv_BW6_761_scalar_mul_G2.json
similarity index 100%
rename from tests/backend/vectors/tv_BW6_761_scalar_mul_G2.json
rename to tests/math/vectors/tv_BW6_761_scalar_mul_G2.json
diff --git a/tests/backend/vectors/tv_h2c_v7_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json b/tests/math/vectors/tv_h2c_v7_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json
similarity index 100%
rename from tests/backend/vectors/tv_h2c_v7_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json
rename to tests/math/vectors/tv_h2c_v7_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json
diff --git a/tests/backend/vectors/tv_h2c_v8_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json b/tests/math/vectors/tv_h2c_v8_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json
similarity index 100%
rename from tests/backend/vectors/tv_h2c_v8_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json
rename to tests/math/vectors/tv_h2c_v8_BLS12_381_hash_to_G2_SHA256_SSWU_RO.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/README.md b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/README.md
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/README.md
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/README.md
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x0000000000000000000000000000000000000000000000000000000000000000.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x0000000000000000000000000000000000000000000000000000000000000000.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x0000000000000000000000000000000000000000000000000000000000000000.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x0000000000000000000000000000000000000000000000000000000000000000.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x5656565656565656565656565656565656565656565656565656565656565656.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x5656565656565656565656565656565656565656565656565656565656565656.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x5656565656565656565656565656565656565656565656565656565656565656.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0x5656565656565656565656565656565656565656565656565656565656565656.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0xabababababababababababababababababababababababababababababababab.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0xabababababababababababababababababababababababababababababababab.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0xabababababababababababababababababababababababababababababababab.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_0xabababababababababababababababababababababababababababababababab.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_infinity_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_infinity_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_infinity_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_infinity_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_na_signatures.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_na_signatures.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_na_signatures.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_na_signatures.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_single_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_single_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_single_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate/aggregate_single_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_infinity_pubkey.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_infinity_pubkey.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_infinity_pubkey.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_infinity_pubkey.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_infinity_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_infinity_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_infinity_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_infinity_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_na_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_na_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_na_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_na_pubkeys_and_na_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_tampered_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_tampered_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_tampered_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_tampered_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_valid.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_valid.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_valid.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/aggregate_verify/aggregate_verify_valid.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_invalid_forged_signature_set.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_invalid_forged_signature_set.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_invalid_forged_signature_set.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_invalid_forged_signature_set.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_valid_simple_signature_set.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_valid_simple_signature_set.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_valid_simple_signature_set.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/batch_verify/batch_verify_valid_simple_signature_set.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_false_b_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_false_b_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_false_b_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_false_b_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_true_b_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_true_b_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_true_b_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_infinity_with_true_b_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_G1.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_G1.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_G1.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_G1.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_curve.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_curve.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_curve.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_not_in_curve.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_few_bytes.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_few_bytes.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_few_bytes.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_few_bytes.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_many_bytes.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_many_bytes.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_many_bytes.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_too_many_bytes.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_a_flag_true.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_a_flag_true.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_a_flag_true.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_a_flag_true.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_x_nonzero.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_x_nonzero.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_x_nonzero.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_b_flag_and_x_nonzero.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_wrong_c_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_wrong_c_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_wrong_c_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_with_wrong_c_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_equal_to_modulus.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_equal_to_modulus.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_equal_to_modulus.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_equal_to_modulus.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_greater_than_modulus.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_greater_than_modulus.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_greater_than_modulus.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_fails_x_greater_than_modulus.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_correct_point.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_correct_point.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_correct_point.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_correct_point.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_infinity_with_true_b_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_infinity_with_true_b_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_infinity_with_true_b_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G1/deserialization_succeeds_infinity_with_true_b_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_false_b_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_false_b_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_false_b_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_false_b_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_true_b_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_true_b_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_true_b_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_infinity_with_true_b_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_G2.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_G2.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_G2.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_G2.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_curve.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_curve.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_curve.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_not_in_curve.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_few_bytes.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_few_bytes.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_few_bytes.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_few_bytes.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_many_bytes.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_many_bytes.