// Copyright (c) 2014-2015, The Monero Project // // All rights reserved. // // Redistribution and use in source and binary forms, with or without modification, are // permitted provided that the following conditions are met: // // 1. Redistributions of source code must retain the above copyright notice, this list of // conditions and the following disclaimer. // // 2. Redistributions in binary form must reproduce the above copyright notice, this list // of conditions and the following disclaimer in the documentation and/or other // materials provided with the distribution. // // 3. Neither the name of the copyright holder nor the names of its contributors may be // used to endorse or promote products derived from this software without specific // prior written permission. // // THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS" AND ANY // EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF // MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL // THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, // SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, // PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS // INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, // STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF // THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE. // // Parts of this file are originally copyright (c) 2012-2013 The Cryptonote developers #include #include #include "warnings.h" #include "crypto-ops.h" DISABLE_VS_WARNINGS(4146 4244) /* Predeclarations */ static void fe_mul(fe, const fe, const fe); static void fe_sq(fe, const fe); static void fe_tobytes(unsigned char *, const fe); static void ge_madd(ge_p1p1 *, const ge_p3 *, const ge_precomp *); static void ge_msub(ge_p1p1 *, const ge_p3 *, const ge_precomp *); static void ge_p2_0(ge_p2 *); static void ge_p3_dbl(ge_p1p1 *, const ge_p3 *); static void ge_sub(ge_p1p1 *, const ge_p3 *, const ge_cached *); static void fe_divpowm1(fe, const fe, const fe); /* Common functions */ static uint64_t load_3(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; return result; } static uint64_t load_4(const unsigned char *in) { uint64_t result; result = (uint64_t) in[0]; result |= ((uint64_t) in[1]) << 8; result |= ((uint64_t) in[2]) << 16; result |= ((uint64_t) in[3]) << 24; return result; } /* From fe_0.c */ /* h = 0 */ static void fe_0(fe h) { h[0] = 0; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } /* From fe_1.c */ /* h = 1 */ static void fe_1(fe h) { h[0] = 1; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } /* From fe_add.c */ /* h = f + g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static void fe_add(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t h0 = f0 + g0; int32_t h1 = f1 + g1; int32_t h2 = f2 + g2; int32_t h3 = f3 + g3; int32_t h4 = f4 + g4; int32_t h5 = f5 + g5; int32_t h6 = f6 + g6; int32_t h7 = f7 + g7; int32_t h8 = f8 + g8; int32_t h9 = f9 + g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* From fe_cmov.c */ /* Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0. Preconditions: b in {0,1}. */ static void fe_cmov(fe f, const fe g, unsigned int b) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t x0 = f0 ^ g0; int32_t x1 = f1 ^ g1; int32_t x2 = f2 ^ g2; int32_t x3 = f3 ^ g3; int32_t x4 = f4 ^ g4; int32_t x5 = f5 ^ g5; int32_t x6 = f6 ^ g6; int32_t x7 = f7 ^ g7; int32_t x8 = f8 ^ g8; int32_t x9 = f9 ^ g9; assert((((b - 1) & ~b) | ((b - 2) & ~(b - 1))) == (unsigned int) -1); b = -b; x0 &= b; x1 &= b; x2 &= b; x3 &= b; x4 &= b; x5 &= b; x6 &= b; x7 &= b; x8 &= b; x9 &= b; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; } /* From fe_copy.c */ /* h = f */ static void fe_copy(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; h[0] = f0; h[1] = f1; h[2] = f2; h[3] = f3; h[4] = f4; h[5] = f5; h[6] = f6; h[7] = f7; h[8] = f8; h[9] = f9; } /* From fe_invert.c */ static void fe_invert(fe out, const fe z) { fe t0; fe t1; fe t2; fe t3; int i; fe_sq(t0, z); fe_sq(t1, t0); fe_sq(t1, t1); fe_mul(t1, z, t1); fe_mul(t0, t0, t1); fe_sq(t2, t0); fe_mul(t1, t1, t2); fe_sq(t2, t1); for (i = 0; i < 4; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t2, t1); for (i = 0; i < 9; ++i) { fe_sq(t2, t2); } fe_mul(t2, t2, t1); fe_sq(t3, t2); for (i = 0; i < 19; ++i) { fe_sq(t3, t3); } fe_mul(t2, t3, t2); fe_sq(t2, t2); for (i = 0; i < 9; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t2, t1); for (i = 0; i < 49; ++i) { fe_sq(t2, t2); } fe_mul(t2, t2, t1); fe_sq(t3, t2); for (i = 0; i < 99; ++i) { fe_sq(t3, t3); } fe_mul(t2, t3, t2); fe_sq(t2, t2); for (i = 0; i < 49; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); fe_sq(t1, t1); for (i = 0; i < 4; ++i) { fe_sq(t1, t1); } fe_mul(out, t1, t0); return; } /* From fe_isnegative.c */ /* return 1 if f is in {1,3,5,...,q-2} return 0 if f is in {0,2,4,...,q-1} Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static int fe_isnegative(const fe f) { unsigned char s[32]; fe_tobytes(s, f); return s[0] & 1; } /* From fe_isnonzero.c, modified */ static int fe_isnonzero(const fe f) { unsigned char s[32]; fe_tobytes(s, f); return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1; } /* From fe_mul.c */ /* h = f * g Can overlap h with f or g. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. |g| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* Notes on implementation strategy: Using schoolbook multiplication. Karatsuba would save a little in some cost models. Most multiplications by 2 and 19 are 32-bit precomputations; cheaper than 64-bit postcomputations. There is one remaining multiplication by 19 in the carry chain; one *19 precomputation can be merged into this, but the resulting data flow is considerably less clean. There are 12 carries below. 