From 65305960326d539ca11864a377019e0fb1a72e8c Mon Sep 17 00:00:00 2001 From: Mamy Ratsimbazafy Date: Sat, 10 Oct 2020 18:53:48 +0200 Subject: [PATCH] Endomorphism acceleration for BN254-Nogami (#102) --- benchmarks/bench_ec_g1.nim | 2 +- benchmarks/bench_ec_g2.nim | 2 +- benchmarks/bench_elliptic_template.nim | 2 +- constantine.nimble | 1 + constantine/curves/bn254_nogami_glv.nim | 63 ++ constantine/curves/zoo_glv.nim | 10 +- constantine/elliptic/ec_scalar_mul.nim | 5 +- tests/t_ec_sage_bn254_nogami.nim | 36 + .../tv_BN254_Nogami_scalar_mul_G1.json | 492 +++++++++ .../tv_BN254_Nogami_scalar_mul_G2.json | 980 ++++++++++++++++++ 10 files changed, 1587 insertions(+), 6 deletions(-) create mode 100644 constantine/curves/bn254_nogami_glv.nim create mode 100644 tests/t_ec_sage_bn254_nogami.nim create mode 100644 tests/vectors/tv_BN254_Nogami_scalar_mul_G1.json create mode 100644 tests/vectors/tv_BN254_Nogami_scalar_mul_G2.json diff --git a/benchmarks/bench_ec_g1.nim b/benchmarks/bench_ec_g1.nim index 18538d6..3925474 100644 --- a/benchmarks/bench_ec_g1.nim +++ b/benchmarks/bench_ec_g1.nim @@ -32,7 +32,7 @@ const Iters = 10_000 const MulIters = 100 const AvailableCurves = [ # P224, - # BN254_Nogami, + BN254_Nogami, BN254_Snarks, # Curve25519, # P256, diff --git a/benchmarks/bench_ec_g2.nim b/benchmarks/bench_ec_g2.nim index 7cd810b..22a4829 100644 --- a/benchmarks/bench_ec_g2.nim +++ b/benchmarks/bench_ec_g2.nim @@ -33,7 +33,7 @@ const Iters = 10_000 const MulIters = 500 const AvailableCurves = [ # P224, - # BN254_Nogami, + BN254_Nogami, BN254_Snarks, # Curve25519, # P256, diff --git a/benchmarks/bench_elliptic_template.nim b/benchmarks/bench_elliptic_template.nim index e6463e6..92b2fc9 100644 --- a/benchmarks/bench_elliptic_template.nim +++ b/benchmarks/bench_elliptic_template.nim @@ -175,7 +175,7 @@ proc scalarMulGenericBench*(T: typedesc, window: static int, iters: int) = let exponent = rng.random_unsafe(BigInt[bits]) - bench("EC ScalarMul " & $bits & "-bit Generic " & G1_or_G2 & " (window = " & $window & ')', T, iters): + bench("EC ScalarMul " & $bits & "-bit " & G1_or_G2 & " (window-" & $window & ", generic)", T, iters): r = P r.scalarMulGeneric(exponent, window) diff --git a/constantine.nimble b/constantine.nimble index 4bf6248..9ad0b9e 100644 --- a/constantine.nimble +++ b/constantine.nimble @@ -114,6 +114,7 @@ const testDesc: seq[tuple[path: string, useGMP: bool]] = @[ # Elliptic curve arithmetic vs Sagemath ("tests/t_ec_frobenius.nim", false), + ("tests/t_ec_sage_bn254_nogami.nim", false), ("tests/t_ec_sage_bn254_snarks.nim", false), ("tests/t_ec_sage_bls12_377.nim", false), ("tests/t_ec_sage_bls12_381.nim", false), diff --git a/constantine/curves/bn254_nogami_glv.nim b/constantine/curves/bn254_nogami_glv.nim new file mode 100644 index 0000000..83ecf4b --- /dev/null +++ b/constantine/curves/bn254_nogami_glv.nim @@ -0,0 +1,63 @@ +# 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 + ../config/[curves, type_bigint, type_fp], + ../io/[io_bigints, io_fields] + +# BN254_Nogami G1 +# ------------------------------------------------------------ + +const BN254_Nogami_cubicRootOfUnity_mod_p* = + Fp[BN254_Nogami].fromHex"0x25236482400000017080eb4000000006181800000000000cd98000000000000b" + +const BN254_Nogami_Lattice_G1* = ( + # (BigInt, isNeg) + ((BigInt[127].fromHex"0x61818000000000020400000000000003", true), + (BigInt[64].fromHex"0x8100000000000001", false)), + ((BigInt[64].fromHex"0x8100000000000001", false), + (BigInt[127].fromHex"0x61818000000000028500000000000004", false)) +) + +const BN254_Nogami_Babai_G1* = ( + # (BigInt, isNeg) + (BigInt[130].fromHex"0x2a01fab7e04a017bd3a22fc67c12a7c5c", true), + (BigInt[66].fromHex"0x37937ca688a6b4904", false) +) + + +# BN254_Nogami G2 +# ------------------------------------------------------------ + +const BN254_Nogami_Lattice_G2* = ( + # (BigInt, isNeg) + ((BigInt[64].fromHex"0x8100000000000001", false), + (BigInt[63].fromHex"0x4080000000000001", true), + (BigInt[63].fromHex"0x4080000000000000", true), + (BigInt[63].fromHex"0x4080000000000001", true)), + ((BigInt[63].fromHex"0x4080000000000000", false), + (BigInt[63].fromHex"0x4080000000000001", false), + (BigInt[63].fromHex"0x4080000000000001", false), + (BigInt[64].fromHex"0x8100000000000002", true)), + ((BigInt[63].fromHex"0x4080000000000001", true), + (BigInt[63].fromHex"0x4080000000000001", false), + (BigInt[63].fromHex"0x4080000000000001", true), + (BigInt[64].fromHex"0x8100000000000001", true)), + ((BigInt[64].fromHex"0x8100000000000002", false), + (BigInt[63].fromHex"0x4080000000000000", false), + (BigInt[63].fromHex"0x4080000000000001", true), + (BigInt[63].fromHex"0x4080000000000001", false)) +) + +const BN254_Nogami_Babai_G2* = ( + # (BigInt, isNeg) + (BigInt[192].fromHex"0xa957fab5402a55fc0d305f177b0b3c3e78cd599c2aa84979", false), + (BigInt[192].fromHex"0xa957fab5402a55fc0d305f177b0b3c43aea10938fa493703", false), + (BigInt[192].fromHex"0xa957fab5402a55fc0d305f177b0b3c4035693ed06fddedfe", true), + (BigInt[192].fromHex"0xa957fab5402a55fead500a957fab53fbb2f05603ebd2c5d5", false) +) diff --git a/constantine/curves/zoo_glv.nim b/constantine/curves/zoo_glv.nim index 6a9f421..55e0e3f 100644 --- a/constantine/curves/zoo_glv.nim +++ b/constantine/curves/zoo_glv.nim @@ -12,7 +12,7 @@ import ../towers, ./bls12_377_glv, ./bls12_381_glv, - # ./bn254_nogami_glv, + ./bn254_nogami_glv, ./bn254_snarks_glv {.experimental: "dynamicBindSym".