diff options
Diffstat (limited to 'src/crypto/shen_ed25519_ref/crypto-ops-old.c')
| -rw-r--r-- | src/crypto/shen_ed25519_ref/crypto-ops-old.c | 3008 |
1 files changed, 0 insertions, 3008 deletions
diff --git a/src/crypto/shen_ed25519_ref/crypto-ops-old.c b/src/crypto/shen_ed25519_ref/crypto-ops-old.c deleted file mode 100644 index 88e6c09ac..000000000 --- a/src/crypto/shen_ed25519_ref/crypto-ops-old.c +++ /dev/null @@ -1,3008 +0,0 @@ -// 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 <stdint.h> //standard -#include <assert.h> //standard - -//#include "warnings.h" //where is this?? -#include "crypto-ops.h" //fine - -//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 */ - -//x -//u -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; -} - -//x -//u -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 -*/ - -//x -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 -*/ - -//x -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}. -*/ - -//x -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 -*/ - -//x -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 */ - -//x using fermat -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. -*/ - -//x -static int fe_isnegative(const fe f) { - unsigned char s[32]; - fe_tobytes(s, f); - return s[0] & 1; -} - -/* From fe_isnonzero.c, modified */ - -//x -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. -*/ - -//x -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. -*/ - -//x -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<y<1. - - Write r=h-pq. - Have 0<=r<=p-1=2^255-20. - Thus 0<=r+19(2^-255)r<r+19(2^-255)2^255<=2^255-1. - - Write x=r+19(2^-255)r+y. - Then 0<x<2^255 so floor(2^(-255)x) = 0 so floor(q+2^(-255)x) = q. - - Have q+2^(-255)x = 2^(-255)(h + 19 2^(-25) h9 + 2^(-1)) - so floor(2^(-255)(h + 19 2^(-25) h9 + 2^(-1))) = q. -*/ - -static void fe_tobytes(unsigned char *s, const fe h) { - int32_t h0 = h[0]; - int32_t h1 = h[1]; - int32_t h2 = h[2]; - int32_t h3 = h[3]; - int32_t h4 = h[4]; - int32_t h5 = h[5]; - int32_t h6 = h[6]; - int32_t h7 = h[7]; - int32_t h8 = h[8]; - int32_t h9 = h[9]; - int32_t q; - int32_t carry0; - int32_t carry1; - int32_t carry2; - int32_t carry3; - int32_t carry4; - int32_t carry5; - int32_t carry6; - int32_t carry7; - int32_t carry8; - int32_t carry9; - - q = (19 * h9 + (((int32_t) 1) << 24)) >> 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 */ - -//x -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; - - //this loop just makes a binary string out of a - //e.g. a = {3, 0, 0, ...} then r = 110000.... - 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; - } - } - } - } -} - -//double scalar mult precomp -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. -*/ - -//this is a really simple alg. actually -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);/* A, 3A, 5A, 7A, 9A, 11A, 13A, 15A */ - - ge_p2_0(r); - - for (i = 255; i >= 0; --i) { - //so this gets us to the highest i such that both have a nonzero - if (aslide[i] || bslide[i]) break; - } - - for (; i >= 0; --i) { - ge_p2_dbl(&t, r);//simple double and add - - 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 */ -//this is like xrecover .. -//x -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); //this is mapping X to X * sqrt(-1) c.f. 3.1 in hisil, dong, etc. - } - - 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 -*/ - -//x -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 -*/ - -//x -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 -*/ - -//x -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 -*/ - -//x -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 */ - -//x -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 -*/ - -//x -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 */ - -//x -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 -*/ - -//x -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 -*/ - -//x -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 -*/ - -//x -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 */ - -//x -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 */ - -//x -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 */ - -//x -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); - //note, these are indexing from 1, 3, 5, etc. - for (i = 1; i < 64; i += 2) { - select(&t, i / 2, e[i]); //here's where you grab multiples of the basepoint .. - //so must be doing e P = (e[0] (2^4)^0 P + e[1] (2^4)^1 P + e[2] (2^4)^2 P + ...) - //except, probably writing in big-endian to make more sense.. - //and the e[i] P are going to be pre-computed... - //so have to wonder if by precomputing more, if can save time?? - 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); - - //note, these are indexing from 0, 2, 4, etc. - 