diff options
Diffstat (limited to 'src/crypto/elliptic/p256_generic.go')
| -rw-r--r-- | src/crypto/elliptic/p256_generic.go | 475 |
1 files changed, 469 insertions, 6 deletions
diff --git a/src/crypto/elliptic/p256_generic.go b/src/crypto/elliptic/p256_generic.go index 7f8fab5398..22dde23109 100644 --- a/src/crypto/elliptic/p256_generic.go +++ b/src/crypto/elliptic/p256_generic.go @@ -1,14 +1,477 @@ -// Copyright 2016 The Go Authors. All rights reserved. +// Copyright 2013 The Go Authors. All rights reserved. // Use of this source code is governed by a BSD-style // license that can be found in the LICENSE file. -//go:build !amd64 && !s390x && !arm64 && !ppc64le +//go:build !amd64 && !arm64 package elliptic -var p256 p256Curve +// This file contains a constant-time, 32-bit implementation of P256. -func initP256Arch() { - // Use pure Go implementation. - p256 = p256Curve{p256Params} +import "math/big" + +type p256Curve struct { + *CurveParams +} + +func (curve p256Curve) Params() *CurveParams { + return curve.CurveParams +} + +// p256GetScalar endian-swaps the big-endian scalar value from in and writes it +// to out. If the scalar is equal or greater than the order of the group, it's +// reduced modulo that order. +func p256GetScalar(out *[32]byte, in []byte) { + n := new(big.Int).SetBytes(in) + var scalarBytes []byte + + if n.Cmp(p256Params.N) >= 0 || len(in) > len(out) { + n.Mod(n, p256Params.N) + scalarBytes = n.Bytes() + } else { + scalarBytes = in + } + + for i, v := range scalarBytes { + out[len(scalarBytes)-(1+i)] = v + } +} + +func (p256Curve) ScalarBaseMult(scalar []byte) (x, y *big.Int) { + var scalarReversed [32]byte + p256GetScalar(&scalarReversed, scalar) + + var x1, y1, z1 [p256Limbs]uint32 + p256ScalarBaseMult(&x1, &y1, &z1, &scalarReversed) + return p256ToAffine(&x1, &y1, &z1) +} + +func (p256Curve) ScalarMult(bigX, bigY *big.Int, scalar []byte) (x, y *big.Int) { + var scalarReversed [32]byte + p256GetScalar(&scalarReversed, scalar) + + var px, py, x1, y1, z1 [p256Limbs]uint32 + p256FromBig(&px, bigX) + p256FromBig(&py, bigY) + p256ScalarMult(&x1, &y1, &z1, &px, &py, &scalarReversed) + return p256ToAffine(&x1, &y1, &z1) +} + +// p256Precomputed contains precomputed values to aid the calculation of scalar +// multiples of the base point, G. It's actually two, equal length, tables +// concatenated. +// +// The first table contains (x,y) field element pairs for 16 multiples of the +// base point, G. +// +// Index | Index (binary) | Value +// 0 | 0000 | 0G (all zeros, omitted) +// 1 | 0001 | G +// 2 | 0010 | 2**64G +// 3 | 0011 | 2**64G + G +// 4 | 0100 | 2**128G +// 5 | 0101 | 2**128G + G +// 6 | 0110 | 2**128G + 2**64G +// 7 | 0111 | 2**128G + 2**64G + G +// 8 | 1000 | 2**192G +// 9 | 1001 | 2**192G + G +// 10 | 1010 | 2**192G + 2**64G +// 11 | 1011 | 2**192G + 2**64G + G +// 12 | 1100 | 2**192G + 2**128G +// 13 | 1101 | 2**192G + 2**128G + G +// 14 | 1110 | 2**192G + 2**128G + 2**64G +// 15 | 1111 | 2**192G + 2**128G + 2**64G + G +// +// The second table follows the same style, but the terms are 2**32G, +// 2**96G, 2**160G, 2**224G. +// +// This is ~2KB of data. +var p256Precomputed = [p256Limbs * 2 * 15 * 2]uint32{ + 0x11522878, 0xe730d41, 0xdb60179, 0x4afe2ff, 0x12883add, 0xcaddd88, 0x119e7edc, 0xd4a6eab, 0x3120bee, + 0x1d2aac15, 0xf25357c, 0x19e45cdd, 0x5c721d0, 0x1992c5a5, 0xa237487, 0x154ba21, 0x14b10bb, 0xae3fe3, + 0xd41a576, 0x922fc51, 0x234994f, 0x60b60d3, 0x164586ae, 0xce95f18, 0x1fe49073, 0x3fa36cc, 0x5ebcd2c, + 0xb402f2f, 0x15c70bf, 0x1561925c, 0x5a26704, 0xda91e90, 0xcdc1c7f, 0x1ea12446, 0xe1ade1e, 0xec91f22, + 0x26f7778, 0x566847e, 0xa0bec9e, 0x234f453, 0x1a31f21a, 0xd85e75c, 0x56c7109, 0xa267a00, 0xb57c050, + 0x98fb57, 0xaa837cc, 0x60c0792, 0xcfa5e19, 0x61bab9e, 0x589e39b, 0xa324c5, 0x7d6dee7, 0x2976e4b, + 0x1fc4124a, 0xa8c244b, 0x1ce86762, 0xcd61c7e, 0x1831c8e0, 0x75774e1, 0x1d96a5a9, 0x843a649, 0xc3ab0fa, + 0x6e2e7d5, 0x7673a2a, 0x178b65e8, 0x4003e9b, 0x1a1f11c2, 0x7816ea, 0xf643e11, 0x58c43df, 0xf423fc2, + 0x19633ffa, 0x891f2b2, 0x123c231c, 0x46add8c, 0x54700dd, 0x59e2b17, 0x172db40f, 0x83e277d, 0xb0dd609, + 0xfd1da12, 0x35c6e52, 0x19ede20c, 0xd19e0c0, 0x97d0f40, 0xb015b19, 0x449e3f5, 0xe10c9e, 0x33ab581, + 0x56a67ab, 0x577734d, 0x1dddc062, 0xc57b10d, 0x149b39d, 0x26a9e7b, 0xc35df9f, 0x48764cd, 0x76dbcca, + 0xca4b366, 0xe9303ab, 0x1a7480e7, 0x57e9e81, 0x1e13eb50, 0xf466cf3, 0x6f16b20, 0x4ba3173, 0xc168c33, + 0x15cb5439, 0x6a38e11, 0x73658bd, 0xb29564f, 0x3f6dc5b, 0x53b97e, 0x1322c4c0, 0x65dd7ff, 0x3a1e4f6, + 0x14e614aa, 0x9246317, 0x1bc83aca, 0xad97eed, 0xd38ce4a, 0xf82b006, 0x341f077, 0xa6add89, 0x4894acd, + 0x9f162d5, 0xf8410ef, 0x1b266a56, 0xd7f223, 0x3e0cb92, 0xe39b672, 0x6a2901a, 0x69a8556, 0x7e7c0, + 0x9b7d8d3, 0x309a80, 0x1ad05f7f, 0xc2fb5dd, 0xcbfd41d, 0x9ceb638, 0x1051825c, 0xda0cf5b, 0x812e881, + 0x6f35669, 0x6a56f2c, 0x1df8d184, 0x345820, 0x1477d477, 0x1645db1, 0xbe80c51, 0xc22be3e, 0xe35e65a, + 0x1aeb7aa0, 0xc375315, 0xf67bc99, 0x7fdd7b9, 0x191fc1be, 0x61235d, 0x2c184e9, 0x1c5a839, 0x47a1e26, + 0xb7cb456, 0x93e225d, 0x14f3c6ed, 0xccc1ac9, 0x17fe37f3, 0x4988989, 0x1a90c502, 0x2f32042, 0xa17769b, + 0xafd8c7c, 0x8191c6e, 0x1dcdb237, 0x16200c0, 0x107b32a1, 0x66c08db, 0x10d06a02, 0x3fc93, 0x5620023, + 0x16722b27, 0x68b5c59, 0x270fcfc, 0xfad0ecc, 0xe5de1c2, 0xeab466b, 0x2fc513c, 0x407f75c, 0xbaab133, + 0x9705fe9, 0xb88b8e7, 0x734c993, 0x1e1ff8f, 0x19156970, 0xabd0f00, 