} @@ -35,3 +35,11 @@ template lattice*(F: typedesc[Fp or Fp2]): untyped = macro getCubicRootOfUnity_mod_p*(C: static Curve): untyped = ## Get a non-trivial cubic root of unity (mod p) with p the prime field result = bindSym($C & "_cubicRootOfUnity_mod_p") + +func hasEndomorphismAcceleration*(C: static Curve): bool = + C in { + BN254_Nogami, + BN254_Snarks, + BLS12_377, + BLS12_381 + } diff --git a/constantine/elliptic/ec_scalar_mul.nim b/constantine/elliptic/ec_scalar_mul.nim index 624784d..3e1d1dd 100644 --- a/constantine/elliptic/ec_scalar_mul.nim +++ b/constantine/elliptic/ec_scalar_mul.nim @@ -12,6 +12,7 @@ import ../arithmetic, ../towers, ../io/io_bigints, + ../curves/zoo_glv, ./ec_endomorphism_accel # ############################################################ @@ -238,9 +239,9 @@ func scalarMul*[EC]( ## Endomorphism acceleration requires: ## - Cofactor to be cleared ## - 0 <= scalar < curve order - ## this will not automatically + ## Those will be assumed to maintain constant-time property when BigInt.bits <= EC.F.C.getCurveOrderBitwidth() and - EC.F.C in {BN254_Snarks, BLS12_377, BLS12_381}: + EC.F.C.hasEndomorphismAcceleration(): when EC.F is Fp: P.scalarMulGLV_m2w2(scalar) elif EC.F is Fp2: diff --git a/tests/t_ec_sage_bn254_nogami.nim b/tests/t_ec_sage_bn254_nogami.nim new file mode 100644 index 0000000..8023e85 --- /dev/null +++ b/tests/t_ec_sage_bn254_nogami.nim @@ -0,0 +1,36 @@ +# 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 + # Internals + ../constantine/config/[type_fp, curves], + ../constantine/towers, + ../constantine/elliptic/ec_shortweierstrass_jacobian, + ../constantine/elliptic/ec_shortweierstrass_projective, + # Test utilities + ./t_ec_sage_template + +run_scalar_mul_test_vs_sage( + ECP_ShortW_Proj[Fp[BN254_Nogami], NotOnTwist], + "t_ec_sage_bn254_nogami_g1_projective" +) + +run_scalar_mul_test_vs_sage( + ECP_ShortW_Jac[Fp[BN254_Nogami], NotOnTwist], + "t_ec_sage_bn254_nogami_g1_jacobian" +) + +run_scalar_mul_test_vs_sage( + ECP_ShortW_Proj[Fp2[BN254_Nogami], OnTwist], + "t_ec_sage_bn254_nogami_g2_projective" +) + +run_scalar_mul_test_vs_sage( + ECP_ShortW_Jac[Fp2[BN254_Nogami], OnTwist], + "t_ec_sage_bn254_nogami_g2_jacobian" +) diff --git a/tests/vectors/tv_BN254_Nogami_scalar_mul_G1.json b/tests/vectors/tv_BN254_Nogami_scalar_mul_G1.json new file mode 100644 index 0000000..17233dd --- /dev/null +++ b/tests/vectors/tv_BN254_Nogami_scalar_mul_G1.json @@ -0,0 +1,492 @@ +{ + "curve": "BN254_Nogami", + "group": "G1", + "modulus": "0x2523648240000001ba344d80000000086121000000000013a700000000000013", + "order": "0x2523648240000001ba344d8000000007ff9f800000000010a10000000000000d", + "cofactor": "0x1", + "form": "short_weierstrass", + "a": "0x0", + "b": "0x2", + "vectors": [ + { + "id": 0, + "P": { + "x": "0xe08a292f940cfb361cc82bc24ca564f51453708c9745a9cf8707b11c84bc448", + "y": "0x1fc4e075b4ed6426cbec03997d19d24916de06d962498d6de12cf60e8636e047" + }, + "scalar": "0x20025a0c74b9e838a55061e47b889f590ab06860ea8ec5bc21fe0ca80f7f29a9", + "Q": { + "x": "0x980b5af72bfa4a0eef02c170031cf8fc315a9cba4c9c54339b7a210e4707d1e", + "y": "0x284c4861c0234ec9282ee3b00ef16586d5c67a84219294a16f747007acfb619" + } + }, + { + "id": 