# 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. # ############################################################ # # Template tests for elliptic curve operations # # ############################################################ import # Standard library std/[unittest, times], # Internals ../../constantine/platforms/abstractions, ../../constantine/math/config/curves, ../../constantine/math/[arithmetic, extension_fields], ../../constantine/math/elliptic/[ ec_shortweierstrass_affine, ec_shortweierstrass_jacobian, ec_shortweierstrass_projective, ec_twistededwards_affine, ec_twistededwards_projective, ec_scalar_mul], ../../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, abstractions, arithmetic # Generic sandwich type RandomGen* = enum Uniform HighHammingWeight Long01Sequence func random_point*(rng: var RngState, EC: typedesc, randZ: bool, gen: RandomGen): EC {.noInit.} = if not randZ: if gen == Uniform: result = rng.random_unsafe(EC) elif gen == HighHammingWeight: result = rng.random_highHammingWeight(EC) else: result = rng.random_long01Seq(EC) else: if gen == Uniform: result = rng.random_unsafe_with_randZ(EC) elif gen == HighHammingWeight: result = rng.random_highHammingWeight_with_randZ(EC) else: result = rng.random_long01Seq_with_randZ(EC) template pairingGroup(EC: typedesc): string = when EC is (ECP_ShortW_Aff or ECP_ShortW_Prj or ECP_ShortW_Jac): when EC.G == G1: "G1" else: "G2" else: "" proc run_EC_addition_tests*( ec: typedesc, Iters: static int, moduleName: string ) = var rng: RngState let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32 rng.seed(seed) echo "\n------------------------------------------------------\n" echo moduleName, " xoshiro512** seed: ", seed const G1_or_G2 = pairingGroup(ec) const testSuiteDesc = "Elliptic curve in " & $ec.F.C.getEquationForm() & " form with projective coordinates" suite testSuiteDesc & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": test "The infinity point is the neutral element w.r.t. to EC " & G1_or_G2 & " addition": proc test(EC: typedesc, randZ: bool, gen: RandomGen) = var inf {.noInit.}: EC inf.setInf() check: bool inf.isInf() for _ in 0 ..< Iters: var r{.noInit.}: EC let P = rng.random_point(EC, randZ, gen) r.sum(P, inf) check: bool(r == P) r.sum(inf, P) check: bool(r == P) test(ec, randZ = false, gen = Uniform) test(ec, randZ = true, gen = Uniform) test(ec, randZ = false, gen = HighHammingWeight) test(ec, randZ = true, gen = HighHammingWeight) test(ec, randZ = false, gen = Long01Sequence) test(ec, randZ = true, gen = Long01Sequence) test "Adding opposites gives an infinity point": proc test(EC: typedesc, randZ: bool, gen: RandomGen) = for _ in 0 ..< Iters: var r{.noInit.}: EC let P = rng.random_point(EC, randZ, gen) var Q = P Q.neg() r.sum(P, Q) check: bool r.isInf() r.sum(Q, P) check: bool r.isInf() test(ec, randZ = false, gen = Uniform) test(ec, randZ = true, gen = Uniform) test(ec, randZ = false, gen = HighHammingWeight) test(ec, randZ = true, gen = HighHammingWeight) test(ec, randZ = false, gen = Long01Sequence) test(ec, randZ = true, gen = Long01Sequence) test "EC " & G1_or_G2 & " add is commutative": proc test(EC: typedesc, randZ: bool, gen: RandomGen) = for _ in 0 ..< Iters: var r0{.noInit.}, r1{.noInit.}: EC let P = rng.random_point(EC, randZ, gen) let Q = rng.random_point(EC, randZ, gen) r0.sum(P, Q) r1.sum(Q, P) check: bool(r0 == r1) test(ec, randZ = false, gen = Uniform) test(ec, randZ = true, gen = Uniform) test(ec, randZ = false, gen = HighHammingWeight) test(ec, randZ = true, gen = HighHammingWeight) test(ec, randZ = false, gen = Long01Sequence) test(ec, randZ = true, gen = Long01Sequence) test "EC " & G1_or_G2 & " add is associative": proc test(EC: typedesc, randZ: bool, gen: RandomGen) = for _ in 0 ..