0x10469ea7, 0x3293ac0, 0xcdc98aa, + 0x1d843fd, 0xe14bfe8, 0x15be825f, 0x8b5212, 0xeb3fb67, 0x81cbd29, 0xbc62f16, 0x2b6fcc7, 0xf5a4e29, + 0x13560b66, 0xc0b6ac2, 0x51ae690, 0xd41e271, 0xf3e9bd4, 0x1d70aab, 0x1029f72, 0x73e1c35, 0xee70fbc, + 0xad81baf, 0x9ecc49a, 0x86c741e, 0xfe6be30, 0x176752e7, 0x23d416, 0x1f83de85, 0x27de188, 0x66f70b8, + 0x181cd51f, 0x96b6e4c, 0x188f2335, 0xa5df759, 0x17a77eb6, 0xfeb0e73, 0x154ae914, 0x2f3ec51, 0x3826b59, + 0xb91f17d, 0x1c72949, 0x1362bf0a, 0xe23fddf, 0xa5614b0, 0xf7d8f, 0x79061, 0x823d9d2, 0x8213f39, + 0x1128ae0b, 0xd095d05, 0xb85c0c2, 0x1ecb2ef, 0x24ddc84, 0xe35e901, 0x18411a4a, 0xf5ddc3d, 0x3786689, + 0x52260e8, 0x5ae3564, 0x542b10d, 0x8d93a45, 0x19952aa4, 0x996cc41, 0x1051a729, 0x4be3499, 0x52b23aa, + 0x109f307e, 0x6f5b6bb, 0x1f84e1e7, 0x77a0cfa, 0x10c4df3f, 0x25a02ea, 0xb048035, 0xe31de66, 0xc6ecaa3, + 0x28ea335, 0x2886024, 0x1372f020, 0xf55d35, 0x15e4684c, 0xf2a9e17, 0x1a4a7529, 0xcb7beb1, 0xb2a78a1, + 0x1ab21f1f, 0x6361ccf, 0x6c9179d, 0xb135627, 0x1267b974, 0x4408bad, 0x1cbff658, 0xe3d6511, 0xc7d76f, + 0x1cc7a69, 0xe7ee31b, 0x54fab4f, 0x2b914f, 0x1ad27a30, 0xcd3579e, 0xc50124c, 0x50daa90, 0xb13f72, + 0xb06aa75, 0x70f5cc6, 0x1649e5aa, 0x84a5312, 0x329043c, 0x41c4011, 0x13d32411, 0xb04a838, 0xd760d2d, + 0x1713b532, 0xbaa0c03, 0x84022ab, 0x6bcf5c1, 0x2f45379, 0x18ae070, 0x18c9e11e, 0x20bca9a, 0x66f496b, + 0x3eef294, 0x67500d2, 0xd7f613c, 0x2dbbeb, 0xb741038, 0xe04133f, 0x1582968d, 0xbe985f7, 0x1acbc1a, + 0x1a6a939f, 0x33e50f6, 0xd665ed4, 0xb4b7bd6, 0x1e5a3799, 0x6b33847, 0x17fa56ff, 0x65ef930, 0x21dc4a, + 0x2b37659, 0x450fe17, 0xb357b65, 0xdf5efac, 0x15397bef, 0x9d35a7f, 0x112ac15f, 0x624e62e, 0xa90ae2f, + 0x107eecd2, 0x1f69bbe, 0x77d6bce, 0x5741394, 0x13c684fc, 0x950c910, 0x725522b, 0xdc78583, 0x40eeabb, + 0x1fde328a, 0xbd61d96, 0xd28c387, 0x9e77d89, 0x12550c40, 0x759cb7d, 0x367ef34, 0xae2a960, 0x91b8bdc, + 0x93462a9, 0xf469ef, 0xb2e9aef, 0xd2ca771, 0x54e1f42, 0x7aaa49, 0x6316abb, 0x2413c8e, 0x5425bf9, + 0x1bed3e3a, 0xf272274, 0x1f5e7326, 0x6416517, 0xea27072, 0x9cedea7, 0x6e7633, 0x7c91952, 0xd806dce, + 0x8e2a7e1, 0xe421e1a, 0x418c9e1, 0x1dbc890, 0x1b395c36, 0xa1dc175, 0x1dc4ef73, 0x8956f34, 0xe4b5cf2, + 0x1b0d3a18, 0x3194a36, 0x6c2641f, 0xe44124c, 0xa2f4eaa, 0xa8c25ba, 0xf927ed7, 0x627b614, 0x7371cca, + 0xba16694, 0x417bc03, 0x7c0a7e3, 0x9c35c19, 0x1168a205, 0x8b6b00d, 0x10e3edc9, 0x9c19bf2, 0x5882229, + 0x1b2b4162, 0xa5cef1a, 0x1543622b, 0x9bd433e, 0x364e04d, 0x7480792, 0x5c9b5b3, 0xe85ff25, 0x408ef57, + 0x1814cfa4, 0x121b41b, 0xd248a0f, 0x3b05222, 0x39bb16a, 0xc75966d, 0xa038113, 0xa4a1769, 0x11fbc6c, + 0x917e50e, 0xeec3da8, 0x169d6eac, 0x10c1699, 0xa416153, 0xf724912, 0x15cd60b7, 0x4acbad9, 0x5efc5fa, + 0xf150ed7, 