| /* Copyright (c) 2015, Google Inc. |
| * |
| * Permission to use, copy, modify, and/or distribute this software for any |
| * purpose with or without fee is hereby granted, provided that the above |
| * copyright notice and this permission notice appear in all copies. |
| * |
| * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES |
| * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF |
| * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY |
| * SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES |
| * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN ACTION |
| * OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF OR IN |
| * CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE. */ |
| |
| /* This code is mostly taken from the ref10 version of Ed25519 in SUPERCOP |
| * 20141124 (http://bench.cr.yp.to/supercop.html). That code is released as |
| * public domain but this file has the ISC license just to keep licencing |
| * simple. |
| * |
| * The field functions are shared by Ed25519 and X25519 where possible. */ |
| |
| #include <openssl/curve25519.h> |
| |
| #include <string.h> |
| |
| #include <openssl/cpu.h> |
| #include <openssl/mem.h> |
| #include <openssl/rand.h> |
| #include <openssl/sha.h> |
| |
| #include "internal.h" |
| |
| |
| /* fe means field element. Here the field is \Z/(2^255-19). An element t, |
| * entries t[0]...t[9], represents the integer t[0]+2^26 t[1]+2^51 t[2]+2^77 |
| * t[3]+2^102 t[4]+...+2^230 t[9]. Bounds on each t[i] vary depending on |
| * context. */ |
| typedef int32_t fe[10]; |
| |
| static uint64_t load_3(const uint8_t *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 uint8_t *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; |
| } |
| |
| static void fe_frombytes(fe h, const uint8_t *s) { |
| /* Ignores top bit of h. */ |
| 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; |
| |
| 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[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; |
| } |
| |
| /* 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(uint8_t *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; |
| } |
| |
| /* h = f */ |
| static void fe_copy(fe h, const fe f) { |
| memmove(h, f, sizeof(int32_t) * 10); |
| } |
| |
| /* h = 0 */ |
| static void fe_0(fe h) { memset(h, 0, sizeof(int32_t) * 10); } |
| |
| /* h = 1 */ |
| static void fe_1(fe h) { |
| memset(h, 0, sizeof(int32_t) * 10); |
| h[0] = 1; |
| } |
| |
| /* 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) { |
| unsigned i; |
| for (i = 0; i < 10; i++) { |
| h[i] = f[i] + g[i]; |
| } |
| } |
| |
| /* 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) { |
| unsigned i; |
| for (i = 0; i < 10; i++) { |
| h[i] = f[i] - g[i]; |
| } |
| } |
| |
| /* 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; |
| } |
| |
| /* 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; |
| } |
| |
| static void fe_invert(fe out, const fe z) { |
| fe t0; |
| fe t1; |
| fe t2; |
| fe t3; |
| int i; |
| |
| fe_sq(t0, z); |
| for (i = 1; i < 1; ++i) { |
| fe_sq(t0, t0); |
| } |
| fe_sq(t1, t0); |