< Iters: let a = rng.random_point(EC, randZ, gen) let b = rng.random_point(EC, randZ, gen) let c = rng.random_point(EC, randZ, gen) var tmp1{.noInit.}, tmp2{.noInit.}: EC # r0 = (a + b) + c tmp1.sum(a, b) tmp2.sum(tmp1, c) let r0 = tmp2 # r1 = a + (b + c) tmp1.sum(b, c) tmp2.sum(a, tmp1) let r1 = tmp2 # r2 = (a + c) + b tmp1.sum(a, c) tmp2.sum(tmp1, b) let r2 = tmp2 # r3 = a + (c + b) tmp1.sum(c, b) tmp2.sum(a, tmp1) let r3 = tmp2 # r4 = (c + a) + b tmp1.sum(c, a) tmp2.sum(tmp1, b) let r4 = tmp2 # ... check: bool(r0 == r1) bool(r0 == r2) bool(r0 == r3) bool(r0 == r4) test(ec, randZ = false, gen = Uniform) test(ec, randZ = true, gen = Uniform) test(ec, randZ = false, gen = HighHammingWeight) test(ec, randZ = true, gen = HighHammingWeight) test(ec, randZ = false, gen = Long01Sequence) test(ec, randZ = true, gen = Long01Sequence) test "EC " & G1_or_G2 & " double and EC " & G1_or_G2 & " add are consistent": proc test(EC: typedesc, randZ: bool, gen: RandomGen) = for _ in 0 ..< Iters: let a = rng.random_point(EC, randZ, gen) var r0{.noInit.}, r1{.noInit.}: EC r0.double(a) r1.sum(a, a) check: bool(r0 == r1) test(ec, randZ = false, gen = Uniform) test(ec, randZ = true, gen = Uniform) test(ec, randZ = false, gen = HighHammingWeight) test(ec, randZ = true, gen = HighHammingWeight) test(ec, randZ = false, gen = Long01Sequence) test(ec, randZ = true, gen = Long01Sequence) proc run_EC_mul_sanity_tests*( ec: typedesc, ItersMul: static int, moduleName: string ) = # Random seed for reproducibility var rng: RngState let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32 rng.seed(seed) echo "\n------------------------------------------------------\n" echo moduleName, " xoshiro512** seed: ", seed const G1_or_G2 = pairingGroup(ec) const testSuiteDesc = "Elliptic curve in " & $ec.F.C.getEquationForm() & " form" suite testSuiteDesc & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": test "EC " & G1_or_G2 & " mul [0]P == Inf": proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = for _ in 0 ..< ItersMul: let a = rng.random_point(EC, randZ, gen) var impl = a reference = a impl.scalarMulGeneric(BigInt[bits]()) reference.unsafe_ECmul_double_add(BigInt[bits]()) check: bool(impl.isInf()) bool(reference.isInf()) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) test "EC " & G1_or_G2 & " mul [1]P == P": proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = for _ in 0 ..< ItersMul: let a = rng.random_point(EC, randZ, gen) var exponent{.noInit.}: BigInt[bits] exponent.setOne() var impl = a reference = a impl.scalarMulGeneric(exponent) reference.unsafe_ECmul_double_add(exponent) check: bool(impl == a) bool(reference == a) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) test "EC " & G1_or_G2 & " mul [2]P == P.double()": proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = for _ in 0 ..< ItersMul: let a = rng.random_point(EC, randZ, gen) var doubleA{.noInit.}: EC doubleA.double(a) let exponent = BigInt[bits].fromUint(2) var impl = a reference = a impl.scalarMulGeneric(exponent) reference.unsafe_ECmul_double_add(exponent) check: bool(impl == doubleA) bool(reference == doubleA) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) proc run_EC_mul_distributive_tests*( ec: typedesc, ItersMul: static int, moduleName: string ) = # Random seed for reproducibility var rng: RngState let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32 rng.seed(seed) echo "\n------------------------------------------------------\n" echo moduleName, " xoshiro512** seed: ", seed const G1_or_G2 = pairingGroup(ec) const testSuiteDesc = "Elliptic curve in " & $ec.F.C.getEquationForm() & " form" suite testSuiteDesc & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": test "EC " & G1_or_G2 & " mul is distributive over EC add": proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = for _ in 0 ..