0x122b51, 0x1104b40a, 0xcb7f442, 0xfbb28ff, 0x6ac53ca, 0x196142cc, 0x7bf0fa9, 0x957651, + 0x4e0f215, 0xed439f8, 0x3f46bd5, 0x5ace82f, 0x110916b6, 0x6db078, 0xffd7d57, 0xf2ecaac, 0xca86dec, + 0x15d6b2da, 0x965ecc9, 0x1c92b4c2, 0x1f3811, 0x1cb080f5, 0x2d8b804, 0x19d1c12d, 0xf20bd46, 0x1951fa7, + 0xa3656c3, 0x523a425, 0xfcd0692, 0xd44ddc8, 0x131f0f5b, 0xaf80e4a, 0xcd9fc74, 0x99bb618, 0x2db944c, + 0xa673090, 0x1c210e1, 0x178c8d23, 0x1474383, 0x10b8743d, 0x985a55b, 0x2e74779, 0x576138, 0x9587927, + 0x133130fa, 0xbe05516, 0x9f4d619, 0xbb62570, 0x99ec591, 0xd9468fe, 0x1d07782d, 0xfc72e0b, 0x701b298, + 0x1863863b, 0x85954b8, 0x121a0c36, 0x9e7fedf, 0xf64b429, 0x9b9d71e, 0x14e2f5d8, 0xf858d3a, 0x942eea8, + 0xda5b765, 0x6edafff, 0xa9d18cc, 0xc65e4ba, 0x1c747e86, 0xe4ea915, 0x1981d7a1, 0x8395659, 0x52ed4e2, + 0x87d43b7, 0x37ab11b, 0x19d292ce, 0xf8d4692, 0x18c3053f, 0x8863e13, 0x4c146c0, 0x6bdf55a, 0x4e4457d, + 0x16152289, 0xac78ec2, 0x1a59c5a2, 0x2028b97, 0x71c2d01, 0x295851f, 0x404747b, 0x878558d, 0x7d29aa4, + 0x13d8341f, 0x8daefd7, 0x139c972d, 0x6b7ea75, 0xd4a9dde, 0xff163d8, 0x81d55d7, 0xa5bef68, 0xb7b30d8, + 0xbe73d6f, 0xaa88141, 0xd976c81, 0x7e7a9cc, 0x18beb771, 0xd773cbd, 0x13f51951, 0x9d0c177, 0x1c49a78, +} + +// Group operations: +// +// Elements of the elliptic curve group are represented in Jacobian +// coordinates: (x, y, z). An affine point (x', y') is x'=x/z**2, y'=y/z**3 in +// Jacobian form. + +// p256PointDouble sets {xOut,yOut,zOut} = 2*{x,y,z}. +// +// See https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#doubling-dbl-2009-l +func p256PointDouble(xOut, yOut, zOut, x, y, z *[p256Limbs]uint32) { + var delta, gamma, alpha, beta, tmp, tmp2 [p256Limbs]uint32 + + p256Square(&delta, z) + p256Square(&gamma, y) + p256Mul(&beta, x, &gamma) + + p256Sum(&tmp, x, &delta) + p256Diff(&tmp2, x, &delta) + p256Mul(&alpha, &tmp, &tmp2) + p256Scalar3(&alpha) + + p256Sum(&tmp, y, z) + p256Square(&tmp, &tmp) + p256Diff(&tmp, &tmp, &gamma) + p256Diff(zOut, &tmp, &delta) + + p256Scalar4(&beta) + p256Square(xOut, &alpha) + p256Diff(xOut, xOut, &beta) + p256Diff(xOut, xOut, &beta) + + p256Diff(&tmp, &beta, xOut) + p256Mul(&tmp, &alpha, &tmp) + p256Square(&tmp2, &gamma) + p256Scalar8(&tmp2) + p256Diff(yOut, &tmp, &tmp2) +} + +// p256PointAddMixed sets {xOut,yOut,zOut} = {x1,y1,z1} + {x2,y2,1}. +// (i.e. the second point is affine.) +// +// See https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl +// +// Note that this function does not handle P+P, infinity+P nor P+infinity +// correctly. +func p256PointAddMixed(xOut, yOut, zOut, x1, y1, z1, x2, y2 *[p256Limbs]uint32) { + var z1z1, z1z1z1, s2, u2, h, i, j, r, rr, v, tmp [p256Limbs]uint32 + + p256Square(&z1z1, z1) + p256Sum(&tmp, z1, z1) + + p256Mul(&u2, x2, &z1z1) + p256Mul(&z1z1z1, z1, &z1z1) + p256Mul(&s2, y2, &z1z1z1) + p256Diff(&h, &u2, x1) + p256Sum(&i, &h, &h) + p256Square(&i, &i) + p256Mul(&j, &h, &i) + p256Diff(&r, &s2, y1) + p256Sum(&r, &r, &r) + p256Mul(&v, x1, &i) + + p256Mul(zOut, &tmp, &h) + p256Square(&rr, &r) + p256Diff(xOut, &rr, &j) + p256Diff(xOut, xOut, &v) + p256Diff(xOut, xOut, &v) + + p256Diff(&tmp, &v, xOut) + p256Mul(yOut, &tmp, &r) + p256Mul(&tmp, y1, &j) + p256Diff(yOut, yOut, &tmp) + p256Diff(yOut, yOut, &tmp) +} + +// p256PointAdd sets {xOut,yOut,zOut} = {x1,y1,z1} + {x2,y2,z2}. +// +// See https://www.hyperelliptic.org/EFD/g1p/auto-shortw-jacobian-0.html#addition-add-2007-bl +// +// Note that this function does not handle P+P, infinity+P nor P+infinity +// correctly. +func p256PointAdd(xOut, yOut, zOut, x1, y1, z1, x2, y2, z2 *[p256Limbs]uint32) { + var z1z1, z1z1z1, z2z2, z2z2z2, s1, s2, u1, u2, h, i, j, r, rr, v, tmp [p256Limbs]uint32 + + p256Square(&z1z1, z1) + p256Square(&z2z2, z2) + p256Mul(&u1, x1, &z2z2) + + p256Sum(&tmp, z1, z2) + p256Square(&tmp, &tmp) + p256Diff(&tmp, &tmp, &z1z1) + p256Diff(&tmp, &tmp, &z2z2) + + p256Mul(&z2z2z2, z2, &z2z2) + p256Mul(&s1, y1, &z2z2z2) + + p256Mul(&u2, x2, &z1z1) + p256Mul(&z1z1z1, z1, &z1z1) + p256Mul(&s2, y2, &z1z1z1) + p256Diff(&h, &u2, &u1) + p256Sum(&i, &h, &h) + p256Square(&i, &i) + p256Mul(&j, &h, &i) + p256Diff(&r, &s2, &s1) + p256Sum(&r, &r, &r) + p256Mul(&v, &u1, &i) + + p256Mul(zOut, &tmp, &h) + p256Square(&rr, &r) + p256Diff(xOut, &rr, &j) + p256Diff(xOut, xOut, &v) + p256Diff(xOut, xOut, &v) + + p256Diff(&tmp, &v, xOut) + p256Mul(yOut, &tmp, &r) + p256Mul(&tmp, &s1, &j) + p256Diff(yOut, yOut, &tmp) + p256Diff(yOut, yOut, &tmp) +} + +// p256SelectAffinePoint sets {out_x,out_y} to the index'th entry of table. +// +// On entry: index < 16, table[0] must be zero. +func p256SelectAffinePoint(xOut, yOut *[p256Limbs]uint32, table []uint32, index uint32) { + for i := range xOut { + xOut[i] = 0 + } + for i := range yOut { + yOut[i] = 0 + } + + for i := uint32(1); i < 16; i++ { + mask := i ^ index + mask |= mask >> 2 + mask |= mask >> 1 + mask &= 1 + mask-- + for j := range xOut { + xOut[j] |= table[0] & mask + table = table[1:] + } + for j := range yOut { + yOut[j] |= table[0] & mask + table = table[1:] + } + } +} + +// p256SelectJacobianPoint sets {out_x,out_y,out_z} to the index'th entry of +// table. +// +// On entry: index < 16, table[0] must be zero. +func p256SelectJacobianPoint(xOut, yOut, zOut *[p256Limbs]uint32, table *[16][3][p256Limbs]uint32, index uint32) { + for i := range xOut { + xOut[i] = 0 + } + for i := range yOut { + yOut[i] = 0 + } + for i := range zOut { + zOut[i] = 