| for (i = 1; i < 2; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(t1, z, t1); |
| fe_mul(t0, t0, t1); |
| fe_sq(t2, t0); |
| for (i = 1; i < 1; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t1, t1, t2); |
| fe_sq(t2, t1); |
| for (i = 1; i < 5; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t1, t2, t1); |
| fe_sq(t2, t1); |
| for (i = 1; i < 10; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t2, t2, t1); |
| fe_sq(t3, t2); |
| for (i = 1; i < 20; ++i) { |
| fe_sq(t3, t3); |
| } |
| fe_mul(t2, t3, t2); |
| fe_sq(t2, t2); |
| for (i = 1; i < 10; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t1, t2, t1); |
| fe_sq(t2, t1); |
| for (i = 1; i < 50; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t2, t2, t1); |
| fe_sq(t3, t2); |
| for (i = 1; i < 100; ++i) { |
| fe_sq(t3, t3); |
| } |
| fe_mul(t2, t3, t2); |
| fe_sq(t2, t2); |
| for (i = 1; i < 50; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t1, t2, t1); |
| fe_sq(t1, t1); |
| for (i = 1; i < 5; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(out, t1, t0); |
| } |
| |
| /* 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) { |
| unsigned i; |
| for (i = 0; i < 10; i++) { |
| h[i] = -f[i]; |
| } |
| } |
| |
| /* 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 b) { |
| b = 0-b; |
| unsigned i; |
| for (i = 0; i < 10; i++) { |
| int32_t x = f[i] ^ g[i]; |
| x &= b; |
| f[i] ^= x; |
| } |
| } |
| |
| /* return 0 if f == 0 |
| * return 1 if f != 0 |
| * |
| * Preconditions: |
| * |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ |
| static int fe_isnonzero(const fe f) { |
| uint8_t s[32]; |
| fe_tobytes(s, f); |
| |
| static const uint8_t zero[32] = {0}; |
| return CRYPTO_memcmp(s, zero, sizeof(zero)) != 0; |
| } |
| |
| /* 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) { |
| uint8_t s[32]; |
| fe_tobytes(s, f); |
| return s[0] & 1; |
| } |
| |
| /* 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; |
| } |
| |
| static void fe_pow22523(fe out, const fe z) { |
| fe t0; |
| fe t1; |
| fe t2; |
| int i; |
| |
| fe_sq(t0, z); |
| for (i = 1; i < 1; ++i) { |
| fe_sq(t0, t0); |
| } |
| fe_sq(t1, t0); |
| for (i = 1; i < 2; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(t1, z, t1); |
| fe_mul(t0, t0, t1); |
| fe_sq(t0, t0); |
| for (i = 1; i < 1; ++i) { |
| fe_sq(t0, t0); |
| } |
| fe_mul(t0, t1, t0); |
| fe_sq(t1, t0); |
| for (i = 1; i < 5; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(t0, t1, t0); |
| fe_sq(t1, t0); |
| for (i = 1; i < 10; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(t1, t1, t0); |
| fe_sq(t2, t1); |
| for (i = 1; i < 20; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t1, t2, t1); |
| fe_sq(t1, t1); |
| for (i = 1; i < 10; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(t0, t1, t0); |
| fe_sq(t1, t0); |
| for (i = 1; i < 50; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(t1, t1, t0); |
| fe_sq(t2, t1); |
| for (i = 1; i < 100; ++i) { |
| fe_sq(t2, t2); |
| } |
| fe_mul(t1, t2, t1); |
| fe_sq(t1, t1); |
| for (i = 1; i < 50; ++i) { |
| fe_sq(t1, t1); |
| } |
| fe_mul(t0, t1, t0); |
| fe_sq(t0, t0); |
| for (i = 1; i < 2; ++i) { |
| fe_sq(t0, t0); |
| } |