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 -*/ - -//x -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 */ - -//x -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. -*/ - -//x -void sc_reduce(unsigned char *s) { - //the point is to load in 21 bits at a time.. - //Mininero should give you the ints 2097151, the shifts below, and either load 3 or 4 - int64_t s0 = 2097151 & load_3(s); //2097151 is 21 1's in binary, so there are possible 5 bits left over.. - int64_t s1 = 2097151 & (load_4(s + 2) >> 5); //now you start at 2^16, so you have to move right 5 bits to 2^21.., the 2 comes from the fact that you loaded 3 last time.. - int64_t s2 = 2097151 & (load_3(s + 5) >> 2); //in last one you had bits 22 ->42, you are starting at (2^8)^5 = 2^40, so need to move right 2 bits... - int64_t s3 = 2097151 & (load_4(s + 7) >> 7); //etc... - int64_t s4 = 2097151 & (load_4(s + 10) >> 4); //ahh, these are "int 64;s" - int64_t s5 = 2097151 & (load_3(s + 13) >> 1); //not uint 64s - 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); //note no &2097151 here .. - //so rather than doing 24 = 512 - //we've done 23 = 504 - //so curve size rather than - //size of s - //this should be handled - //at the end with those - //two extra reductions - 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; - //17 carries because 11, 12, ... 16 = #digits in l - - //reduce first 105 bits.. to go from 504 to 399 - //Note that 683901 * 2^(5*21) - 136657 * 2^(4 * 21) + ... - 66643 = 27742317777372353535851937790883648493, which is c in the curve order.. - s11 += s23 * 666643; // =1430509 - 2 ^ 21 //note there is a 12 step difference, 12^21 = 252 - //so you subtract q 12^21 and then add c at each step.. - //just have to be careful of the carries .. - //If you are using unsigned int's, you had better carry at each step - //so the first step is to factorize 252 and whatever radix - //must be in those factors.. - s12 += s23 * 470296; // = 1626855 - 2^21 - 1 - s13 += s23 * 654183; // = 1442968 - 2 ^ 21 - 1? - s14 -= s23 * 997805; //note the negative ones are same as result from toDigits - s15 += s23 * 136657; // 1960495 - 2 ** 21 - s16 -= s23 * 683901; //note negative ones are same - - s10 += s22 * 666643; //22 - 10 = 12, 12 * 21 = 252 - s11 += s22 * 470296; - s12 += s22 * 654183; - s13 -= s22 * 997805; - s14 += s22 * 136657; - s15 -= s22 * 683901; - - s9 += s21 * 666643; //21 - 9 = 12 - 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; - //so we repeat this until we get down to s11 - //note that 11 * 21 = 231 - - //1st carry... - //note span = 6 here - carry6 = (s6 + (1<<20)) >> 21; s7 += carry6; s6 -= carry6 << 21;//take parts that are more than 21 bits in new s6 and add to s7.. - 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; - - //span = 5 here - 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; - - //reduce 105 bits to go from 399 to 294 - s5 += s17 * 666643; //17 - 5 = 12 = 252/21 - 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; //12 - 0 = 12.. - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - //2nd carry - 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; - - //reduce another 21 bits... go from 294 to 273 - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - s12 = 0; - - //3rd carry - 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; - - //reduce last 21 bits to go from 273 to get to 2^252.. - s0 += s12 * 666643; - s1 += s12 * 470296; - s2 += s12 * 654183; - s3 -= s12 * 997805; - s4 += s12 * 136657; - s5 -= s12 * 683901; - - //carry - 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; - - //go from 2^[256/12]'s to 2^[256/32]'s - s[0] = s0 >> 0; - s[1] = s0 >> 8; - s[2] = (s0 >> 16) | (s1 << 5); // | since there is no overlap - 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 */ -/* (u / v)^(m + 1) */ -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); - } -} - -//assume Bi has precomputed multiples -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 */ //precomps - 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); - } -} - -//x -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); -} - -//x -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 -} - -//x -void sc_0(unsigned char *s) { - int i; - for (i = 0; i < 32; i++) { - s[i] = 0; - } -} - -//x -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; -} - -//x -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; -} - -//x -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. -*/ - -//x -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 */ -//x c.f. lt in 32 bit ref -static int64_t signum(int64_t a) { - return (a >> 63) - ((-a) >> 63); -} - -//x -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; -} - -//x -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; -} |