0 + } + + // The implicit value at index 0 is all zero. We don't need to perform that + // iteration of the loop because we already set out_* to zero. + for i := uint32(1); i < 16; i++ { + mask := i ^ index + mask |= mask >> 2 + mask |= mask >> 1 + mask &= 1 + mask-- + for j := range xOut { + xOut[j] |= table[i][0][j] & mask + } + for j := range yOut { + yOut[j] |= table[i][1][j] & mask + } + for j := range zOut { + zOut[j] |= table[i][2][j] & mask + } + } +} + +// p256GetBit returns the bit'th bit of scalar. +func p256GetBit(scalar *[32]uint8, bit uint) uint32 { + return uint32(((scalar[bit>>3]) >> (bit & 7)) & 1) +} + +// p256ScalarBaseMult sets {xOut,yOut,zOut} = scalar*G where scalar is a +// little-endian number. Note that the value of scalar must be less than the +// order of the group. +func p256ScalarBaseMult(xOut, yOut, zOut *[p256Limbs]uint32, scalar *[32]uint8) { + nIsInfinityMask := ^uint32(0) + var pIsNoninfiniteMask, mask, tableOffset uint32 + var px, py, tx, ty, tz [p256Limbs]uint32 + + for i := range xOut { + xOut[i] = 0 + } + for i := range yOut { + yOut[i] = 0 + } + for i := range zOut { + zOut[i] = 0 + } + + // The loop adds bits at positions 0, 64, 128 and 192, followed by + // positions 32,96,160 and 224 and does this 32 times. + for i := uint(0); i < 32; i++ { + if i != 0 { + p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) + } + tableOffset = 0 + for j := uint(0); j <= 32; j += 32 { + bit0 := p256GetBit(scalar, 31-i+j) + bit1 := p256GetBit(scalar, 95-i+j) + bit2 := p256GetBit(scalar, 159-i+j) + bit3 := p256GetBit(scalar, 223-i+j) + index := bit0 | (bit1 << 1) | (bit2 << 2) | (bit3 << 3) + + p256SelectAffinePoint(&px, &py, p256Precomputed[tableOffset:], index) + tableOffset += 30 * p256Limbs + + // Since scalar is less than the order of the group, we know that + // {xOut,yOut,zOut} != {px,py,1}, unless both are zero, which we handle + // below. + p256PointAddMixed(&tx, &ty, &tz, xOut, yOut, zOut, &px, &py) + // The result of pointAddMixed is incorrect if {xOut,yOut,zOut} is zero + // (a.k.a. the point at infinity). We handle that situation by + // copying the point from the table. + p256CopyConditional(xOut, &px, nIsInfinityMask) + p256CopyConditional(yOut, &py, nIsInfinityMask) + p256CopyConditional(zOut, &p256One, nIsInfinityMask) + + // Equally, the result is also wrong if the point from the table is + // zero, which happens when the index is zero. We handle that by + // only copying from {tx,ty,tz} to {xOut,yOut,zOut} if index != 0. + pIsNoninfiniteMask = nonZeroToAllOnes(index) + mask = pIsNoninfiniteMask & ^nIsInfinityMask + p256CopyConditional(xOut, &tx, mask) + p256CopyConditional(yOut, &ty, mask) + p256CopyConditional(zOut, &tz, mask) + // If