| fe_mul(out, t0, z); |
| } |
| |
| /* ge means group element. |
| |
| * Here the group is the set of pairs (x,y) of field elements (see fe.h) |
| * satisfying -x^2 + y^2 = 1 + d x^2y^2 |
| * where d = -121665/121666. |
| * |
| * Representations: |
| * ge_p2 (projective): (X:Y:Z) satisfying x=X/Z, y=Y/Z |
| * ge_p3 (extended): (X:Y:Z:T) satisfying x=X/Z, y=Y/Z, XY=ZT |
| * ge_p1p1 (completed): ((X:Z),(Y:T)) satisfying x=X/Z, y=Y/T |
| * ge_precomp (Duif): (y+x,y-x,2dxy) */ |
| |
| typedef struct { |
| fe X; |
| fe Y; |
| fe Z; |
| } ge_p2; |
| |
| typedef struct { |
| fe X; |
| fe Y; |
| fe Z; |
| fe T; |
| } ge_p3; |
| |
| typedef struct { |
| fe X; |
| fe Y; |
| fe Z; |
| fe T; |
| } ge_p1p1; |
| |
| typedef struct { |
| fe yplusx; |
| fe yminusx; |
| fe xy2d; |
| } ge_precomp; |
| |
| typedef struct { |
| fe YplusX; |
| fe YminusX; |
| fe Z; |
| fe T2d; |
| } ge_cached; |
| |
| static void ge_tobytes(uint8_t *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; |
| } |
| |
| static void ge_p3_tobytes(uint8_t *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; |
| } |
| |
| static const fe d = {-10913610, 13857413, -15372611, 6949391, 114729, |
| -8787816, -6275908, -3247719, -18696448, -12055116}; |
| |
| static const fe sqrtm1 = {-32595792, -7943725, 9377950, 3500415, 12389472, |
| -272473, -25146209, -2005654, 326686, 11406482}; |
| |
| static int ge_frombytes_vartime(ge_p3 *h, const uint8_t *s) { |
| fe u; |
| fe v; |
| fe v3; |
| fe vxx; |
| fe check; |
| |
| fe_frombytes(h->Y, s); |
| fe_1(h->Z); |
| fe_sq(u, h->Y); |
| fe_mul(v, u, d); |
| fe_sub(u, u, h->Z); /* u = y^2-1 */ |
| fe_add(v, v, h->Z); /* v = dy^2+1 */ |
| |
| fe_sq(v3, v); |
| fe_mul(v3, v3, v); /* v3 = v^3 */ |
| fe_sq(h->X, v3); |
| fe_mul(h->X, h->X, v); |
| fe_mul(h->X, h->X, u); /* x = uv^7 */ |
| |
| fe_pow22523(h->X, h->X); /* x = (uv^7)^((q-5)/8) */ |
| fe_mul(h->X, h->X, v3); |
| fe_mul(h->X, h->X, u); /* 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, sqrtm1); |
| } |
| |
| if (fe_isnegative(h->X) != (s[31] >> 7)) { |
| fe_neg(h->X, h->X); |
| } |
| |
| fe_mul(h->T, h->X, h->Y); |
| return 0; |
| } |
| |
| static void ge_p2_0(ge_p2 *h) { |
| fe_0(h->X); |
| fe_1(h->Y); |
| fe_1(h->Z); |
| } |
| |
| static void ge_p3_0(ge_p3 *h) { |
| fe_0(h->X); |
| fe_1(h->Y); |
| fe_1(h->Z); |
| fe_0(h->T); |
| } |
| |
| static void ge_precomp_0(ge_precomp *h) { |
| fe_1(h->yplusx); |
| fe_1(h->yminusx); |
| fe_0(h->xy2d); |
| } |
| |
| /* r = p */ |
| static 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); |
| } |
| |
| static const fe d2 = {-21827239, -5839606, -30745221, 13898782, 229458, |
| 15978800, -12551817, -6495438, 29715968, 9444199}; |
| |
| /* r = p */ |
| static 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, d2); |
| } |
| |
| /* r = p */ |
| static 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); |
| } |
| |
| /* r = p */ |
| static 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); |
| } |
| |
| /* r = 2 * p */ |
| static 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); |
| } |
| |
| /* 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); |
| } |
| |