< ItersMul: let a = rng.random_point(EC, randZ, gen) let b = rng.random_point(EC, randZ, gen) let exponent = rng.random_unsafe(BigInt[bits]) # [k](a + b) - Factorized var fImpl{.noInit.}: EC fReference{.noInit.}: EC fImpl.sum(a, b) fReference.sum(a, b) fImpl.scalarMulGeneric(exponent) fReference.unsafe_ECmul_double_add(exponent) # [k]a + [k]b - Distributed var kaImpl = a var kaRef = a kaImpl.scalarMulGeneric(exponent) kaRef.unsafe_ECmul_double_add(exponent) var kbImpl = b var kbRef = b kbImpl.scalarMulGeneric(exponent) kbRef.unsafe_ECmul_double_add(exponent) var kakbImpl{.noInit.}, kakbRef{.noInit.}: EC kakbImpl.sum(kaImpl, kbImpl) kakbRef.sum(kaRef, kbRef) check: bool(fImpl == kakbImpl) bool(fReference == kakbRef) bool(fImpl == fReference) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) proc run_EC_mul_vs_ref_impl*( ec: typedesc, ItersMul: static int, moduleName: string ) = # Random seed for reproducibility var rng: RngState let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32 rng.seed(seed) echo "\n------------------------------------------------------\n" echo moduleName, " xoshiro512** seed: ", seed const G1_or_G2 = pairingGroup(ec) const testSuiteDesc = "Elliptic curve in " & $ec.F.C.getEquationForm() & " form" suite testSuiteDesc & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": test "EC " & G1_or_G2 & " mul constant-time is equivalent to a simple double-and-add algorithm": proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = for _ in 0 ..< ItersMul: let a = rng.random_point(EC, randZ, gen) let exponent = rng.random_unsafe(BigInt[bits]) var impl = a reference = a impl.scalarMulGeneric(exponent) reference.unsafe_ECmul_double_add(exponent) check: bool(impl == reference) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) proc run_EC_mixed_add_impl*( ec: typedesc, Iters: static int, moduleName: string ) = # Random seed for reproducibility var rng: RngState let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32 rng.seed(seed) echo "\n------------------------------------------------------\n" echo moduleName, " xoshiro512** seed: ", seed when ec.G == G1: const G1_or_G2 = "G1" else: const G1_or_G2 = "G2" const testSuiteDesc = "Elliptic curve mixed addition for Short Weierstrass form" suite testSuiteDesc & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": test "EC " & G1_or_G2 & " mixed addition is consistent with general addition": proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = for _ in 0 ..< Iters: let a = rng.random_point(EC, randZ, gen) let b = rng.random_point(EC, randZ, gen) var bAff: ECP_ShortW_Aff[EC.F, EC.G] bAff.affine(b) var r_generic, r_mixed: EC r_generic.sum(a, b) r_mixed.madd(a, bAff) check: bool(r_generic == r_mixed) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) proc run_EC_subgroups_cofactors_impl*( ec: typedesc, ItersMul: static int, moduleName: string ) = # Random seed for reproducibility var rng: RngState let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32 rng.seed(seed) echo "\n------------------------------------------------------\n" echo moduleName, " xoshiro512** seed: ", seed when ec.G == G1: const G1_or_G2 = "G1" else: const G1_or_G2 = "G2" const testSuiteDesc = "Elliptic curve subgroup check and cofactor clearing" suite testSuiteDesc & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": test "Effective cofactor matches accelerated cofactor clearing" & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = for _ in 0 ..