10 of them are 2-way parallelizable and vectorizable. Can get away with 11 carries, but then data flow is much deeper. With tighter constraints on inputs can squeeze carries into int32. */ static void fe_mul(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t g1_19 = 19 * g1; /* 1.959375*2^29 */ int32_t g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ int32_t g3_19 = 19 * g3; int32_t g4_19 = 19 * g4; int32_t g5_19 = 19 * g5; int32_t g6_19 = 19 * g6; int32_t g7_19 = 19 * g7; int32_t g8_19 = 19 * g8; int32_t g9_19 = 19 * g9; int32_t f1_2 = 2 * f1; int32_t f3_2 = 2 * f3; int32_t f5_2 = 2 * f5; int32_t f7_2 = 2 * f7; int32_t f9_2 = 2 * f9; int64_t f0g0 = f0 * (int64_t) g0; int64_t f0g1 = f0 * (int64_t) g1; int64_t f0g2 = f0 * (int64_t) g2; int64_t f0g3 = f0 * (int64_t) g3; int64_t f0g4 = f0 * (int64_t) g4; int64_t f0g5 = f0 * (int64_t) g5; int64_t f0g6 = f0 * (int64_t) g6; int64_t f0g7 = f0 * (int64_t) g7; int64_t f0g8 = f0 * (int64_t) g8; int64_t f0g9 = f0 * (int64_t) g9; int64_t f1g0 = f1 * (int64_t) g0; int64_t f1g1_2 = f1_2 * (int64_t) g1; int64_t f1g2 = f1 * (int64_t) g2; int64_t f1g3_2 = f1_2 * (int64_t) g3; int64_t f1g4 = f1 * (int64_t) g4; int64_t f1g5_2 = f1_2 * (int64_t) g5; int64_t f1g6 = f1 * (int64_t) g6; int64_t f1g7_2 = f1_2 * (int64_t) g7; int64_t f1g8 = f1 * (int64_t) g8; int64_t f1g9_38 = f1_2 * (int64_t) g9_19; int64_t f2g0 = f2 * (int64_t) g0; int64_t f2g1 = f2 * (int64_t) g1; int64_t f2g2 = f2 * (int64_t) g2; int64_t f2g3 = f2 * (int64_t) g3; int64_t f2g4 = f2 * (int64_t) g4; int64_t f2g5 = f2 * (int64_t) g5; int64_t f2g6 = f2 * (int64_t) g6; int64_t f2g7 = f2 * (int64_t) g7; int64_t f2g8_19 = f2 * (int64_t) g8_19; int64_t f2g9_19 = f2 * (int64_t) g9_19; int64_t f3g0 = f3 * (int64_t) g0; int64_t f3g1_2 = f3_2 * (int64_t) g1; int64_t f3g2 = f3 * (int64_t) g2; int64_t f3g3_2 = f3_2 * (int64_t) g3; int64_t f3g4 = f3 * (int64_t) g4; int64_t f3g5_2 = f3_2 * (int64_t) g5; int64_t f3g6 = f3 * (int64_t) g6; int64_t f3g7_38 = f3_2 * (int64_t) g7_19; int64_t f3g8_19 = f3 * (int64_t) g8_19; int64_t f3g9_38 = f3_2 * (int64_t) g9_19; int64_t f4g0 = f4 * (int64_t) g0; int64_t f4g1 = f4 * (int64_t) g1; int64_t f4g2 = f4 * (int64_t) g2; int64_t f4g3 = f4 * (int64_t) g3; int64_t f4g4 = f4 * (int64_t) g4; int64_t f4g5 = f4 * (int64_t) g5; int64_t f4g6_19 = f4 * (int64_t) g6_19; int64_t f4g7_19 = f4 * (int64_t) g7_19; int64_t f4g8_19 = f4 * (int64_t) g8_19; int64_t f4g9_19 = f4 * (int64_t) g9_19; int64_t f5g0 = f5 * (int64_t) g0; int64_t f5g1_2 = f5_2 * (int64_t) g1; int64_t f5g2 = f5 * (int64_t) g2; int64_t f5g3_2 = f5_2 * (int64_t) g3; int64_t f5g4 = f5 * (int64_t) g4; int64_t f5g5_38 = f5_2 * (int64_t) g5_19; int64_t f5g6_19 = f5 * (int64_t) g6_19; int64_t f5g7_38 = f5_2 * (int64_t) g7_19; int64_t f5g8_19 = f5 * (int64_t) g8_19; int64_t f5g9_38 = f5_2 * (int64_t) g9_19; int64_t f6g0 = f6 * (int64_t) g0; int64_t f6g1 = f6 * (int64_t) g1; int64_t f6g2 = f6 * (int64_t) g2; int64_t f6g3 = f6 * (int64_t) g3; int64_t f6g4_19 = f6 * (int64_t) g4_19; int64_t f6g5_19 = f6 * (int64_t) g5_19; int64_t f6g6_19 = f6 * (int64_t) g6_19; int64_t f6g7_19 = f6 * (int64_t) g7_19; int64_t f6g8_19 = f6 * (int64_t) g8_19; int64_t f6g9_19 = f6 * (int64_t) g9_19; int64_t f7g0 = f7 * (int64_t) g0; int64_t f7g1_2 = f7_2 * (int64_t) g1; int64_t f7g2 = f7 * (int64_t) g2; int64_t f7g3_38 = f7_2 * (int64_t) g3_19; int64_t f7g4_19 = f7 * (int64_t) g4_19; int64_t f7g5_38 = f7_2 * (int64_t) g5_19; int64_t f7g6_19 = f7 * (int64_t) g6_19; int64_t f7g7_38 = f7_2 * (int64_t) g7_19; int64_t f7g8_19 = f7 * (int64_t) g8_19; int64_t f7g9_38 = f7_2 * (int64_t) g9_19; int64_t f8g0 = f8 * (int64_t) g0; int64_t f8g1 = f8 * (int64_t) g1; int64_t f8g2_19 = f8 * (int64_t) g2_19; int64_t f8g3_19 = f8 * (int64_t) g3_19; int64_t f8g4_19 = f8 * (int64_t) g4_19; int64_t f8g5_19 = f8 * (int64_t) g5_19; int64_t f8g6_19 = f8 * (int64_t) g6_19; int64_t f8g7_19 = f8 * (int64_t) g7_19; int64_t f8g8_19 = f8 * (int64_t) g8_19; int64_t f8g9_19 = f8 * (int64_t) g9_19; int64_t f9g0 = f9 * (int64_t) g0; int64_t f9g1_38 = f9_2 * (int64_t) g1_19; int64_t f9g2_19 = f9 * (int64_t) g2_19; int64_t f9g3_38 = f9_2 * (int64_t) g3_19; int64_t f9g4_19 = f9 * (int64_t) g4_19; int64_t f9g5_38 = f9_2 * (int64_t) g5_19; int64_t f9g6_19 = f9 * (int64_t) g6_19; int64_t f9g7_38 = f9_2 * (int64_t) g7_19; int64_t f9g8_19 = f9 * (int64_t) g8_19; int64_t f9g9_38 = f9_2 * (int64_t) g9_19; int64_t h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; int64_t h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; int64_t h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; int64_t h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; int64_t h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; int64_t h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; int64_t h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; int64_t h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; int64_t h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; int64_t h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; /* |h0| <= (1.65*1.65*2^52*(1+19+19+19+19)+1.65*1.65*2^50*(38+38+38+38+38)) i.e. |h0| <= 1.4*2^60; narrower ranges for h2, h4, h6, h8 |h1| <= (1.65*1.65*2^51*(1+1+19+19+19+19+19+19+19+19)) i.e. |h1| <= 1.7*2^59; narrower ranges for h3, h5, h7, h9 */ carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; /* |h0| <= 2^25 */ /* |h4| <= 2^25 */ /* |h1| <= 1.71*2^59 */ /* |h5| <= 1.71*2^59 */ carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; /* |h1| <= 2^24; from now on fits into int32 */ /* |h5| <= 2^24; from now on fits into int32 */ /* |h2| <= 1.41*2^60 */ /* |h6| <= 1.41*2^60 */ carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; /* |h2| <= 2^25; from now on fits into int32 unchanged */ /* |h6| <= 2^25; from now on fits into int32 unchanged */ /* |h3| <= 1.71*2^59 */ /* |h7| <= 1.71*2^59 */ carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; /* |h3| <= 2^24; from now on fits into int32 unchanged */ /* |h7| <= 2^24; from now on fits into int32 unchanged */ /* |h4| <= 1.72*2^34 */ /* |h8| <= 1.41*2^60 */ carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; /* |h4| <= 2^25; from now on fits into int32 unchanged */ /* |h8| <= 2^25; from now on fits into int32 unchanged */ /* |h5| <= 1.01*2^24 */ /* |h9| <= 1.71*2^59 */ carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; /* |h9| <= 2^24; from now on fits into int32 unchanged */ /* |h0| <= 1.1*2^39 */ carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; /* |h0| <= 2^25; from now on fits into int32 unchanged */ /* |h1| <= 1.01*2^24 */ h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* From fe_neg.c */ /* h = -f Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ static void fe_neg(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t h0 = -f0; int32_t h1 = -f1; int32_t h2 = -f2; int32_t h3 = -f3; int32_t h4 = -f4; int32_t h5 = -f5; int32_t h6 = -f6; int32_t h7 = -f7; int32_t h8 = -f8; int32_t h9 = -f9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* From fe_sq.c */ /* h = f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ static void fe_sq(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* From fe_sq2.c */ /* h = 2 * f * f Can overlap h with f. Preconditions: |f| bounded by 1.65*2^26,1.65*2^25,1.65*2^26,1.65*2^25,etc. Postconditions: |h| bounded by 1.01*2^25,1.01*2^24,1.01*2^25,1.01*2^24,etc. */ /* See fe_mul.c for