| /* 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); |
| } |
| |
| /* 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); |
| } |
| |
| /* r = p + q */ |
| static 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); |
| } |
| |
| /* 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); |
| } |
| |
| static uint8_t equal(signed char b, signed char c) { |
| uint8_t ub = b; |
| uint8_t uc = c; |
| uint8_t 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 void cmov(ge_precomp *t, ge_precomp *u, uint8_t b) { |
| fe_cmov(t->yplusx, u->yplusx, b); |
| fe_cmov(t->yminusx, u->yminusx, b); |
| fe_cmov(t->xy2d, u->xy2d, b); |
| } |
| |
| #if defined(OPENSSL_SMALL) |
| |
| /* This block of code replaces the standard base-point table with a much smaller |
| * one. The standard table is 30,720 bytes while this one is just 960. |
| * |
| * This table contains 15 pairs of group elements, (x, y), where each field |
| * element is serialised with |fe_tobytes|. If |i| is the index of the group |
| * element then consider i+1 as a four-bit number: (i₀, i₁, i₂, i₃) (where i₀ |
| * is the most significant bit). The value of the group element is then: |
| * (i₀×2^192 + i₁×2^128 + i₂×2^64 + i₃)G, where G is the generator. */ |
| static const uint8_t k25519SmallPrecomp[15 * 2 * 32] = { |
| 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9, 0xb2, 0xa7, 0x25, 0x95, |
| 0x60, 0xc7, 0x2c, 0x69, 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0, |
| 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21, 0x58, 0x66, 0x66, 0x66, |
| 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, |
| 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, |
| 0x66, 0x66, 0x66, 0x66, 0x02, 0xa2, 0xed, 0xf4, 0x8f, 0x6b, 0x0b, 0x3e, |
| 0xeb, 0x35, 0x1a, 0xd5, 0x7e, 0xdb, 0x78, 0x00, 0x96, 0x8a, 0xa0, 0xb4, |
| 0xcf, 0x60, 0x4b, 0xd4, 0xd5, 0xf9, 0x2d, 0xbf, 0x88, 0xbd, 0x22, 0x62, |
| 0x13, 0x53, 0xe4, 0x82, 0x57, 0xfa, 0x1e, 0x8f, 0x06, 0x2b, 0x90, 0xba, |
| 0x08, 0xb6, 0x10, 0x54, 0x4f, 0x7c, 0x1b, 0x26, 0xed, 0xda, 0x6b, 0xdd, |
| 0x25, 0xd0, 0x4e, 0xea, 0x42, 0xbb, 0x25, 0x03, 0xa2, 0xfb, 0xcc, 0x61, |
| 0x67, 0x06, 0x70, 0x1a, 0xc4, 0x78, 0x3a, 0xff, 0x32, 0x62, 0xdd, 0x2c, |
| 0xab, 0x50, 0x19, 0x3b, 0xf2, 0x9b, 0x7d, 0xb8, 0xfd, 0x4f, 0x29, 0x9c, |
| 0xa7, 0x91, 0xba, 0x0e, 0x46, 0x5e, 0x51, 0xfe, 0x1d, 0xbf, 0xe5, 0xe5, |
| 0x9b, 0x95, 0x0d, 0x67, 0xf8, 0xd1, 0xb5, 0x5a, 0xa1, 0x93, 0x2c, 0xc3, |
| 0xde, 0x0e, 0x97, 0x85, 0x2d, 0x7f, 0xea, 0xab, 0x3e, 0x47, 0x30, 0x18, |
| 0x24, 0xe8, 0xb7, 0x60, 0xae, 0x47, 0x80, 0xfc, 0xe5, 0x23, 0xe7, 0xc2, |
| 0xc9, 0x85, 0xe6, 0x98, 0xa0, 0x29, 0x4e, 0xe1, 0x84, 0x39, 0x2d, 0x95, |
| 0x2c, 0xf3, 0x45, 0x3c, 0xff, 0xaf, 0x27, 0x4c, 0x6b, 0xa6, 0xf5, 0x4b, |
| 0x11, 0xbd, 0xba, 0x5b, 0x9e, 0xc4, 0xa4, 0x51, 0x1e, 0xbe, 0xd0, 0x90, |
| 0x3a, 0x9c, 0xc2, 0x26, 0xb6, 0x1e, 0xf1, 0x95, 0x7d, 0xc8, 0x6d, 0x52, |
| 0xe6, 0x99, 0x2c, 0x5f, 0x9a, 0x96, 0x0c, 0x68, 0x29, 0xfd, 0xe2, 0xfb, |
| 0xe6, 0xbc, 0xec, 0x31, 0x08, 0xec, 0xe6, 0xb0, 0x53, 0x60, 0xc3, 0x8c, |
| 0xbe, 0xc1, 0xb3, 0x8a, 0x8f, 0xe4, 0x88, 0x2b, 0x55, 0xe5, 0x64, 0x6e, |