< ItersMul: let P = rng.random_point(EC, randZ, gen) var cPeff = P var cPfast = P cPeff.clearCofactorReference() cPfast.clearCofactorFast() check: bool(cPeff == cPfast) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) test "Subgroup checks and cofactor clearing consistency": var inSubgroup = 0 var offSubgroup = 0 proc test(EC: typedesc, bits: static int, randZ: bool, gen: RandomGen) = stdout.write " " for _ in 0 ..< ItersMul: let P = rng.random_point(EC, randZ, gen) var rP = P rP.scalarMulGeneric(EC.F.C.getCurveOrder()) if bool rP.isInf(): inSubgroup += 1 doAssert bool P.isInSubgroup(), "Subgroup check issue on " & $EC & " with P: " & P.toHex() else: offSubgroup += 1 doAssert not bool P.isInSubgroup(), "Subgroup check issue on " & $EC & " with P: " & P.toHex() var Q = P var rQ: typeof(rP) Q.clearCofactor() rQ = Q rQ.scalarMulGeneric(EC.F.C.getCurveOrder()) doAssert bool rQ.isInf(), "Cofactor clearing issue on " & $EC & " with Q: " & Q.toHex() doAssert bool Q.isInSubgroup(), "Subgroup check issue on " & $EC & " with Q: " & Q.toHex() stdout.write '.' stdout.write '\n' test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Uniform) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = HighHammingWeight) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = false, gen = Long01Sequence) test(ec, bits = ec.F.C.getCurveOrderBitwidth(), randZ = true, gen = Long01Sequence) echo " [SUCCESS] Test finished with ", inSubgroup, " points in ", G1_or_G2, " subgroup and ", offSubgroup, " points on curve but not in subgroup (before cofactor clearing)" proc run_EC_affine_conversion*( ec: typedesc, Iters: static int, moduleName: string ) = # Random seed for reproducibility var rng: RngState let seed = uint32(getTime().toUnix() and (1'i64 shl 32 - 1)) # unixTime mod 2^32 rng.seed(seed) echo "\n------------------------------------------------------\n" echo moduleName, " xoshiro512** seed: ", seed const G1_or_G2 = pairingGroup(ec) const testSuiteDesc = "Elliptic curve in " & $ec.F.C.getEquationForm() & " form" suite testSuiteDesc & " - " & $ec & " - [" & $WordBitwidth & "-bit mode]": test "EC " & G1_or_G2 & " batchAffine is consistent with single affine conversion": proc test(EC: typedesc, gen: RandomGen) = const batchSize = 10 for _ in 0 ..< Iters: var Ps: array[batchSize, EC] for i in 0 ..< batchSize: Ps[i] = rng.random_point(EC, randZ = true, gen) var Qs, Rs: array[batchSize, affine(EC)] for i in 0 ..< batchSize: Qs[i].affine(Ps[i]) Rs.batchAffine(Ps) for i in countdown(batchSize-1, 0): doAssert bool(Qs[i] == Rs[i]), block: var s: string s &= "Mismatch on iteration " & $i s &= "\nFailing batch for " & $EC & " (" & $WordBitwidth & "-bit)" s &= "\n [" for i in 0 ..< batchSize: s &= "\n" & Ps[i].toHex(indent = 4) if i != batchSize-1: s &= "," s &= "\n ]" s &= "\nFailing inversions for " & $EC & " (" & $WordBitwidth & "-bit)" s &= "\n [" for i in 0 ..< batchSize: s &= "\n" & Rs[i].toHex(indent = 4) if i != batchSize-1: s &= "," s &= "\n ]" s &= "\nExpected inversions for " & $EC & " (" & $WordBitwidth & "-bit)" s &= "\n [" for i in 0 ..