1, + "P": { + "x": "0x39bc19c41835082f86ca046b71875b051575072e4d6a4aeedac31eee34b07df", + "y": "0x2cc399530f3a93af016d1d26e5044a083d9dc9da040252589685761ba843d30" + }, + "scalar": "0x157a3e1ff9dabccced9746e19855a9438098be6d734f07d1c069aa1bd05b8d87", + "Q": { + "x": "0x1861e042361fdfef752daf293796c240f65ab237c007791e215aa1e9a5079f4c", + "y": "0xe2c33eb15582fe270ccf74c63eb8b5024228a74fa684f7708e2095020e179cc" + } + }, + { + "id": 2, + "P": { + "x": "0xdf2ff288f44313dc9ddb54de269c6424aaf7164dc5e67917066ea5dfa0d0f1e", + "y": "0x5410ad2d4b58704f7e5cf88690cfbc779d3053803aea566a0f9e3a2ecf2bd52" + }, + "scalar": "0x273bf6c679d8e880034590d16c007bbabc6c65ed870a263b5d1ce7375c18fd7", + "Q": { + "x": "0x47c572da2d5689e2fa67e9407cff8009aead7b29244d721eb93a78efa2941", + "y": "0x1c7083e1ab7eada5b4546ef603af5e8dcb3cd3e345fcdd1558c5929159a3da27" + } + }, + { + "id": 3, + "P": { + "x": "0x1cefe2112033a045a3faee0337fb38c77f24290262dd9ba8d79eb280e2f9d32a", + "y": "0x665b74188d4c06e1050cbb7aa438f6aa46cd482a445b3a91a1b1c8f08b4d662" + }, + "scalar": "0x235e630485f974edbbd138e9079eb54d06d03a50228dbdfdbaa567b1fae19f82", + "Q": { + "x": "0x529bc0e057a0ef87990e6106846ffa208d23eefdece1f57b5844d63b8f1958d", + "y": "0x1e8bb860c4e7cbe8797185902ad7bc0b58d1e2670b59ad7e28b755387206464f" + } + }, + { + "id": 4, + "P": { + "x": "0x148523f92df8d037353fd0bdc6d0febc88c9e1bc568d72c80c58438f6295dc59", + "y": "0xcb0c12d9ce7a415bc1c55879a54ca7c620f80f0e6d37e3eb0180629202a39f2" + }, + "scalar": "0x3845ad0148f76bdf14f752268eafb065c7272721784a8c6bd3a5fa736332b94", + "Q": { + "x": "0x50a411c760331eec7b1df6a314773af471ae8605de42a576ce56a376aa4b454", + "y": "0x21f8017c6aa00425971a073ed49f398c7b99e15498ab4d0415cabd833fd44755" + } + }, + { + "id": 5, + "P": { + "x": "0x1323cb93cf5f33ebf21d2c0ba56e1c39fd0e75b1623d3ab160fed44a37ee1bda", + "y": "0x12560d91f79f79c618ed649c877c817541fe1d2fe0ef4bfd4fcbd35c93617f5b" + }, + "scalar": "0x252f232224ad7d89266c28d1289098f03226fa84e7905b0df4e1f6cc4e2e897", + "Q": { + "x": "0x157f2decb5edaebb2adff666fe4d7e5d4286b5126f4ea301ba3cb7e332ca7ced", + "y": "0x23c1a82e2fce0c3bb24bc6464d10124ca76c7424a5a845d361ae4d8c5be5d2e7" + } + }, + { + "id": 6, + "P": { + "x": "0x3a7e0e36a933e9ad5732235e93cec84ae8db3104348bf24312ffcdf8e0e78a9", + "y": "0x145e2d9789d0b912bc27bacfa11940af58861be1583031a1d0fd2fdaacd65c04" + }, + "scalar": "0x175ed37fdee061c78e28d668a26add87007ab0d11ad699cba0cb13ae35b8215b", + "Q": { + "x": "0xed7ee0ade320865d11c844ad125d5c776d3d6f4424d4e95ab40258062e7b0c5", + "y": "0x3fe36be38d5bbd918c9859b66ea6da7d6a7a0020c76cd5c46363c5926007399" + } + }, + { + "id": 7, + "P": { + "x": "0x2337a09e7b42b83857758f3f4d0c2d0e21368a72b93f72ed172c413782db489f", + "y": "0x12ee0bfb064fd1cf6b76735331156f34615b10a9b494fc96159741f3015a529b" + }, + "scalar": "0x26e5ca7f4b418fc9eb7d7b7f44ed1c4357fa71695ad59299d4404c55a295d64", + "Q": { + "x": "0xd5d46a9af0cfb9d215acbdcc5289ad6fa644c11369ee711929bffa6e85a93f5", + "y": "0x792fdf3f5a6c8a370456c77f0890af6bca27cdd59e73e3aa7928cc153749bfd" + } + }, + { + "id": 8, + "P": { + "x": 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