| 0x9b, 0xd0, 0xaf, 0x7b, 0x64, 0x2a, 0x35, 0x25, 0x10, 0x52, 0xc5, 0x9e, |
| 0x58, 0x11, 0x39, 0x36, 0x45, 0x51, 0xb8, 0x39, 0x93, 0xfc, 0x9d, 0x6a, |
| 0xbe, 0x58, 0xcb, 0xa4, 0x0f, 0x51, 0x3c, 0x38, 0x05, 0xca, 0xab, 0x43, |
| 0x63, 0x0e, 0xf3, 0x8b, 0x41, 0xa6, 0xf8, 0x9b, 0x53, 0x70, 0x80, 0x53, |
| 0x86, 0x5e, 0x8f, 0xe3, 0xc3, 0x0d, 0x18, 0xc8, 0x4b, 0x34, 0x1f, 0xd8, |
| 0x1d, 0xbc, 0xf2, 0x6d, 0x34, 0x3a, 0xbe, 0xdf, 0xd9, 0xf6, 0xf3, 0x89, |
| 0xa1, 0xe1, 0x94, 0x9f, 0x5d, 0x4c, 0x5d, 0xe9, 0xa1, 0x49, 0x92, 0xef, |
| 0x0e, 0x53, 0x81, 0x89, 0x58, 0x87, 0xa6, 0x37, 0xf1, 0xdd, 0x62, 0x60, |
| 0x63, 0x5a, 0x9d, 0x1b, 0x8c, 0xc6, 0x7d, 0x52, 0xea, 0x70, 0x09, 0x6a, |
| 0xe1, 0x32, 0xf3, 0x73, 0x21, 0x1f, 0x07, 0x7b, 0x7c, 0x9b, 0x49, 0xd8, |
| 0xc0, 0xf3, 0x25, 0x72, 0x6f, 0x9d, 0xed, 0x31, 0x67, 0x36, 0x36, 0x54, |
| 0x40, 0x92, 0x71, 0xe6, 0x11, 0x28, 0x11, 0xad, 0x93, 0x32, 0x85, 0x7b, |
| 0x3e, 0xb7, 0x3b, 0x49, 0x13, 0x1c, 0x07, 0xb0, 0x2e, 0x93, 0xaa, 0xfd, |
| 0xfd, 0x28, 0x47, 0x3d, 0x8d, 0xd2, 0xda, 0xc7, 0x44, 0xd6, 0x7a, 0xdb, |
| 0x26, 0x7d, 0x1d, 0xb8, 0xe1, 0xde, 0x9d, 0x7a, 0x7d, 0x17, 0x7e, 0x1c, |
| 0x37, 0x04, 0x8d, 0x2d, 0x7c, 0x5e, 0x18, 0x38, 0x1e, 0xaf, 0xc7, 0x1b, |
| 0x33, 0x48, 0x31, 0x00, 0x59, 0xf6, 0xf2, 0xca, 0x0f, 0x27, 0x1b, 0x63, |
| 0x12, 0x7e, 0x02, 0x1d, 0x49, 0xc0, 0x5d, 0x79, 0x87, 0xef, 0x5e, 0x7a, |
| 0x2f, 0x1f, 0x66, 0x55, 0xd8, 0x09, 0xd9, 0x61, 0x38, 0x68, 0xb0, 0x07, |
| 0xa3, 0xfc, 0xcc, 0x85, 0x10, 0x7f, 0x4c, 0x65, 0x65, 0xb3, 0xfa, 0xfa, |
| 0xa5, 0x53, 0x6f, 0xdb, 0x74, 0x4c, 0x56, 0x46, 0x03, 0xe2, 0xd5, 0x7a, |
| 0x29, 0x1c, 0xc6, 0x02, 0xbc, 0x59, 0xf2, 0x04, 0x75, 0x63, 0xc0, 0x84, |
| 0x2f, 0x60, 0x1c, 0x67, 0x76, 0xfd, 0x63, 0x86, 0xf3, 0xfa, 0xbf, 0xdc, |
| 0xd2, 0x2d, 0x90, 0x91, 0xbd, 0x33, 0xa9, 0xe5, 0x66, 0x0c, 0xda, 0x42, |
| 0x27, 0xca, 0xf4, 0x66, 0xc2, 0xec, 0x92, 0x14, 0x57, 0x06, 0x63, 0xd0, |
| 0x4d, 0x15, 0x06, 0xeb, 0x69, 0x58, 0x4f, 0x77, 0xc5, 0x8b, 0xc7, 0xf0, |
| 0x8e, 0xed, 0x64, 0xa0, 0xb3, 0x3c, 0x66, 0x71, 0xc6, 0x2d, 0xda, 0x0a, |
| 0x0d, 0xfe, 0x70, 0x27, 0x64, 0xf8, 0x27, 0xfa, 0xf6, 0x5f, 0x30, 0xa5, |
| 0x0d, 0x6c, 0xda, 0xf2, 0x62, 0x5e, 0x78, 0x47, 0xd3, 0x66, 0x00, 0x1c, |
| 0xfd, 0x56, 0x1f, 0x5d, 0x3f, 0x6f, 0xf4, 0x4c, 0xd8, 0xfd, 0x0e, 0x27, |
| 0xc9, 0x5c, 0x2b, 0xbc, 0xc0, 0xa4, 0xe7, 0x23, 0x29, 0x02, 0x9f, 0x31, |
| 0xd6, 0xe9, 0xd7, 0x96, 0xf4, 0xe0, 0x5e, 0x0b, 0x0e, 0x13, 0xee, 0x3c, |
| 0x09, 0xed, 0xf2, 0x3d, 0x76, 0x91, 0xc3, 0xa4, 0x97, 0xae, 0xd4, 0x87, |
| 0xd0, 0x5d, 0xf6, 0x18, 0x47, 0x1f, 0x1d, 0x67, 0xf2, 0xcf, 0x63, 0xa0, |
| 0x91, 0x27, 0xf8, 0x93, 0x45, 0x75, 0x23, 0x3f, 0xd1, 0xf1, 0xad, 0x23, |
| 0xdd, 0x64, 0x93, 0x96, 0x41, 0x70, 0x7f, 0xf7, 0xf5, 0xa9, 0x89, 0xa2, |
| 0x34, 0xb0, 0x8d, 0x1b, 0xae, 0x19, 0x15, 0x49, 0x58, 0x23, 0x6d, 0x87, |
| 0x15, 0x4f, 0x81, 0x76, 0xfb, 0x23, 0xb5, 0xea, 0xcf, 0xac, 0x54, 0x8d, |
| 0x4e, 0x42, 0x2f, 0xeb, 0x0f, 0x63, 0xdb, 0x68, 0x37, 0xa8, 0xcf, 0x8b, |
| 0xab, 0xf5, 0xa4, 0x6e, 0x96, 0x2a, 0xb2, 0xd6, 0xbe, 0x9e, 0xbd, 0x0d, |
| 0xb4, 0x42, 0xa9, 0xcf, 0x01, 0x83, 0x8a, 0x17, 0x47, 0x76, 0xc4, 0xc6, |
| 0x83, 0x04, 0x95, 0x0b, 0xfc, 0x11, 0xc9, 0x62, 0xb8, 0x0c, 0x76, 0x84, |