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_many_bytes.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_too_many_bytes.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_a_flag_true.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_a_flag_true.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_a_flag_true.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_a_flag_true.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_x_nonzero.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_x_nonzero.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_x_nonzero.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_b_flag_and_x_nonzero.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_wrong_c_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_wrong_c_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_wrong_c_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_with_wrong_c_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_equal_to_modulus.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_equal_to_modulus.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_equal_to_modulus.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_equal_to_modulus.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_greater_than_modulus.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_greater_than_modulus.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_greater_than_modulus.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xim_greater_than_modulus.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_equal_to_modulus.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_equal_to_modulus.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_equal_to_modulus.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_equal_to_modulus.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_greater_than_modulus.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_greater_than_modulus.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_greater_than_modulus.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_fails_xre_greater_than_modulus.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_correct_point.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_correct_point.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_correct_point.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_correct_point.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_infinity_with_true_b_flag.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_infinity_with_true_b_flag.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_infinity_with_true_b_flag.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/deserialization_G2/deserialization_succeeds_infinity_with_true_b_flag.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_4f079f946446fabf.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_4f079f946446fabf.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_4f079f946446fabf.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_4f079f946446fabf.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_5a38e6b4017fe4dd.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_5a38e6b4017fe4dd.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_5a38e6b4017fe4dd.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_5a38e6b4017fe4dd.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_a698ea45b109f303.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_a698ea45b109f303.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_a698ea45b109f303.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_extra_pubkey_a698ea45b109f303.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_infinity_pubkey.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_infinity_pubkey.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_infinity_pubkey.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_infinity_pubkey.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_infinity_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_infinity_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_infinity_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_infinity_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_na_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_na_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_na_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_na_pubkeys_and_na_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_3d7576f3c0e3570a.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_3d7576f3c0e3570a.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_3d7576f3c0e3570a.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_3d7576f3c0e3570a.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_5e745ad0c6199a6c.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_5e745ad0c6199a6c.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_5e745ad0c6199a6c.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_5e745ad0c6199a6c.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_652ce62f09290811.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_652ce62f09290811.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_652ce62f09290811.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_tampered_signature_652ce62f09290811.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_3d7576f3c0e3570a.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_3d7576f3c0e3570a.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_3d7576f3c0e3570a.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_3d7576f3c0e3570a.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_5e745ad0c6199a6c.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_5e745ad0c6199a6c.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_5e745ad0c6199a6c.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_5e745ad0c6199a6c.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_652ce62f09290811.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_652ce62f09290811.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_652ce62f09290811.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/fast_aggregate_verify/fast_aggregate_verify_valid_652ce62f09290811.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__2782afaa8406d038.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__2782afaa8406d038.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__2782afaa8406d038.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__2782afaa8406d038.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__7590bd067999bbfb.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__7590bd067999bbfb.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__7590bd067999bbfb.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__7590bd067999bbfb.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__a54942c8e365f378.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__a54942c8e365f378.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__a54942c8e365f378.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__a54942c8e365f378.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__c938b486cf69e8f7.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__c938b486cf69e8f7.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__c938b486cf69e8f7.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/hash_to_G2/hash_to_G2__c938b486cf69e8f7.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_11b8c7cad5238946.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_11b8c7cad5238946.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_11b8c7cad5238946.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_11b8c7cad5238946.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_142f678a8d05fcd1.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_142f678a8d05fcd1.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_142f678a8d05fcd1.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_142f678a8d05fcd1.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_37286e1a6d1f6eb3.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_37286e1a6d1f6eb3.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_37286e1a6d1f6eb3.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_37286e1a6d1f6eb3.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_7055381f640f2c1d.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_7055381f640f2c1d.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_7055381f640f2c1d.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_7055381f640f2c1d.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_84d45c9c7cca6b92.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_84d45c9c7cca6b92.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_84d45c9c7cca6b92.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_84d45c9c7cca6b92.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_8cd3d4d0d9a5b265.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_8cd3d4d0d9a5b265.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_8cd3d4d0d9a5b265.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_8cd3d4d0d9a5b265.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_c82df61aa3ee60fb.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_c82df61aa3ee60fb.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_c82df61aa3ee60fb.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_c82df61aa3ee60fb.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_d0e28d7e76eb6e9c.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_d0e28d7e76eb6e9c.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_d0e28d7e76eb6e9c.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_d0e28d7e76eb6e9c.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_f2ae1097e7d0e18b.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_f2ae1097e7d0e18b.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_f2ae1097e7d0e18b.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_f2ae1097e7d0e18b.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_zero_privkey.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_zero_privkey.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_zero_privkey.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/sign/sign_case_zero_privkey.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_infinity_pubkey_and_infinity_signature.