discussion of implementation strategy. */ static void fe_sq2(fe h, const fe f) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t f0_2 = 2 * f0; int32_t f1_2 = 2 * f1; int32_t f2_2 = 2 * f2; int32_t f3_2 = 2 * f3; int32_t f4_2 = 2 * f4; int32_t f5_2 = 2 * f5; int32_t f6_2 = 2 * f6; int32_t f7_2 = 2 * f7; int32_t f5_38 = 38 * f5; /* 1.959375*2^30 */ int32_t f6_19 = 19 * f6; /* 1.959375*2^30 */ int32_t f7_38 = 38 * f7; /* 1.959375*2^30 */ int32_t f8_19 = 19 * f8; /* 1.959375*2^30 */ int32_t f9_38 = 38 * f9; /* 1.959375*2^30 */ int64_t f0f0 = f0 * (int64_t) f0; int64_t f0f1_2 = f0_2 * (int64_t) f1; int64_t f0f2_2 = f0_2 * (int64_t) f2; int64_t f0f3_2 = f0_2 * (int64_t) f3; int64_t f0f4_2 = f0_2 * (int64_t) f4; int64_t f0f5_2 = f0_2 * (int64_t) f5; int64_t f0f6_2 = f0_2 * (int64_t) f6; int64_t f0f7_2 = f0_2 * (int64_t) f7; int64_t f0f8_2 = f0_2 * (int64_t) f8; int64_t f0f9_2 = f0_2 * (int64_t) f9; int64_t f1f1_2 = f1_2 * (int64_t) f1; int64_t f1f2_2 = f1_2 * (int64_t) f2; int64_t f1f3_4 = f1_2 * (int64_t) f3_2; int64_t f1f4_2 = f1_2 * (int64_t) f4; int64_t f1f5_4 = f1_2 * (int64_t) f5_2; int64_t f1f6_2 = f1_2 * (int64_t) f6; int64_t f1f7_4 = f1_2 * (int64_t) f7_2; int64_t f1f8_2 = f1_2 * (int64_t) f8; int64_t f1f9_76 = f1_2 * (int64_t) f9_38; int64_t f2f2 = f2 * (int64_t) f2; int64_t f2f3_2 = f2_2 * (int64_t) f3; int64_t f2f4_2 = f2_2 * (int64_t) f4; int64_t f2f5_2 = f2_2 * (int64_t) f5; int64_t f2f6_2 = f2_2 * (int64_t) f6; int64_t f2f7_2 = f2_2 * (int64_t) f7; int64_t f2f8_38 = f2_2 * (int64_t) f8_19; int64_t f2f9_38 = f2 * (int64_t) f9_38; int64_t f3f3_2 = f3_2 * (int64_t) f3; int64_t f3f4_2 = f3_2 * (int64_t) f4; int64_t f3f5_4 = f3_2 * (int64_t) f5_2; int64_t f3f6_2 = f3_2 * (int64_t) f6; int64_t f3f7_76 = f3_2 * (int64_t) f7_38; int64_t f3f8_38 = f3_2 * (int64_t) f8_19; int64_t f3f9_76 = f3_2 * (int64_t) f9_38; int64_t f4f4 = f4 * (int64_t) f4; int64_t f4f5_2 = f4_2 * (int64_t) f5; int64_t f4f6_38 = f4_2 * (int64_t) f6_19; int64_t f4f7_38 = f4 * (int64_t) f7_38; int64_t f4f8_38 = f4_2 * (int64_t) f8_19; int64_t f4f9_38 = f4 * (int64_t) f9_38; int64_t f5f5_38 = f5 * (int64_t) f5_38; int64_t f5f6_38 = f5_2 * (int64_t) f6_19; int64_t f5f7_76 = f5_2 * (int64_t) f7_38; int64_t f5f8_38 = f5_2 * (int64_t) f8_19; int64_t f5f9_76 = f5_2 * (int64_t) f9_38; int64_t f6f6_19 = f6 * (int64_t) f6_19; int64_t f6f7_38 = f6 * (int64_t) f7_38; int64_t f6f8_38 = f6_2 * (int64_t) f8_19; int64_t f6f9_38 = f6 * (int64_t) f9_38; int64_t f7f7_38 = f7 * (int64_t) f7_38; int64_t f7f8_38 = f7_2 * (int64_t) f8_19; int64_t f7f9_76 = f7_2 * (int64_t) f9_38; int64_t f8f8_19 = f8 * (int64_t) f8_19; int64_t f8f9_38 = f8 * (int64_t) f9_38; int64_t f9f9_38 = f9 * (int64_t) f9_38; int64_t h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; int64_t h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; int64_t h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; int64_t h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; int64_t h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; int64_t h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; int64_t h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; int64_t h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; int64_t h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; int64_t h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; h0 += h0; h1 += h1; h2 += h2; h3 += h3; h4 += h4; h5 += h5; h6 += h6; h7 += h7; h8 += h8; h9 += h9; carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* From fe_sub.c */ /* h = f - g Can overlap h with f or g. Preconditions: |f| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. |g| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. Postconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static void fe_sub(fe h, const fe f, const fe g) { int32_t f0 = f[0]; int32_t f1 = f[1]; int32_t f2 = f[2]; int32_t f3 = f[3]; int32_t f4 = f[4]; int32_t f5 = f[5]; int32_t f6 = f[6]; int32_t f7 = f[7]; int32_t f8 = f[8]; int32_t f9 = f[9]; int32_t g0 = g[0]; int32_t g1 = g[1]; int32_t g2 = g[2]; int32_t g3 = g[3]; int32_t g4 = g[4]; int32_t g5 = g[5]; int32_t g6 = g[6]; int32_t g7 = g[7]; int32_t g8 = g[8]; int32_t g9 = g[9]; int32_t h0 = f0 - g0; int32_t h1 = f1 - g1; int32_t h2 = f2 - g2; int32_t h3 = f3 - g3; int32_t h4 = f4 - g4; int32_t h5 = f5 - g5; int32_t h6 = f6 - g6; int32_t h7 = f7 - g7; int32_t h8 = f8 - g8; int32_t h9 = f9 - g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* From fe_tobytes.c */ /* Preconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Write p=2^255-19; q=floor(h/p). Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). Proof: Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). Then 0> 25; q = (h0 + q) >> 26; q = (h1 + q) >> 25; q = (h2 + q) >> 26; q = (h3 + q) >> 25; q = (h4 + q) >> 26; q = (h5 + q) >> 25; q = (h6 + q) >> 26; q = (h7 + q) >> 25; q = (h8 + q) >> 26; q = (h9 + q) >> 25; /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ h0 += 19 * q; /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = h9 >> 25; h9 -= carry9 << 25; /* h10 = carry9 */ /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. Have h0+...+2^230 h9 between 0 and 2^255-1; evidently 2^255 h10-2^255 q = 0. Goal: Output h0+...+2^230 h9. */ s[0] = h0 >> 0; s[1] = h0 >> 8; s[2] = h0 >> 16; s[3] = (h0 >> 24) | (h1 << 2); s[4] = h1 >> 6; s[5] = h1 >> 14; s[6] = (h1 >> 22) | (h2 << 3); s[7] = h2 >> 5; s[8] = h2 >> 13; s[9] = (h2 >> 21) | (h3 << 5); s[10] = h3 >> 3; s[11] = h3 >> 11; s[12] = (h3 >> 19) | (h4 << 6); s[13] = h4 >> 2; s[14] = h4 >> 10; s[15] = h4 >> 18; s[16] = h5 >> 0; s[17] = h5 >> 8; s[18] = h5 >> 16; s[19] = (h5 >> 24) | (h6 << 1); s[20] = h6 >> 7; s[21] = h6 >> 15; s[22] = (h6 >> 23) | (h7 << 3); s[23] = h7 >> 5; s[24] = h7 >> 13; s[25] = (h7 >> 21) | (h8 << 4); s[26] = h8 >> 4; s[27] = h8 >> 12; s[28] = (h8 >> 20) | (h9 << 6); s[29] = h9 >> 2; s[30] = h9 >> 10; s[31] = h9 >> 18; } /* From ge_add.c */ void ge_add(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->YplusX); fe_mul(r->Y, r->Y, q->YminusX); fe_mul(r->T, q->T2d, p->T); fe_mul(r->X, p->Z, q->Z); fe_add(t0, r->X, r->X); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_add(r->Z, t0, r->T); fe_sub(r->T, t0, r->T); } /* From ge_double_scalarmult.c, modified */ static void slide(signed char *r, const unsigned char *a) { int i; int b; int k; for (i = 0; i < 256; ++i) { r[i] = 1 & (a[i >> 3] >> (i & 7)); } for (i = 0; i < 256; ++i) { if (r[i]) { for (b = 1; b <= 6 && i + b < 256; ++b) { if (r[i + b]) { if (r[i] + (r[i + b] << b) <= 15) { r[i] += r[i + b] << b; r[i + b] = 0; } else if (r[i] - (r[i + b] << b) >= -15) { r[i] -= r[i + b] << b; for (k = i + b; k < 256; ++k) { if (!r[k]) { r[k] = 1; break; } r[k] = 0; } } else break; } } } } } void ge_dsm_precomp(ge_dsmp r, const ge_p3 *s) { ge_p1p1 t; ge_p3 s2, u; ge_p3_to_cached(&r[0], s); ge_p3_dbl(&t, s); ge_p1p1_to_p3(&s2, &t); ge_add(&t, &s2, &r[0]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[1], &u); ge_add(&t, &s2, &r[1]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[2], &u); ge_add(&t, &s2, &r[2]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[3], &u); ge_add(&t, &s2, &r[3]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[4], &u); ge_add(&t, &s2, &r[4]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[5], &u); ge_add(&t, &s2, &r[5]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[6], &u); ge_add(&t, &s2, &r[6]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&r[7], &u); } /* r = a * A + b * B where a = a[0]+256*a[1]+...