| 0xd9, 0xb9, 0x37, 0xfa, 0xfc, 0x7c, 0xc2, 0x6d, 0x58, 0x3e, 0xb3, 0x04, |
| 0xbb, 0x8c, 0x8f, 0x48, 0xbc, 0x91, 0x27, 0xcc, 0xf9, 0xb7, 0x22, 0x19, |
| 0x83, 0x2e, 0x09, 0xb5, 0x72, 0xd9, 0x54, 0x1c, 0x4d, 0xa1, 0xea, 0x0b, |
| 0xf1, 0xc6, 0x08, 0x72, 0x46, 0x87, 0x7a, 0x6e, 0x80, 0x56, 0x0a, 0x8a, |
| 0xc0, 0xdd, 0x11, 0x6b, 0xd6, 0xdd, 0x47, 0xdf, 0x10, 0xd9, 0xd8, 0xea, |
| 0x7c, 0xb0, 0x8f, 0x03, 0x00, 0x2e, 0xc1, 0x8f, 0x44, 0xa8, 0xd3, 0x30, |
| 0x06, 0x89, 0xa2, 0xf9, 0x34, 0xad, 0xdc, 0x03, 0x85, 0xed, 0x51, 0xa7, |
| 0x82, 0x9c, 0xe7, 0x5d, 0x52, 0x93, 0x0c, 0x32, 0x9a, 0x5b, 0xe1, 0xaa, |
| 0xca, 0xb8, 0x02, 0x6d, 0x3a, 0xd4, 0xb1, 0x3a, 0xf0, 0x5f, 0xbe, 0xb5, |
| 0x0d, 0x10, 0x6b, 0x38, 0x32, 0xac, 0x76, 0x80, 0xbd, 0xca, 0x94, 0x71, |
| 0x7a, 0xf2, 0xc9, 0x35, 0x2a, 0xde, 0x9f, 0x42, 0x49, 0x18, 0x01, 0xab, |
| 0xbc, 0xef, 0x7c, 0x64, 0x3f, 0x58, 0x3d, 0x92, 0x59, 0xdb, 0x13, 0xdb, |
| 0x58, 0x6e, 0x0a, 0xe0, 0xb7, 0x91, 0x4a, 0x08, 0x20, 0xd6, 0x2e, 0x3c, |
| 0x45, 0xc9, 0x8b, 0x17, 0x79, 0xe7, 0xc7, 0x90, 0x99, 0x3a, 0x18, 0x25, |
| }; |
| |
| static void ge_scalarmult_base(ge_p3 *h, const uint8_t a[32]) { |
| /* k25519SmallPrecomp is first expanded into matching |ge_precomp| |
| * elements. */ |
| ge_precomp multiples[15]; |
| |
| unsigned i; |
| for (i = 0; i < 15; i++) { |
| const uint8_t *bytes = &k25519SmallPrecomp[i*(2 * 32)]; |
| fe x, y; |
| fe_frombytes(x, bytes); |
| fe_frombytes(y, bytes + 32); |
| |
| ge_precomp *out = &multiples[i]; |
| fe_add(out->yplusx, y, x); |
| fe_sub(out->yminusx, y, x); |
| fe_mul(out->xy2d, x, y); |
| fe_mul(out->xy2d, out->xy2d, d2); |
| } |
| |
| /* See the comment above |k25519SmallPrecomp| about the structure of the |
| * precomputed elements. This loop does 64 additions and 64 doublings to |
| * calculate the result. */ |
| ge_p3_0(h); |
| |
| for (i = 63; i < 64; i--) { |
| unsigned j; |
| signed char index = 0; |
| |
| for (j = 0; j < 4; j++) { |
| const uint8_t bit = 1 & (a[(8 * j) + (i / 8)] >> (i & 7)); |
| index |= (bit << j); |
| } |
| |
| ge_precomp e; |
| ge_precomp_0(&e); |
| |
| for (j = 1; j < 16; j++) { |
| cmov(&e, &multiples[j-1], equal(index, j)); |
| } |
| |
| ge_cached cached; |
| ge_p1p1 r; |
| ge_p3_to_cached(&cached, h); |
| ge_add(&r, h, &cached); |
| ge_p1p1_to_p3(h, &r); |
| |
| ge_madd(&r, h, &e); |
| ge_p1p1_to_p3(h, &r); |
| } |
| } |
| |
| #else |
| |
| /* k25519Precomp[i][j] = (j+1)*256^i*B */ |
| static ge_precomp k25519Precomp[32][8] = { |
| { |
| { |
| {25967493, -14356035, 29566456, 3660896, -12694345, 4014787, |
| 27544626, -11754271, -6079156, 2047605}, |
| {-12545711, 934262, -2722910, 3049990, -727428, 9406986, 12720692, |
| 5043384, 19500929, -15469378}, |
| {-8738181, 4489570, 9688441, -14785194, 10184609, -12363380, |
| 29287919, 11864899, -24514362, -4438546}, |
| }, |
| { |
| {-12815894, -12976347, -21581243, 11784320, -25355658, -2750717, |
| -11717903, -3814571, -358445, -10211303}, |
| {-21703237, 6903825, 27185491, 6451973, -29577724, -9554005, |
| -15616551, 11189268, -26829678, -5319081}, |
| {26966642, 11152617, 32442495, 15396054, 14353839, -12752335, |