p was not zero, then n is now non-zero. + nIsInfinityMask &^= pIsNoninfiniteMask + } + } +} + +// p256PointToAffine converts a Jacobian point to an affine point. If the input +// is the point at infinity then it returns (0, 0) in constant time. +func p256PointToAffine(xOut, yOut, x, y, z *[p256Limbs]uint32) { + var zInv, zInvSq [p256Limbs]uint32 + + p256Invert(&zInv, z) + p256Square(&zInvSq, &zInv) + p256Mul(xOut, x, &zInvSq) + p256Mul(&zInv, &zInv, &zInvSq) + p256Mul(yOut, y, &zInv) +} + +// p256ToAffine returns a pair of *big.Int containing the affine representation +// of {x,y,z}. +func p256ToAffine(x, y, z *[p256Limbs]uint32) (xOut, yOut *big.Int) { + var xx, yy [p256Limbs]uint32 + p256PointToAffine(&xx, &yy, x, y, z) + return p256ToBig(&xx), p256ToBig(&yy) +} + +// p256ScalarMult sets {xOut,yOut,zOut} = scalar*{x,y}. +func p256ScalarMult(xOut, yOut, zOut, x, y *[p256Limbs]uint32, scalar *[32]uint8) { + var px, py, pz, tx, ty, tz [p256Limbs]uint32 + var precomp [16][3][p256Limbs]uint32 + var nIsInfinityMask, index, pIsNoninfiniteMask, mask uint32 + + // We precompute 0,1,2,... times {x,y}. + precomp[1][0] = *x + precomp[1][1] = *y + precomp[1][2] = p256One + + for i := 2; i < 16; i += 2 { + p256PointDouble(&precomp[i][0], &precomp[i][1], &precomp[i][2], &precomp[i/2][0], &precomp[i/2][1], &precomp[i/2][2]) + p256PointAddMixed(&precomp[i+1][0], &precomp[i+1][1], &precomp[i+1][2], &precomp[i][0], &precomp[i][1], &precomp[i][2], x, y) + } + + for i := range xOut { + xOut[i] = 0 + } + for i := range yOut { + yOut[i] = 0 + } + for i := range zOut { + zOut[i] = 0 + } + nIsInfinityMask = ^uint32(0) + + // We add in a window of four bits each iteration and do this 64 times. + for i := 0; i < 64; i++ { + if i != 0 { + p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) + p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) + p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) + p256PointDouble(xOut, yOut, zOut, xOut, yOut, zOut) + } + + index = uint32(scalar[31-i/2]) + if (i & 1) == 1 { + index &= 15 + } else { + index >>= 4 + } + + // See the comments in scalarBaseMult about handling infinities. + p256SelectJacobianPoint(&px, &py, &pz, &precomp, index) + p256PointAdd(&tx, &ty, &tz, xOut, yOut, zOut, &px, &py, &pz) + p256CopyConditional(xOut, &px, nIsInfinityMask) + p256CopyConditional(yOut, &py, nIsInfinityMask) + p256CopyConditional(zOut, &pz, nIsInfinityMask) + + pIsNoninfiniteMask = nonZeroToAllOnes(index) + mask = pIsNoninfiniteMask & ^nIsInfinityMask + p256CopyConditional(xOut, &tx, mask) + p256CopyConditional(yOut, &ty, mask) + p256CopyConditional(zOut, &tz, mask) + nIsInfinityMask &^= pIsNoninfiniteMask + } } |