+256^31 a[31]. and b = b[0]+256*b[1]+...+256^31 b[31]. B is the Ed25519 base point (x,4/5) with x positive. */ void ge_double_scalarmult_base_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b) { signed char aslide[256]; signed char bslide[256]; ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ ge_p1p1 t; ge_p3 u; int i; slide(aslide, a); slide(bslide, b); ge_dsm_precomp(Ai, A); ge_p2_0(r); for (i = 255; i >= 0; --i) { if (aslide[i] || bslide[i]) break; } for (; i >= 0; --i) { ge_p2_dbl(&t, r); if (aslide[i] > 0) { ge_p1p1_to_p3(&u, &t); ge_add(&t, &u, &Ai[aslide[i]/2]); } else if (aslide[i] < 0) { ge_p1p1_to_p3(&u, &t); ge_sub(&t, &u, &Ai[(-aslide[i])/2]); } if (bslide[i] > 0) { ge_p1p1_to_p3(&u, &t); ge_madd(&t, &u, &ge_Bi[bslide[i]/2]); } else if (bslide[i] < 0) { ge_p1p1_to_p3(&u, &t); ge_msub(&t, &u, &ge_Bi[(-bslide[i])/2]); } ge_p1p1_to_p2(r, &t); } } /* From ge_frombytes.c, modified */ int ge_frombytes_vartime(ge_p3 *h, const unsigned char *s) { fe u; fe v; fe vxx; fe check; /* From fe_frombytes.c */ int64_t h0 = load_4(s); int64_t h1 = load_3(s + 4) << 6; int64_t h2 = load_3(s + 7) << 5; int64_t h3 = load_3(s + 10) << 3; int64_t h4 = load_3(s + 13) << 2; int64_t h5 = load_4(s + 16); int64_t h6 = load_3(s + 20) << 7; int64_t h7 = load_3(s + 23) << 5; int64_t h8 = load_3(s + 26) << 4; int64_t h9 = (load_3(s + 29) & 8388607) << 2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; /* Validate the number to be canonical */ if (h9 == 33554428 && h8 == 268435440 && h7 == 536870880 && h6 == 2147483520 && h5 == 4294967295 && h4 == 67108860 && h3 == 134217720 && h2 == 536870880 && h1 == 1073741760 && h0 >= 4294967277) { return -1; } carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; h->Y[0] = h0; h->Y[1] = h1; h->Y[2] = h2; h->Y[3] = h3; h->Y[4] = h4; h->Y[5] = h5; h->Y[6] = h6; h->Y[7] = h7; h->Y[8] = h8; h->Y[9] = h9; /* End fe_frombytes.c */ fe_1(h->Z); fe_sq(u, h->Y); fe_mul(v, u, fe_d); fe_sub(u, u, h->Z); /* u = y^2-1 */ fe_add(v, v, h->Z); /* v = dy^2+1 */ fe_divpowm1(h->X, u, v); /* x = uv^3(uv^7)^((q-5)/8) */ fe_sq(vxx, h->X); fe_mul(vxx, vxx, v); fe_sub(check, vxx, u); /* vx^2-u */ if (fe_isnonzero(check)) { fe_add(check, vxx, u); /* vx^2+u */ if (fe_isnonzero(check)) { return -1; } fe_mul(h->X, h->X, fe_sqrtm1); } if (fe_isnegative(h->X) != (s[31] >> 7)) { /* If x = 0, the sign must be positive */ if (!fe_isnonzero(h->X)) { return -1; } fe_neg(h->X, h->X); } fe_mul(h->T, h->X, h->Y); return 0; } /* From ge_madd.c */ /* r = p + q */ static void ge_madd(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->yplusx); fe_mul(r->Y, r->Y, q->yminusx); fe_mul(r->T, q->xy2d, p->T); fe_add(t0, p->Z, p->Z); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_add(r->Z, t0, r->T); fe_sub(r->T, t0, r->T); } /* From ge_msub.c */ /* r = p - q */ static void ge_msub(ge_p1p1 *r, const ge_p3 *p, const ge_precomp *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->yminusx); fe_mul(r->Y, r->Y, q->yplusx); fe_mul(r->T, q->xy2d, p->T); fe_add(t0, p->Z, p->Z); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_sub(r->Z, t0, r->T); fe_add(r->T, t0, r->T); } /* From ge_p1p1_to_p2.c */ /* r = p */ void ge_p1p1_to_p2(ge_p2 *r, const ge_p1p1 *p) { fe_mul(r->X, p->X, p->T); fe_mul(r->Y, p->Y, p->Z); fe_mul(r->Z, p->Z, p->T); } /* From ge_p1p1_to_p3.c */ /* r = p */ void ge_p1p1_to_p3(ge_p3 *r, const ge_p1p1 *p) { fe_mul(r->X, p->X, p->T); fe_mul(r->Y, p->Y, p->Z); fe_mul(r->Z, p->Z, p->T); fe_mul(r->T, p->X, p->Y); } /* From ge_p2_0.c */ static void ge_p2_0(ge_p2 *h) { fe_0(h->X); fe_1(h->Y); fe_1(h->Z); } /* From ge_p2_dbl.c */ /* r = 2 * p */ void ge_p2_dbl(ge_p1p1 *r, const ge_p2 *p) { fe t0; fe_sq(r->X, p->X); fe_sq(r->Z, p->Y); fe_sq2(r->T, p->Z); fe_add(r->Y, p->X, p->Y); fe_sq(t0, r->Y); fe_add(r->Y, r->Z, r->X); fe_sub(r->Z, r->Z, r->X); fe_sub(r->X, t0, r->Y); fe_sub(r->T, r->T, r->Z); } /* From ge_p3_0.c */ static void ge_p3_0(ge_p3 *h) { fe_0(h->X); fe_1(h->Y); fe_1(h->Z); fe_0(h->T); } /* From ge_p3_dbl.c */ /* r = 2 * p */ static void ge_p3_dbl(ge_p1p1 *r, const ge_p3 *p) { ge_p2 q; ge_p3_to_p2(&q, p); ge_p2_dbl(r, &q); } /* From ge_p3_to_cached.c */ /* r = p */ void ge_p3_to_cached(ge_cached *r, const ge_p3 *p) { fe_add(r->YplusX, p->Y, p->X); fe_sub(r->YminusX, p->Y, p->X); fe_copy(r->Z, p->Z); fe_mul(r->T2d, p->T, fe_d2); } /* From ge_p3_to_p2.c */ /* r = p */ void ge_p3_to_p2(ge_p2 *r, const ge_p3 *p) { fe_copy(r->X, p->X); fe_copy(r->Y, p->Y); fe_copy(r->Z, p->Z); } /* From ge_p3_tobytes.c */ void ge_p3_tobytes(unsigned char *s, const ge_p3 *h) { fe recip; fe x; fe y; fe_invert(recip, h->Z); fe_mul(x, h->X, recip); fe_mul(y, h->Y, recip); fe_tobytes(s, y); s[31] ^= fe_isnegative(x) << 7; } /* From ge_precomp_0.c */ static void ge_precomp_0(ge_precomp *h) { fe_1(h->yplusx); fe_1(h->yminusx); fe_0(h->xy2d); } /* From ge_scalarmult_base.c */ static unsigned char equal(signed char b, signed char c) { unsigned char ub = b; unsigned char uc = c; unsigned char x = ub ^ uc; /* 0: yes; 1..255: no */ uint32_t y = x; /* 0: yes; 1..255: no */ y -= 1; /* 4294967295: yes; 0..254: no */ y >>= 31; /* 1: yes; 0: no */ return y; } static unsigned char negative(signed char b) { unsigned long long x = b; /* 18446744073709551361..18446744073709551615: yes; 0..255: no */ x >>= 63; /* 1: yes; 0: no */ return x; } static void ge_precomp_cmov(ge_precomp *t, const ge_precomp *u, unsigned char b) { fe_cmov(t->yplusx, u->yplusx, b); fe_cmov(t->yminusx, u->yminusx, b); fe_cmov(t->xy2d, u->xy2d, b); } static void select(ge_precomp *t, int pos, signed char b) { ge_precomp minust; unsigned char bnegative = negative(b); unsigned char babs = b - (((-bnegative) & b) << 1); ge_precomp_0(t); ge_precomp_cmov(t, &ge_base[pos][0], equal(babs, 1)); ge_precomp_cmov(t, &ge_base[pos][1], equal(babs, 2)); ge_precomp_cmov(t, &ge_base[pos][2], equal(babs, 3)); ge_precomp_cmov(t, &ge_base[pos][3], equal(babs, 4)); ge_precomp_cmov(t, &ge_base[pos][4], equal(babs, 5)); ge_precomp_cmov(t, &ge_base[pos][5], equal(babs, 6)); ge_precomp_cmov(t, &ge_base[pos][6], equal(babs, 7)); ge_precomp_cmov(t, &ge_base[pos][7], equal(babs, 8)); fe_copy(minust.yplusx, t->yminusx); fe_copy(minust.yminusx, t->yplusx); fe_neg(minust.xy2d, t->xy2d); ge_precomp_cmov(t, &minust, bnegative); } /* h = a * B where a = a[0]+256*a[1]+...