| -3128826, -9541118, -15472047, -4166697}, |
| }, |
| { |
| {15636291, -9688557, 24204773, -7912398, 616977, -16685262, |
| 27787600, -14772189, 28944400, -1550024}, |
| {16568933, 4717097, -11556148, -1102322, 15682896, -11807043, |
| 16354577, -11775962, 7689662, 11199574}, |
| {30464156, -5976125, -11779434, -15670865, 23220365, 15915852, |
| 7512774, 10017326, -17749093, -9920357}, |
| }, |
| { |
| {-17036878, 13921892, 10945806, -6033431, 27105052, -16084379, |
| -28926210, 15006023, 3284568, -6276540}, |
| {23599295, -8306047, -11193664, -7687416, 13236774, 10506355, |
| 7464579, 9656445, 13059162, 10374397}, |
| {7798556, 16710257, 3033922, 2874086, 28997861, 2835604, 32406664, |
| -3839045, -641708, -101325}, |
| }, |
| { |
| {10861363, 11473154, 27284546, 1981175, -30064349, 12577861, |
| 32867885, 14515107, -15438304, 10819380}, |
| {4708026, 6336745, 20377586, 9066809, -11272109, 6594696, -25653668, |
| 12483688, -12668491, 5581306}, |
| {19563160, 16186464, -29386857, 4097519, 10237984, -4348115, |
| 28542350, 13850243, -23678021, -15815942}, |
| }, |
| { |
| {-15371964, -12862754, 32573250, 4720197, -26436522, 5875511, |
| -19188627, -15224819, -9818940, -12085777}, |
| {-8549212, 109983, 15149363, 2178705, 22900618, 4543417, 3044240, |
| -15689887, 1762328, 14866737}, |
| {-18199695, -15951423, -10473290, 1707278, -17185920, 3916101, |
| -28236412, 3959421, 27914454, 4383652}, |
| }, |
| { |
| {5153746, 9909285, 1723747, -2777874, 30523605, 5516873, 19480852, |
| 5230134, -23952439, -15175766}, |
| {-30269007, -3463509, 7665486, 10083793, 28475525, 1649722, |
| 20654025, 16520125, 30598449, 7715701}, |
| {28881845, 14381568, 9657904, 3680757, -20181635, 7843316, |
| -31400660, 1370708, 29794553, -1409300}, |
| }, |
| { |
| {14499471, -2729599, -33191113, -4254652, 28494862, 14271267, |
| 30290735, 10876454, -33154098, 2381726}, |
| {-7195431, -2655363, -14730155, 462251, -27724326, 3941372, |
| -6236617, 3696005, -32300832, 15351955}, |
| {27431194, 8222322, 16448760, -3907995, -18707002, 11938355, |
| -32961401, -2970515, 29551813, 10109425}, |
| }, |
| }, |
| { |
| { |
| {-13657040, -13155431, -31283750, 11777098, 21447386, 6519384, |
| -2378284, -1627556, 10092783, -4764171}, |
| {27939166, 14210322, 4677035, 16277044, -22964462, -12398139, |
| -32508754, 12005538, -17810127, 12803510}, |
| {17228999, -15661624, -1233527, 300140, -1224870, -11714777, |
| 30364213, -9038194, 18016357, 4397660}, |
| }, |
| { |
| {-10958843, -7690207, 4776341, -14954238, 27850028, -15602212, |
| -26619106, 14544525, -17477504, 982639}, |
| {29253598, 15796703, -2863982, -9908884, 10057023, 3163536, 7332899, |
| -4120128, -21047696, 9934963}, |
| {5793303, 16271923, -24131614, -10116404, 29188560, 1206517, |
| -14747930, 4559895, -30123922, -10897950}, |
| }, |
| { |
| {-27643952, -11493006, 16282657, -11036493, 28414021, -15012264, |
| 24191034, 4541697, -13338309, 5500568}, |
| {12650548, -1497113, 9052871, 11355358, -17680037, -8400164, |
| -17430592, 12264343, 10874051, 13524335}, |
| {25556948, -3045990, 714651, 2510400, 23394682, -10415330, 33119038, |
| 5080568, -22528059, 5376628}, |
| }, |
