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

@@ -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

benchmarks/bench_blueprint.nim

@@ -14,7 +14,7 @@
 
 import
   # Internal
-  ../constantine/backend/config/common,
+  ../constantine/platforms/abstractions,
   # Helpers
   ../helpers/prng_unsafe,
   ./platforms,

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,

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,

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)

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

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,

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,

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,

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,

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,

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,

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

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,

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,

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,

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,

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

benchmarks/bench_sha256.nim

@@ -1,6 +1,6 @@
 import
   # Internals
-  ../constantine/backend/hashes,
+  ../constantine/hashes,
   # Helpers
   ../helpers/prng_unsafe,
   ./bench_blueprint

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,

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,

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,

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,

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

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):

constantine/backend/primitives/static_for.nim

@@ -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)
-    )

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
 

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]
 
 # ############################################################
 #

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
 
 # ############################################################
 #

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](

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
 
 # ############################################################
 #

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
 
 # ############################################################

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
 # --------------------------------------------------------------------------------

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
 
 # ############################################################
 #                                                            #

constantine/math/arithmetic/assembly/limbs_asm_modular_x86.nim

@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #

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

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

constantine/math/arithmetic/assembly/limbs_asm_mul_x86.nim

@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #

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

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
 
 # ############################################################

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
 
 # ############################################################

constantine/math/arithmetic/assembly/limbs_asm_x86.nim

@@ -10,8 +10,7 @@ import
   # Standard library
   std/macros,
   # Internal
-  ../../config/common,
-  ../../primitives
+  ../../../platforms/abstractions
 
 # ############################################################
 #

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,

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,

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.
 

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,

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
 

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

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: [].}

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:

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

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:

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

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"
 

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

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
 
 # ############################################################

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

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

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
 

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
 

constantine/math/curves/bls12_377_constants.nim

@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------

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

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
 # -----------------------------------------------------------------

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
 # ------------------------------------------------------------

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
 

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

constantine/math/curves/bls12_381_constants.nim

@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------

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

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
 # -----------------------------------------------------------------

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
 # -----------------------------------------------------------------

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
 # -----------------------------------------------------------------

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
 # ------------------------------------------------------------

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
 # -----------------------------------------------------------------

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

constantine/math/curves/bn254_nogami_constants.nim

@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------

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

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
 # -----------------------------------------------------------------

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
 # ------------------------------------------------------------

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
 # -----------------------------------------------------------------

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]](

constantine/math/curves/bn254_snarks_constants.nim

@@ -8,7 +8,7 @@
 
 import
   ../config/curves,
-  ../io/io_towers
+  ../io/io_extfields
 
 # Curve precomputed parameters
 # -----------------------------------------------------------------

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

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
 # -----------------------------------------------------------------

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
 # ------------------------------------------------------------

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
 # -----------------------------------------------------------------

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]](