+256^31 a[31] B is the Ed25519 base point (x,4/5) with x positive. Preconditions: a[31] <= 127 */ void ge_scalarmult_base(ge_p3 *h, const unsigned char *a) { signed char e[64]; signed char carry; ge_p1p1 r; ge_p2 s; ge_precomp t; int i; for (i = 0; i < 32; ++i) { e[2 * i + 0] = (a[i] >> 0) & 15; e[2 * i + 1] = (a[i] >> 4) & 15; } /* each e[i] is between 0 and 15 */ /* e[63] is between 0 and 7 */ carry = 0; for (i = 0; i < 63; ++i) { e[i] += carry; carry = e[i] + 8; carry >>= 4; e[i] -= carry << 4; } e[63] += carry; /* each e[i] is between -8 and 8 */ ge_p3_0(h); for (i = 1; i < 64; i += 2) { select(&t, i / 2, e[i]); ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r); } ge_p3_dbl(&r, h); ge_p1p1_to_p2(&s, &r); ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r); ge_p2_dbl(&r, &s); ge_p1p1_to_p2(&s, &r); ge_p2_dbl(&r, &s); ge_p1p1_to_p3(h, &r); for (i = 0; i < 64; i += 2) { select(&t, i / 2, e[i]); ge_madd(&r, h, &t); ge_p1p1_to_p3(h, &r); } } /* From ge_sub.c */ /* r = p - q */ static void ge_sub(ge_p1p1 *r, const ge_p3 *p, const ge_cached *q) { fe t0; fe_add(r->X, p->Y, p->X); fe_sub(r->Y, p->Y, p->X); fe_mul(r->Z, r->X, q->YminusX); fe_mul(r->Y, r->Y, q->YplusX); fe_mul(r->T, q->T2d, p->T); fe_mul(r->X, p->Z, q->Z); fe_add(t0, r->X, r->X); fe_sub(r->X, r->Z, r->Y); fe_add(r->Y, r->Z, r->Y); fe_sub(r->Z, t0, r->T); fe_add(r->T, t0, r->T); } /* From ge_tobytes.c */ void ge_tobytes(unsigned char *s, const ge_p2 *h) { fe recip; fe x; fe y; fe_invert(recip, h->Z); fe_mul(x, h->X, recip); fe_mul(y, h->Y, recip); fe_tobytes(s, y); s[31] ^= fe_isnegative(x) << 7; } /* From sc_reduce.c */ /* Input: s[0]+256*s[1]+...+256^63*s[63] = s Output: s[0]+256*s[1]+...+256^31*s[31] = s mod l where l = 2^252 + 27742317777372353535851937790883648493. Overwrites s in place. */ void sc_reduce(unsigned char *s) { int64_t s0 = 2097151 & load_3(s); int64_t s1 = 2097151 & (load_4(s + 2) >> 5); int64_t s2 = 2097151 & (load_3(s + 5) >> 2); int64_t s3 = 2097151 & (load_4(s + 7) >> 7); int64_t s4 = 2097151 & (load_4(s + 10) >> 4); int64_t s5 = 2097151 & (load_3(s + 13) >> 1); int64_t s6 = 2097151 & (load_4(s + 15) >> 6); int64_t s7 = 2097151 & (load_3(s + 18) >> 3); int64_t s8 = 2097151 & load_3(s + 21); int64_t s9 = 2097151 & (load_4(s + 23) >> 5); int64_t s10 = 2097151 & (load_3(s + 26) >> 2); int64_t s11 = 2097151 & (load_4(s + 28) >> 7); int64_t s12 = 2097151 & (load_4(s + 31) >> 4); int64_t s13 = 2097151 & (load_3(s + 34) >> 1); int64_t s14 = 2097151 & (load_4(s + 36) >> 6); int64_t s15 = 2097151 & (load_3(s + 39) >> 3); int64_t s16 = 2097151 & load_3(s + 42); int64_t s17 = 2097151 & (load_4(s + 44) >> 5); int64_t s18 = 2097151 & (load_3(s + 47) >> 2); int64_t s19 = 2097151 & (load_4(s + 49) >> 7); int64_t s20 = 2097151 & (load_4(s + 52) >> 4); int64_t s21 = 2097151 & (load_3(s + 55) >> 1); int64_t s22 = 2097151 & (load_4(s + 57) >> 6); int64_t s23 = (load_4(s + 60) >> 3); int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; int64_t carry12; int64_t carry13; int64_t carry14; int64_t carry15; int64_t carry16; s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 << 5); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 << 2); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 << 7); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 << 4); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 << 1); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 << 6); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 << 3); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 << 5); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 << 2); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 << 7); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } /* New code */ static void fe_divpowm1(fe r, const fe u, const fe v) { fe v3, uv7, t0, t1, t2; int i; fe_sq(v3, v); fe_mul(v3, v3, v); /* v3 = v^3 */ fe_sq(uv7, v3); fe_mul(uv7, uv7, v); fe_mul(uv7, uv7, u); /* uv7 = uv^7 */ /*fe_pow22523(uv7, uv7);*/ /* From fe_pow22523.c */ fe_sq(t0, uv7); fe_sq(t1, t0); fe_sq(t1, t1); fe_mul(t1, uv7, t1); fe_mul(t0, t0, t1); fe_sq(t0, t0); fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 0; i < 4; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 0; i < 9; ++i) { fe_sq(t1, t1); } fe_mul(t1, t1, t0); fe_sq(t2, t1); for (i = 0; i < 19; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); for (i = 0; i < 10; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t1, t0); for (i = 0; i < 49; ++i) { fe_sq(t1, t1); } fe_mul(t1, t1, t0); fe_sq(t2, t1); for (i = 0; i < 99; ++i) { fe_sq(t2, t2); } fe_mul(t1, t2, t1); for (i = 0; i < 50; ++i) { fe_sq(t1, t1); } fe_mul(t0, t1, t0); fe_sq(t0, t0); fe_sq(t0, t0); fe_mul(t0, t0, uv7); /* End fe_pow22523.c */ /* t0 = (uv^7)^((q-5)/8) */ fe_mul(t0, t0, v3); fe_mul(r, t0, u); /* u^(m+1)v^(-(m+1)) */ } static void ge_cached_0(ge_cached *r) { fe_1(r->YplusX); fe_1(r->YminusX); fe_1(r->Z); fe_0(r->T2d); } static void ge_cached_cmov(ge_cached *t, const ge_cached *u, unsigned char b) { fe_cmov(t->YplusX, u->YplusX, b); fe_cmov(t->YminusX, u->YminusX, b); fe_cmov(t->Z, u->Z, b); fe_cmov(t->T2d, u->T2d, b); } /* Assumes that a[31] <= 127 */ void ge_scalarmult(ge_p2 *r, const unsigned char *a, const ge_p3 *A) { signed char e[64]; int carry, carry2, i; ge_cached Ai[8]; /* 1 * A, 2 * A, ..., 8 * A */ ge_p1p1 t; ge_p3 u; carry = 0; /* 0..1 */ for (i = 0; i < 31; i++) { carry += a[i]; /* 0..256 */ carry2 = (carry + 8) >> 4; /* 0..16 */ e[2 * i] = carry - (carry2 << 4); /* -8..7 */ carry = (carry2 + 8) >> 4; /* 0..1 */ e[2 * i + 1] = carry2 - (carry << 4); /* -8..7 */ } carry += a[31]; /* 0..128 */ carry2 = (carry + 8) >> 4; /* 0..8 */ e[62] = carry - (carry2 << 4); /* -8..7 */ e[63] = carry2; /* 0..8 */ ge_p3_to_cached(&Ai[0], A); for (i = 0; i < 7; i++) { ge_add(&t, A, &Ai[i]); ge_p1p1_to_p3(&u, &t); ge_p3_to_cached(&Ai[i + 1], &u); } ge_p2_0(r); for (i = 63; i >= 0; i--) { signed