| { |
| {-26088264, -4011052, -17013699, -3537628, -6726793, 1920897, |
| -22321305, -9447443, 4535768, 1569007}, |
| {-2255422, 14606630, -21692440, -8039818, 28430649, 8775819, |
| -30494562, 3044290, 31848280, 12543772}, |
| {-22028579, 2943893, -31857513, 6777306, 13784462, -4292203, |
| -27377195, -2062731, 7718482, 14474653}, |
| }, |
| { |
| {2385315, 2454213, -22631320, 46603, -4437935, -15680415, 656965, |
| -7236665, 24316168, -5253567}, |
| {13741529, 10911568, -33233417, -8603737, -20177830, -1033297, |
| 33040651, -13424532, -20729456, 8321686}, |
| {21060490, -2212744, 15712757, -4336099, 1639040, 10656336, |
| 23845965, -11874838, -9984458, 608372}, |
| }, |
| { |
| {-13672732, -15087586, -10889693, -7557059, -6036909, 11305547, |
| 1123968, -6780577, 27229399, 23887}, |
| {-23244140, -294205, -11744728, 14712571, -29465699, -2029617, |
| 12797024, -6440308, -1633405, 16678954}, |
| {-29500620, 4770662, -16054387, 14001338, 7830047, 9564805, |
| -1508144, -4795045, -17169265, 4904953}, |
| }, |
| { |
| {24059557, 14617003, 19037157, -15039908, 19766093, -14906429, |
| 5169211, 16191880, 2128236, -4326833}, |
| {-16981152, 4124966, -8540610, -10653797, 30336522, -14105247, |
| -29806336, 916033, -6882542, -2986532}, |
| {-22630907, 12419372, -7134229, -7473371, -16478904, 16739175, |
| 285431, 2763829, 15736322, 4143876}, |
| }, |
| { |
| {2379352, 11839345, -4110402, -5988665, 11274298, 794957, 212801, |
| -14594663, 23527084, -16458268}, |
| {33431127, -11130478, -17838966, -15626900, 8909499, 8376530, |
| -32625340, 4087881, -15188911, -14416214}, |
| {1767683, 7197987, -13205226, -2022635, -13091350, 448826, 5799055, |
| 4357868, -4774191, -16323038}, |
| }, |
| }, |
| { |
| { |
| {6721966, 13833823, -23523388, -1551314, 26354293, -11863321, |
| 23365147, -3949732, 7390890, 2759800}, |
| {4409041, 2052381, 23373853, 10530217, 7676779, -12885954, 21302353, |
| -4264057, 1244380, -12919645}, |
| {-4421239, 7169619, 4982368, -2957590, 30256825, -2777540, 14086413, |
| 9208236, 15886429, 16489664}, |
| }, |
| { |
| {1996075, 10375649, 14346367, 13311202, -6874135, -16438411, |
| -13693198, 398369, -30606455, -712933}, |
| {-25307465, 9795880, -2777414, 14878809, -33531835, 14780363, |
| 13348553, 12076947, -30836462, 5113182}, |
| {-17770784, 11797796, 31950843, 13929123, -25888302, 12288344, |
| -30341101, -7336386, 13847711, 5387222}, |
| }, |
| { |
| {-18582163, -3416217, 17824843, -2340966, 22744343, -10442611, |
| 8763061, 3617786, -19600662, 10370991}, |
| {20246567, -14369378, 22358229, -543712, 18507283, -10413996, |
| 14554437, -8746092, 32232924, 16763880}, |
| {9648505, 10094563, 26416693, 14745928, -30374318, -6472621, |
| 11094161, 15689506, 3140038, -16510092}, |
| }, |
| { |
| {-16160072, 5472695, 31895588, 4744994, 8823515, 10365685, |
| -27224800, 9448613, -28774454, 366295}, |
| {19153450, 11523972, -11096490, -6503142, -24647631, 5420647, |
| 28344573, 8041113, 719605, 11671788}, |
| {8678025, 2694440, -6808014, 2517372, 4964326, 11152271, -15432916, |
| -15266516, 27000813, -10195553}, |
| }, |
| { |
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