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_infinity_pubkey_and_infinity_signature.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_infinity_pubkey_and_infinity_signature.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_infinity_pubkey_and_infinity_signature.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_195246ee3bd3b6ec.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_195246ee3bd3b6ec.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_195246ee3bd3b6ec.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_195246ee3bd3b6ec.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2ea479adf8c40300.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2ea479adf8c40300.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2ea479adf8c40300.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2ea479adf8c40300.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2f09d443ab8a3ac2.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2f09d443ab8a3ac2.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2f09d443ab8a3ac2.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_2f09d443ab8a3ac2.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_3208262581c8fc09.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_3208262581c8fc09.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_3208262581c8fc09.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_3208262581c8fc09.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6b3b17f6962a490c.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6b3b17f6962a490c.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6b3b17f6962a490c.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6b3b17f6962a490c.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6eeb7c52dfd9baf0.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6eeb7c52dfd9baf0.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6eeb7c52dfd9baf0.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_6eeb7c52dfd9baf0.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_8761a0b7e920c323.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_8761a0b7e920c323.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_8761a0b7e920c323.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_8761a0b7e920c323.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_d34885d766d5f705.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_d34885d766d5f705.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_d34885d766d5f705.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_d34885d766d5f705.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_e8a50c445c855360.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_e8a50c445c855360.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_e8a50c445c855360.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_tampered_signature_case_e8a50c445c855360.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_195246ee3bd3b6ec.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_195246ee3bd3b6ec.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_195246ee3bd3b6ec.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_195246ee3bd3b6ec.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2ea479adf8c40300.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2ea479adf8c40300.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2ea479adf8c40300.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2ea479adf8c40300.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2f09d443ab8a3ac2.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2f09d443ab8a3ac2.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2f09d443ab8a3ac2.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_2f09d443ab8a3ac2.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_3208262581c8fc09.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_3208262581c8fc09.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_3208262581c8fc09.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_3208262581c8fc09.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6b3b17f6962a490c.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6b3b17f6962a490c.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6b3b17f6962a490c.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6b3b17f6962a490c.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6eeb7c52dfd9baf0.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6eeb7c52dfd9baf0.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6eeb7c52dfd9baf0.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_6eeb7c52dfd9baf0.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_8761a0b7e920c323.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_8761a0b7e920c323.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_8761a0b7e920c323.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_8761a0b7e920c323.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_d34885d766d5f705.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_d34885d766d5f705.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_d34885d766d5f705.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_d34885d766d5f705.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_e8a50c445c855360.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_e8a50c445c855360.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_e8a50c445c855360.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_valid_case_e8a50c445c855360.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_195246ee3bd3b6ec.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_195246ee3bd3b6ec.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_195246ee3bd3b6ec.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_195246ee3bd3b6ec.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2ea479adf8c40300.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2ea479adf8c40300.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2ea479adf8c40300.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2ea479adf8c40300.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2f09d443ab8a3ac2.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2f09d443ab8a3ac2.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2f09d443ab8a3ac2.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_2f09d443ab8a3ac2.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_3208262581c8fc09.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_3208262581c8fc09.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_3208262581c8fc09.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_3208262581c8fc09.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6b3b17f6962a490c.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6b3b17f6962a490c.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6b3b17f6962a490c.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6b3b17f6962a490c.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6eeb7c52dfd9baf0.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6eeb7c52dfd9baf0.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6eeb7c52dfd9baf0.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_6eeb7c52dfd9baf0.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_8761a0b7e920c323.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_8761a0b7e920c323.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_8761a0b7e920c323.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_8761a0b7e920c323.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_d34885d766d5f705.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_d34885d766d5f705.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_d34885d766d5f705.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_d34885d766d5f705.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_e8a50c445c855360.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_e8a50c445c855360.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_e8a50c445c855360.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verify_wrong_pubkey_case_e8a50c445c855360.json
diff --git a/tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verifycase_one_privkey_47117849458281be.json b/tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verifycase_one_privkey_47117849458281be.json
similarity index 100%
rename from tests/blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verifycase_one_privkey_47117849458281be.json
rename to tests/protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1/verify/verifycase_one_privkey_47117849458281be.json
diff --git a/tests/t_blssig_pop_on_bls12381_g2.nim b/tests/t_blssig_pop_on_bls12381_g2.nim
index 4bd9d8f..f3ce52e 100644
--- a/tests/t_blssig_pop_on_bls12381_g2.nim
+++ b/tests/t_blssig_pop_on_bls12381_g2.nim
@@ -10,7 +10,7 @@ import
   std/[json, os, unittest, strutils],
   pkg/[jsony, stew/byteutils],
   ../constantine/blssig_pop_on_bls12381_g2,
-  ../constantine/backend/io/io_bigints
+  ../constantine/math/io/io_bigints
 
 type
   PubkeyField = object
@@ -51,7 +51,7 @@ const SkippedTests = [
   "deserialization_fails_too_many_bytes.json"
 ]
 
-const TestDir = currentSourcePath.rsplit(DirSep, 1)[0] / "blssig_pop_on_bls12381_g2_test_vectors_v0.1.1"
+const TestDir = currentSourcePath.rsplit(DirSep, 1)[0] / "protocol_blssig_pop_on_bls12381_g2_test_vectors_v0.1.1"
 
 iterator walkTests*(category: string, skipped: var int): (string, string) =
   let testDir = TestDir/category
diff --git a/tests/t_ethereum_evm_precompiles.nim b/tests/t_ethereum_evm_precompiles.nim
index bd246d3..76b679e 100644
--- a/tests/t_ethereum_evm_precompiles.nim
+++ b/tests/t_ethereum_evm_precompiles.nim
@@ -10,11 +10,11 @@ import
   # Standard library
   std/[times, os, strutils, macros],
   # Status
-  stew/byteutils,
+  pkg/stew/byteutils,
   # 3rd party
-  jsony,
+  pkg/jsony,
   # Internals
-  ../constantine/backend/io/io_bigints,
+  ../constantine/math/io/io_bigints,
   ../constantine/ethereum_evm_precompiles
 
 type
diff --git a/tests/t_hash_sha256_vs_openssl.nim b/tests/t_hash_sha256_vs_openssl.nim
index ade7d35..def82c3 100644
--- a/tests/t_hash_sha256_vs_openssl.nim
+++ b/tests/t_hash_sha256_vs_openssl.nim
@@ -1,6 +1,6 @@
 import
   # Internals
-  ../constantine/backend/hashes,
+  ../constantine/hashes,
   # Helpers
   ../helpers/prng_unsafe,
   # Third-party