char b = e[i]; unsigned char bnegative = negative(b); unsigned char babs = b - (((-bnegative) & b) << 1); ge_cached cur, minuscur; ge_p2_dbl(&t, r); ge_p1p1_to_p2(r, &t); ge_p2_dbl(&t, r); ge_p1p1_to_p2(r, &t); ge_p2_dbl(&t, r); ge_p1p1_to_p2(r, &t); ge_p2_dbl(&t, r); ge_p1p1_to_p3(&u, &t); ge_cached_0(&cur); ge_cached_cmov(&cur, &Ai[0], equal(babs, 1)); ge_cached_cmov(&cur, &Ai[1], equal(babs, 2)); ge_cached_cmov(&cur, &Ai[2], equal(babs, 3)); ge_cached_cmov(&cur, &Ai[3], equal(babs, 4)); ge_cached_cmov(&cur, &Ai[4], equal(babs, 5)); ge_cached_cmov(&cur, &Ai[5], equal(babs, 6)); ge_cached_cmov(&cur, &Ai[6], equal(babs, 7)); ge_cached_cmov(&cur, &Ai[7], equal(babs, 8)); fe_copy(minuscur.YplusX, cur.YminusX); fe_copy(minuscur.YminusX, cur.YplusX); fe_copy(minuscur.Z, cur.Z); fe_neg(minuscur.T2d, cur.T2d); ge_cached_cmov(&cur, &minuscur, bnegative); ge_add(&t, &u, &cur); ge_p1p1_to_p2(r, &t); } } void ge_double_scalarmult_precomp_vartime(ge_p2 *r, const unsigned char *a, const ge_p3 *A, const unsigned char *b, const ge_dsmp Bi) { signed char aslide[256]; signed char bslide[256]; ge_dsmp Ai; /* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ ge_p1p1 t; ge_p3 u; int i; slide(aslide, a); slide(bslide, b); ge_dsm_precomp(Ai, A); ge_p2_0(r); for (i = 255; i >= 0; --i) { if (aslide[i] || bslide[i]) break; } for (; i >= 0; --i) { ge_p2_dbl(&t, r); if (aslide[i] > 0) { ge_p1p1_to_p3(&u, &t); ge_add(&t, &u, &Ai[aslide[i]/2]); } else if (aslide[i] < 0) { ge_p1p1_to_p3(&u, &t); ge_sub(&t, &u, &Ai[(-aslide[i])/2]); } if (bslide[i] > 0) { ge_p1p1_to_p3(&u, &t); ge_add(&t, &u, &Bi[bslide[i]/2]); } else if (bslide[i] < 0) { ge_p1p1_to_p3(&u, &t); ge_sub(&t, &u, &Bi[(-bslide[i])/2]); } ge_p1p1_to_p2(r, &t); } } void ge_mul8(ge_p1p1 *r, const ge_p2 *t) { ge_p2 u; ge_p2_dbl(r, t); ge_p1p1_to_p2(&u, r); ge_p2_dbl(r, &u); ge_p1p1_to_p2(&u, r); ge_p2_dbl(r, &u); } void ge_fromfe_frombytes_vartime(ge_p2 *r, const unsigned char *s) { fe u, v, w, x, y, z; unsigned char sign; /* From fe_frombytes.c */ int64_t h0 = load_4(s); int64_t h1 = load_3(s + 4) << 6; int64_t h2 = load_3(s + 7) << 5; int64_t h3 = load_3(s + 10) << 3; int64_t h4 = load_3(s + 13) << 2; int64_t h5 = load_4(s + 16); int64_t h6 = load_3(s + 20) << 7; int64_t h7 = load_3(s + 23) << 5; int64_t h8 = load_3(s + 26) << 4; int64_t h9 = load_3(s + 29) << 2; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; carry9 = (h9 + (int64_t) (1<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (int64_t) (1<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (int64_t) (1<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (int64_t) (1<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (int64_t) (1<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (int64_t) (1<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (int64_t) (1<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (int64_t) (1<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (int64_t) (1<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (int64_t) (1<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; u[0] = h0; u[1] = h1; u[2] = h2; u[3] = h3; u[4] = h4; u[5] = h5; u[6] = h6; u[7] = h7; u[8] = h8; u[9] = h9; /* End fe_frombytes.c */ fe_sq2(v, u); /* 2 * u^2 */ fe_1(w); fe_add(w, v, w); /* w = 2 * u^2 + 1 */ fe_sq(x, w); /* w^2 */ fe_mul(y, fe_ma2, v); /* -2 * A^2 * u^2 */ fe_add(x, x, y); /* x = w^2 - 2 * A^2 * u^2 */ fe_divpowm1(r->X, w, x); /* (w / x)^(m + 1) */ fe_sq(y, r->X); fe_mul(x, y, x); fe_sub(y, w, x); fe_copy(z, fe_ma); if (fe_isnonzero(y)) { fe_add(y, w, x); if (fe_isnonzero(y)) { goto negative; } else { fe_mul(r->X, r->X, fe_fffb1); } } else { fe_mul(r->X, r->X, fe_fffb2); } fe_mul(r->X, r->X, u); /* u * sqrt(2 * A * (A + 2) * w / x) */ fe_mul(z, z, v); /* -2 * A * u^2 */ sign = 0; goto setsign; negative: fe_mul(x, x, fe_sqrtm1); fe_sub(y, w, x); if (fe_isnonzero(y)) { assert((fe_add(y, w, x), !fe_isnonzero(y))); fe_mul(r->X, r->X, fe_fffb3); } else { fe_mul(r->X, r->X, fe_fffb4); } /* r->X = sqrt(A * (A + 2) * w / x) */ /* z = -A */ sign = 1; setsign: if (fe_isnegative(r->X) != sign) { assert(fe_isnonzero(r->X)); fe_neg(r->X, r->X); } fe_add(r->Z, z, w); fe_sub(r->Y, z, w); fe_mul(r->X, r->X, r->Z); #if !defined(NDEBUG) { fe check_x, check_y, check_iz, check_v; fe_invert(check_iz, r->Z); fe_mul(check_x, r->X, check_iz); fe_mul(check_y, r->Y, check_iz); fe_sq(check_x, check_x); fe_sq(check_y, check_y); fe_mul(check_v, check_x, check_y); fe_mul(check_v, fe_d, check_v); fe_add(check_v, check_v, check_x); fe_sub(check_v, check_v, check_y); fe_1(check_x); fe_add(check_v, check_v, check_x); assert(!fe_isnonzero(check_v)); } #endif } void sc_0(unsigned char *s) { int i; for (i = 0; i < 32; i++) { s[i] = 0; } } void sc_reduce32(unsigned char *s) { int64_t s0 = 2097151 & load_3(s); int64_t s1 = 2097151 & (load_4(s + 2) >> 5); int64_t s2 = 2097151 & (load_3(s + 5) >> 2); int64_t s3 = 2097151 & (load_4(s + 7) >> 7); int64_t s4 = 2097151 & (load_4(s + 10) >> 4); int64_t s5 = 2097151 & (load_3(s + 13) >> 1); int64_t s6 = 2097151 & (load_4(s + 15) >> 6); int64_t s7 = 2097151 & (load_3(s + 18) >> 3); int64_t s8 = 2097151 & load_3(s + 21); int64_t s9 = 2097151 & (load_4(s + 23) >> 5); int64_t s10 = 2097151 & (load_3(s + 26) >> 2); int64_t s11 = (load_4(s + 28) >> 7); int64_t s12 = 0; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 << 5); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 << 2); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 << 7); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 << 4); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 << 1); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 << 6); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 << 3); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 << 5); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 << 2); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 << 7); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } void sc_add(unsigned char *s, const unsigned char *a, const unsigned char *b) { int64_t a0 = 2097151 & load_3(a); int64_t a1 = 2097151 & (load_4(a + 2) >> 5); int64_t a2 = 2097151 & (load_3(a + 5) >> 2); int64_t a3 = 2097151 & (load_4(a + 7) >> 7); int64_t a4 = 2097151 & (load_4(a + 10) >> 4); int64_t a5 = 2097151 & (load_3(a + 13) >> 1); int64_t a6 = 2097151 & (load_4(a + 15) >> 6); int64_t a7 = 2097151 & (load_3(a + 18) >> 3); int64_t a8 = 2097151 & load_3(a + 21); int64_t a9 = 2097151 & (load_4(a + 23) >> 5); int64_t a10 = 2097151 & (load_3(a + 26) >> 2); int64_t a11 = (load_4(a + 28) >> 7); int64_t b0 = 2097151 & load_3(b); int64_t b1 = 2097151 & (load_4(b + 2) >> 5); int64_t b2 = 2097151 & (load_3(b + 5) >> 2); int64_t b3 = 2097151 & (load_4(b + 7) >> 7); int64_t b4 = 2097151 & (load_4(b + 10) >> 4); int64_t b5 = 2097151 & (load_3(b + 13) >> 1); int64_t b6 = 2097151 & (load_4(b + 15) >> 6); int64_t b7 = 2097151 & (load_3(b + 18) >> 3); int64_t b8 = 2097151 & load_3(b + 21); int64_t b9 = 2097151 & (load_4(b + 23) >> 5); int64_t b10 = 2097151 & (load_3(b + 26) >> 2); int64_t b11 = (load_4(b + 28) >> 7); int64_t s0 = a0 + b0; int64_t s1 = a1 + b1; int64_t s2 = a2 + b2; int64_t s3 = a3 + b3; int64_t s4 = a4 + b4; int64_t s5 = a5 + b5; int64_t s6 = a6 + b6; int64_t s7 = a7 + b7; int64_t s8 = a8 + b8; int64_t s9 = a9 + b9; int64_t s10 = a10 + b10; int64_t s11 = a11 + b11; int64_t s12 = 0; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 << 5); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 << 2); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 << 7); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 << 4); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 << 1); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 << 6); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 << 3); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 << 5); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 << 2); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 << 7); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } void sc_sub(unsigned char *s, const unsigned char *a, const unsigned char *b) { int64_t a0 = 2097151 & load_3(a); int64_t a1 = 2097151 & (load_4(a + 2) >> 5); int64_t a2 = 2097151 & (load_3(a + 5) >> 2); int64_t a3 = 2097151 & (load_4(a + 7) >> 7); int64_t a4 = 2097151 & (load_4(a + 10) >> 4); int64_t a5 = 2097151 & (load_3(a + 13) >> 1); int64_t a6 = 2097151 & (load_4(a + 15) >> 6); int64_t a7 = 2097151 & (load_3(a + 18) >> 3); int64_t a8 = 2097151 & load_3(a + 21); int64_t a9 = 2097151 & (load_4(a + 23) >> 5); int64_t a10 = 2097151 & (load_3(a + 26) >> 2); int64_t a11 = (load_4(a + 28) >> 7); int64_t b0 = 2097151 & load_3(b); int64_t b1 = 2097151 & (load_4(b + 2) >> 5); int64_t b2 = 2097151 & (load_3(b + 5) >> 2); int64_t b3 = 2097151 & (load_4(b + 7) >> 7); int64_t b4 = 2097151 & (load_4(b + 10) >> 4); int64_t b5 = 2097151 & (load_3(b + 13) >> 1); int64_t b6 = 2097151 & (load_4(b + 15) >> 6); int64_t b7 = 2097151 & (load_3(b + 18) >> 3); int64_t b8 = 2097151 & load_3(b + 21); int64_t b9 = 2097151 & (load_4(b + 23) >> 5); int64_t b10 = 2097151 & (load_3(b + 26) >> 2); int64_t b11 = (load_4(b + 28) >> 7); int64_t s0 = a0 - b0; int64_t s1 = a1 - b1; int64_t s2 = a2 - b2; int64_t s3 = a3 - b3; int64_t s4 = a4 - b4; int64_t s5 = a5 - b5; int64_t s6 = a6 - b6; int64_t s7 = a7 - b7; int64_t s8 = a8 - b8; int64_t s9 = a9 - b9; int64_t s10 = a10 - b10; int64_t s11 = a11 - b11; int64_t s12 = 0; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 << 5); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 << 2); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 << 7); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 << 4); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 << 1); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 << 6); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 << 3); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 << 5); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 << 2); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 << 7); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } /* Input: a[0]+256*a[1]+...+256^31*a[31] = a b[0]+256*b[1]+...+256^31*b[31] = b c[0]+256*c[1]+...+256^31*c[31] = c Output: s[0]+256*s[1]+...+256^31*s[31] = (c-ab) mod l where l = 2^252 + 27742317777372353535851937790883648493. */ void sc_mulsub(unsigned char *s, const unsigned char *a, const unsigned char *b, const unsigned char *c) { int64_t a0 = 2097151 & load_3(a); int64_t a1 = 2097151 & (load_4(a + 2) >> 5); int64_t a2 = 2097151 & (load_3(a + 5) >> 2); int64_t a3 = 2097151 & (load_4(a + 7) >> 7); int64_t a4 = 2097151 & (load_4(a + 10) >> 4); int64_t a5 = 2097151 & (load_3(a + 13) >> 1); int64_t a6 = 2097151 & (load_4(a + 15) >> 6); int64_t a7 = 2097151 & (load_3(a + 18) >> 3); int64_t a8 = 2097151 & load_3(a + 21); int64_t a9 = 2097151 & (load_4(a + 23) >> 5); int64_t a10 = 2097151 & (load_3(a + 26) >> 2); int64_t a11 = (load_4(a + 28) >> 7); int64_t b0 = 2097151 & load_3(b); int64_t b1 = 2097151 & (load_4(b + 2) >> 5); int64_t b2 = 2097151 & (load_3(b + 5) >> 2); int64_t b3 = 2097151 & (load_4(b + 7) >> 7); int64_t b4 = 2097151 & (load_4(b + 10) >> 4); int64_t b5 = 2097151 & (load_3(b + 13) >> 1); int64_t b6 = 2097151 & (load_4(b + 15) >> 6); int64_t b7 = 2097151 & (load_3(b + 18) >> 3); int64_t b8 = 2097151 & load_3(b + 21); int64_t b9 = 2097151 & (load_4(b + 23) >> 5); int64_t b10 = 2097151 & (load_3(b + 26) >> 2); int64_t b11 = (load_4(b + 28) >> 7); int64_t c0 = 2097151 & load_3(c); int64_t c1 = 2097151 & (load_4(c + 2) >> 5); int64_t c2 = 2097151 & (load_3(c + 5) >> 2); int64_t c3 = 2097151 & (load_4(c + 7) >> 7); int64_t c4 = 2097151 & (load_4(c + 10) >> 4); int64_t c5 = 2097151 & (load_3(c + 13) >> 1); int64_t c6 = 2097151 & (load_4(c + 15) >> 6); int64_t c7 = 2097151 & (load_3(c + 18) >> 3); int64_t c8 = 2097151 & load_3(c + 21); int64_t c9 = 2097151 & (load_4(c + 23) >> 5); int64_t c10 = 2097151 & (load_3(c + 26) >> 2); int64_t c11 = (load_4(c + 28) >> 7); int64_t s0; int64_t s1; int64_t s2; int64_t s3; int64_t s4; int64_t s5; int64_t s6; int64_t s7; int64_t s8; int64_t s9; int64_t s10; int64_t s11; int64_t s12; int64_t s13; int64_t s14; int64_t s15; int64_t s16; int64_t s17; int64_t s18; int64_t s19; int64_t s20; int64_t s21; int64_t s22; int64_t s23; int64_t carry0; int64_t carry1; int64_t carry2; int64_t carry3; int64_t carry4; int64_t carry5; int64_t carry6; int64_t carry7; int64_t carry8; int64_t carry9; int64_t carry10; int64_t carry11; int64_t carry12; int64_t carry13; int64_t carry14; int64_t carry15; int64_t carry16; int64_t carry17; int64_t carry18; int64_t carry19; int64_t carry20; int64_t carry21; int64_t carry22; s0 = c0 - a0*b0; s1 = c1 - (a0*b1 + a1*b0); s2 = c2 - (a0*b2 + a1*b1 + a2*b0); s3 = c3 - (a0*b3 + a1*b2 + a2*b1 + a3*b0); s4 = c4 - (a0*b4 + a1*b3 + a2*b2 + a3*b1 + a4*b0); s5 = c5 - (a0*b5 + a1*b4 + a2*b3 + a3*b2 + a4*b1 + a5*b0); s6 = c6 - (a0*b6 + a1*b5 + a2*b4 + a3*b3 + a4*b2 + a5*b1 + a6*b0); s7 = c7 - (a0*b7 + a1*b6 + a2*b5 + a3*b4 + a4*b3 + a5*b2 + a6*b1 + a7*b0); s8 = c8 - (a0*b8 + a1*b7 + a2*b6 + a3*b5 + a4*b4 + a5*b3 + a6*b2 + a7*b1 + a8*b0); s9 = c9 - (a0*b9 + a1*b8 + a2*b7 + a3*b6 + a4*b5 + a5*b4 + a6*b3 + a7*b2 + a8*b1 + a9*b0); s10 = c10 - (a0*b10 + a1*b9 + a2*b8 + a3*b7 + a4*b6 + a5*b5 + a6*b4 + a7*b3 + a8*b2 + a9*b1 + a10*b0); s11 = c11 - (a0*b11 + a1*b10 + a2*b9 + a3*b8 + a4*b7 + a5*b6 + a6*b5 + a7*b4 + a8*b3 + a9*b2 + a10*b1 + a11*b0); s12 = -(a1*b11 + a2*b10 + a3*b9 + a4*b8 + a5*b7 + a6*b6 + a7*b5 + a8*b4 + a9*b3 + a10*b2 + a11*b1); s13 = -(a2*b11 + a3*b10 + a4*b9 + a5*b8 + a6*b7 + a7*b6 + a8*b5 + a9*b4 + a10*b3 + a11*b2); s14 = -(a3*b11 + a4*b10 + a5*b9 + a6*b8 + a7*b7 + a8*b6 + a9*b5 + a10*b4 + a11*b3); s15 = -(a4*b11 + a5*b10 + a6*b9 + a7*b8 + a8*b7 + a9*b6 + a10*b5 + a11*b4); s16 = -(a5*b11 + a6*b10 + a7*b9 + a8*b8 + a9*b7 + a10*b6 + a11*b5); s17 = -(a6*b11 + a7*b10 + a8*b9 + a9*b8 + a10*b7 + a11*b6); s18 = -(a7*b11 + a8*b10 + a9*b9 + a10*b8 + a11*b7); s19 = -(a8*b11 + a9*b10 + a10*b9 + a11*b8); s20 = -(a9*b11 + a10*b10 + a11*b9); s21 = -(a10*b11 + a11*b10); s22 = -a11*b11; s23 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry18 = (s18 + (1<<20)) >> 21; s19 += carry18; s18 -= carry18 << 21; carry20 = (s20 + (1<<20)) >> 21; s21 += carry20; s20 -= carry20 << 21; carry22 = (s22 + (1<<20)) >> 21; s23 += carry22; s22 -= carry22 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; carry17 = (s17 + (1<<20)) >> 21; s18 += carry17; s17 -= carry17 << 21; carry19 = (s19 + (1<<20)) >> 21; s20 += carry19; s19 -= carry19 << 21; carry21 = (s21 + (1<<20)) >> 21; s22 += carry21; s21 -= carry21 << 21; s11 += s23 * 666643; s12 += s23 * 470296; s13 += s23 * 654183; s14 -= s23 * 997805; s15 += s23 * 136657; s16 -= s23 * 683901; s10 += s22 * 666643; s11 += s22 * 470296; s12 += s22 * 654183; s13 -= s22 * 997805; s14 += s22 * 136657; s15 -= s22 * 683901; s9 += s21 * 666643; s10 += s21 * 470296; s11 += s21 * 654183; s12 -= s21 * 997805; s13 += s21 * 136657; s14 -= s21 * 683901; s8 += s20 * 666643; s9 += s20 * 470296; s10 += s20 * 654183; s11 -= s20 * 997805; s12 += s20 * 136657; s13 -= s20 * 683901; s7 += s19 * 666643; s8 += s19 * 470296; s9 += s19 * 654183; s10 -= s19 * 997805; s11 += s19 * 136657; s12 -= s19 * 683901; s6 += s18 * 666643; s7 += s18 * 470296; s8 += s18 * 654183; s9 -= s18 * 997805; s10 += s18 * 136657; s11 -= s18 * 683901; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry12 = (s12 + (1<<20)) >> 21; s13 += carry12; s12 -= carry12 << 21; carry14 = (s14 + (1<<20)) >> 21; s15 += carry14; s14 -= carry14 << 21; carry16 = (s16 + (1<<20)) >> 21; s17 += carry16; s16 -= carry16 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; carry13 = (s13 + (1<<20)) >> 21; s14 += carry13; s13 -= carry13 << 21; carry15 = (s15 + (1<<20)) >> 21; s16 += carry15; s15 -= carry15 << 21; s5 += s17 * 666643; s6 += s17 * 470296; s7 += s17 * 654183; s8 -= s17 * 997805; s9 += s17 * 136657; s10 -= s17 * 683901; s4 += s16 * 666643; s5 += s16 * 470296; s6 += s16 * 654183; s7 -= s16 * 997805; s8 += s16 * 136657; s9 -= s16 * 683901; s3 += s15 * 666643; s4 += s15 * 470296; s5 += s15 * 654183; s6 -= s15 * 997805; s7 += s15 * 136657; s8 -= s15 * 683901; s2 += s14 * 666643; s3 += s14 * 470296; s4 += s14 * 654183; s5 -= s14 * 997805; s6 += s14 * 136657; s7 -= s14 * 683901; s1 += s13 * 666643; s2 += s13 * 470296; s3 += s13 * 654183; s4 -= s13 * 997805; s5 += s13 * 136657; s6 -= s13 * 683901; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = (s0 + (1<<20)) >> 21; s1 += carry0; s0 -= carry0 << 21; carry2 = (s2 + (1<<20)) >> 21; s3 += carry2; s2 -= carry2 << 21; carry4 = (s4 + (1<<20)) >> 21; s5 += carry4; s4 -= carry4 << 21; carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21; carry8 = (s8 + (1<<20)) >> 21; s9 += carry8; s8 -= carry8 << 21; carry10 = (s10 + (1<<20)) >> 21; s11 += carry10; s10 -= carry10 << 21; carry1 = (s1 + (1<<20)) >> 21; s2 += carry1; s1 -= carry1 << 21; carry3 = (s3 + (1<<20)) >> 21; s4 += carry3; s3 -= carry3 << 21; carry5 = (s5 + (1<<20)) >> 21; s6 += carry5; s5 -= carry5 << 21; carry7 = (s7 + (1<<20)) >> 21; s8 += carry7; s7 -= carry7 << 21; carry9 = (s9 + (1<<20)) >> 21; s10 += carry9; s9 -= carry9 << 21; carry11 = (s11 + (1<<20)) >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; s12 = 0; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; carry11 = s11 >> 21; s12 += carry11; s11 -= carry11 << 21; s0 += s12 * 666643; s1 += s12 * 470296; s2 += s12 * 654183; s3 -= s12 * 997805; s4 += s12 * 136657; s5 -= s12 * 683901; carry0 = s0 >> 21; s1 += carry0; s0 -= carry0 << 21; carry1 = s1 >> 21; s2 += carry1; s1 -= carry1 << 21; carry2 = s2 >> 21; s3 += carry2; s2 -= carry2 << 21; carry3 = s3 >> 21; s4 += carry3; s3 -= carry3 << 21; carry4 = s4 >> 21; s5 += carry4; s4 -= carry4 << 21; carry5 = s5 >> 21; s6 += carry5; s5 -= carry5 << 21; carry6 = s6 >> 21; s7 += carry6; s6 -= carry6 << 21; carry7 = s7 >> 21; s8 += carry7; s7 -= carry7 << 21; carry8 = s8 >> 21; s9 += carry8; s8 -= carry8 << 21; carry9 = s9 >> 21; s10 += carry9; s9 -= carry9 << 21; carry10 = s10 >> 21; s11 += carry10; s10 -= carry10 << 21; s[0] = s0 >> 0; s[1] = s0 >> 8; s[2] = (s0 >> 16) | (s1 << 5); s[3] = s1 >> 3; s[4] = s1 >> 11; s[5] = (s1 >> 19) | (s2 << 2); s[6] = s2 >> 6; s[7] = (s2 >> 14) | (s3 << 7); s[8] = s3 >> 1; s[9] = s3 >> 9; s[10] = (s3 >> 17) | (s4 << 4); s[11] = s4 >> 4; s[12] = s4 >> 12; s[13] = (s4 >> 20) | (s5 << 1); s[14] = s5 >> 7; s[15] = (s5 >> 15) | (s6 << 6); s[16] = s6 >> 2; s[17] = s6 >> 10; s[18] = (s6 >> 18) | (s7 << 3); s[19] = s7 >> 5; s[20] = s7 >> 13; s[21] = s8 >> 0; s[22] = s8 >> 8; s[23] = (s8 >> 16) | (s9 << 5); s[24] = s9 >> 3; s[25] = s9 >> 11; s[26] = (s9 >> 19) | (s10 << 2); s[27] = s10 >> 6; s[28] = (s10 >> 14) | (s11 << 7); s[29] = s11 >> 1; s[30] = s11 >> 9; s[31] = s11 >> 17; } /* Assumes that a != INT64_MIN */ static int64_t signum(int64_t a) { return (a >> 63) - ((-a) >> 63); } int sc_check(const unsigned char *s) { int64_t s0 = load_4(s); int64_t s1 = load_4(s + 4); int64_t s2 = load_4(s + 8); int64_t s3 = load_4(s + 12); int64_t s4 = load_4(s + 16); int64_t s5 = load_4(s + 20); int64_t s6 = load_4(s + 24); int64_t s7 = load_4(s + 28); return (signum(1559614444 - s0) + (signum(1477600026 - s1) << 1) + (signum(2734136534 - s2) << 2) + (signum(350157278 - s3) << 3) + (signum(-s4) << 4) + (signum(-s5) << 5) + (signum(-s6) << 6) + (signum(268435456 - s7) << 7)) >> 8; } int sc_isnonzero(const unsigned char *s) { return (((int) (s[0] | s[1] | s[2] | s[3] | s[4] | s[5] | s[6] | s[7] | s[8] | s[9] | s[10] | s[11] | s[12] | s[13] | s[14] | s[15] | s[16] | s[17] | s[18] | s[19] | s[20] | s[21] | s[22] | s[23] | s[24] | s[25] | s[26] | s[27] | s[28] | s[29] | s[30] | s[31]) - 1) >> 8) + 1; }