< batchSize: s &= "\n" & Qs[i].toHex(indent = 4) if i != batchSize-1: s &= "," s &= "\n ]" s test(ec, gen = Uniform) test(ec, gen = HighHammingWeight) test(ec, gen = Long01Sequence) proc run_EC_conversion_failures*( moduleName: string ) = echo "\n------------------------------------------------------\n" echo moduleName suite moduleName & " - [" & $WordBitwidth & "-bit mode]": test "EC batchAffine fuzzing failures ": proc test_bn254_snarks_g1(ECP: type) = type ECP_Aff = ECP_ShortW_Aff[Fp[BN254_Snarks], G1] let Ps = [ ECP.fromHex( x = "0x0e0a76c19a07e01fe56f246f7878652c0b39eb28f5c60b3dd43e438dc50e0d9d", y = "0x04e6da44bc7f802fab3df34ce45d86857327663bc24ff574da48ee2b01a4932e" ), ECP.fromHex( x = "0x2036a21a3d9cc09d8f5f7491fe7e4f44cffd2addf01c6ae587bee7d24f060571", y = "0x2b5f1cc6f1cdb4a6dbaf3c88b9c02ccf984aecbba4830d5aeb33f940cb632d8a" ), ECP.fromHex( x = "0x2fd314a75c6b1f82d70f2edc7b7bf6e7397bc04bc6aaa0584b9e5bbb7689082a", y = "0x111b3b4a697e7a990400eb39f09a9bb559748cea6699535bd114ffb3dcc0b4d1" ), ECP.fromHex( x = "0x0000000000000000000000000000000000000000000000000000000000000000", y = "0x0000000000000000000000000000000000000000000000000000000000000000" ), ECP.fromHex( x = "0x0e0a77c199ffdf2f686ea36f7879462c0a74eb28f5e70b3dd31d438dc58f0d9d", y = "0x0b3938a732020d98793510be6aa312651a5f5369ebbbe41d7fda8fd914b7f264" ), ECP.fromHex( x = "0x0000000007ffffffffffffff80000000000007ffe000000000ffffffffffffff", y = "0x1d9db0f30e3395ee33a70674a31e2854de0665292dd545c10fb3da579d7df916" ), ECP.fromHex( x = "0x000000000000000fffffffffe0000000000007ffffffffffffffffffffffffff", y = "0x2a5c6df4d24efa9ffcf4003e35801dc202d820b59d67ecc65d57cfdf53b4bbc6" ), ECP.fromHex( x = "0x00000000000000000003ffffffc00000000000000c000000000000003ffffffe", y = "0x09f811f84207472ccd6ca00bb1ec3e6132a1c9206adc9ed768871f0005f0d358" ), ECP.fromHex( x = "0x0e0979b99d07df30656ea36f7879462c097beb28f5c8083dd25d448dc58f0ca4", y = "0x1799b22d8780c917ab1c4e15da718c243babc1c51225b5f8298aa570b5029796" ), ECP.fromHex( x = "0x0e0a76c29a07e02f666ea36e806a462c0a78eb25f5c70b3dd35c4b8dc58f0d9c", y = "0x0529cb1ad2552c7979a900ff59551d5dc1f8680c3a4f20d3b9cdcf68b69ec61c" ) ] let Qs = [ ECP_Aff.fromHex( x = "0x0e0a76c19a07e01fe56f246f7878652c0b39eb28f5c60b3dd43e438dc50e0d9d", y = "0x04e6da44bc7f802fab3df34ce45d86857327663bc24ff574da48ee2b01a4932e" ), ECP_Aff.fromHex( x = "0x2036a21a3d9cc09d8f5f7491fe7e4f44cffd2addf01c6ae587bee7d24f060571", y = "0x2b5f1cc6f1cdb4a6dbaf3c88b9c02ccf984aecbba4830d5aeb33f940cb632d8a" ), ECP_Aff.fromHex( x = "0x2fd314a75c6b1f82d70f2edc7b7bf6e7397bc04bc6aaa0584b9e5bbb7689082a", y = "0x111b3b4a697e7a990400eb39f09a9bb559748cea6699535bd114ffb3dcc0b4d1" ), ECP_Aff.fromHex( x = "0x0000000000000000000000000000000000000000000000000000000000000000", y = "0x0000000000000000000000000000000000000000000000000000000000000000" ), ECP_Aff.fromHex( x = "0x0e0a77c199ffdf2f686ea36f7879462c0a74eb28f5e70b3dd31d438dc58f0d9d", y = "0x0b3938a732020d98793510be6aa312651a5f5369ebbbe41d7fda8fd914b7f264" ), ECP_Aff.fromHex( x = "0x0000000007ffffffffffffff80000000000007ffe000000000ffffffffffffff", y = "0x1d9db0f30e3395ee33a70674a31e2854de0665292dd545c10fb3da579d7df916" ), ECP_Aff.fromHex( x = "0x000000000000000fffffffffe0000000000007ffffffffffffffffffffffffff", y = "0x2a5c6df4d24efa9ffcf4003e35801dc202d820b59d67ecc65d57cfdf53b4bbc6" ), ECP_Aff.fromHex( x = "0x00000000000000000003ffffffc00000000000000c000000000000003ffffffe", y = "0x09f811f84207472ccd6ca00bb1ec3e6132a1c9206adc9ed768871f0005f0d358" ), ECP_Aff.fromHex( x = "0x0e0979b99d07df30656ea36f7879462c097beb28f5c8083dd25d448dc58f0ca4", y = "0x1799b22d8780c917ab1c4e15da718c243babc1c51225b5f8298aa570b5029796" ), ECP_Aff.fromHex( x = "0x0e0a76c29a07e02f666ea36e806a462c0a78eb25f5c70b3dd35c4b8dc58f0d9c", y = "0x0529cb1ad2552c7979a900ff59551d5dc1f8680c3a4f20d3b9cdcf68b69ec61c" ) ] var Rs: array[10, ECP_Aff] Rs.batchAffine(Ps) for i in 0 ..< 10: doAssert bool(Qs[i] == Rs[i]) test_bn254_snarks_g1(ECP_ShortW_Prj[Fp[BN254_Snarks], G1]) test_bn254_snarks_g1(ECP_ShortW_Jac[Fp[BN254_Snarks], G1])