| /* ge_operations.c |
| * |
| * Copyright (C) 2006-2015 wolfSSL Inc. |
| * |
| * This file is part of wolfSSL. (formerly known as CyaSSL) |
| * |
| * wolfSSL is free software; you can redistribute it and/or modify |
| * it under the terms of the GNU General Public License as published by |
| * the Free Software Foundation; either version 2 of the License, or |
| * (at your option) any later version. |
| * |
| * wolfSSL is distributed in the hope that it will be useful, |
| * but WITHOUT ANY WARRANTY; without even the implied warranty of |
| * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the |
| * GNU General Public License for more details. |
| * |
| * You should have received a copy of the GNU General Public License |
| * along with this program; if not, write to the Free Software |
| * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA |
| */ |
| |
| /* Based On Daniel J Bernstein's ed25519 Public Domain ref10 work. */ |
| |
| |
| #ifdef HAVE_CONFIG_H |
| #include <config.h> |
| #endif |
| |
| #include <wolfssl/wolfcrypt/settings.h> |
| |
| #ifdef HAVE_ED25519 |
| |
| #include <wolfssl/wolfcrypt/ge_operations.h> |
| #include <wolfssl/wolfcrypt/error-crypt.h> |
| #ifdef NO_INLINE |
| #include <wolfssl/wolfcrypt/misc.h> |
| #else |
| #include <wolfcrypt/src/misc.c> |
| #endif |
| |
| /* |
| 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) |
| */ |
| |
| |
| /* |
| Input: |
| s[0]+256*s[1]+...+256^63*s[63] = s |
| |
| Output: |
| s[0]+256*s[1]+...+256^31*s[31] = s mod l |
| where l = 2^252 + 27742317777372353535851937790883648493. |
| Overwrites s in place. |
| */ |
| void sc_reduce(byte* s) |
| { |
| int64_t s0 = 2097151 & load_3(s); |
| int64_t s1 = 2097151 & (load_4(s + 2) >> 5); |
| int64_t s2 = 2097151 & (load_3(s + 5) >> 2); |
| int64_t s3 = 2097151 & (load_4(s + 7) >> 7); |
| int64_t s4 = 2097151 & (load_4(s + 10) >> 4); |
| int64_t s5 = 2097151 & (load_3(s + 13) >> 1); |
| int64_t s6 = 2097151 & (load_4(s + 15) >> 6); |
| int64_t s7 = 2097151 & (load_3(s + 18) >> 3); |
| int64_t s8 = 2097151 & load_3(s + 21); |
| int64_t s9 = 2097151 & (load_4(s + 23) >> 5); |
| int64_t s10 = 2097151 & (load_3(s + 26) >> 2); |
| int64_t s11 = 2097151 & (load_4(s + 28) >> 7); |
| int64_t s12 = 2097151 & (load_4(s + 31) >> 4); |
| int64_t s13 = 2097151 & (load_3(s + 34) >> 1); |
| int64_t s14 = 2097151 & (load_4(s + 36) >> 6); |
| int64_t s15 = 2097151 & (load_3(s + 39) >> 3); |
| int64_t s16 = 2097151 & load_3(s + 42); |
| int64_t s17 = 2097151 & (load_4(s + 44) >> 5); |
| int64_t s18 = 2097151 & (load_3(s + 47) >> 2); |
| int64_t s19 = 2097151 & (load_4(s + 49) >> 7); |
| int64_t s20 = 2097151 & (load_4(s + 52) >> 4); |
| int64_t s21 = 2097151 & (load_3(s + 55) >> 1); |
| int64_t s22 = 2097151 & (load_4(s + 57) >> 6); |
| int64_t s23 = (load_4(s + 60) >> 3); |
| int64_t carry0; |
| int64_t carry1; |
| int64_t carry2; |
| int64_t carry3; |
| int64_t carry4; |
| int64_t carry5; |
| int64_t carry6; |
| int64_t carry7; |
| int64_t carry8; |
| int64_t carry9; |
| int64_t carry10; |
| int64_t carry11; |
| int64_t carry12; |
| int64_t carry13; |
| int64_t carry14; |
| int64_t carry15; |
| int64_t carry16; |
| |
| s11 += s23 * 666643; |
| s12 += s23 * 470296; |
| s13 += s23 * 654183; |
| s14 -= s23 * 997805; |
| s15 += s23 * 136657; |
| s16 -= s23 * 683901; |
| s23 = 0; |
| |
| s10 += s22 * 666643; |
| s11 += s22 * 470296; |
| s12 += s22 * 654183; |
| s13 -= s22 * 997805; |
| s14 += s22 * 136657; |
| s15 -= s22 * 683901; |
| s22 = 0; |
| |
| s9 += s21 * 666643; |
| s10 += s21 * 470296; |
| s11 += s21 * 654183; |
| s12 -= s21 * 997805; |
| s13 += s21 * 136657; |
| s14 -= s21 * 683901; |
| s21 = 0; |
| |
| s8 += s20 * 666643; |
| s9 += s20 * 470296; |
| s10 += s20 * 654183; |
| s11 -= s20 * 997805; |
| s12 += s20 * 136657; |
| s13 -= s20 * 683901; |
| s20 = 0; |
| |
| s7 += s19 * 666643; |
| s8 += s19 * 470296; |
| s9 += s19 * 654183; |
| s10 -= s19 * 997805; |
| s11 += s19 * 136657; |
| s12 -= s19 * 683901; |
| s19 = 0; |
| |
| s6 += s18 * 666643; |
| s7 += s18 * 470296; |
| s8 += s18 * 654183; |
| s9 -= s18 * 997805; |
| s10 += s18 * 136657; |
| s11 -= s18 * 683901; |
| s18 = 0; |
| |
| 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; |
| s17 = 0; |
| |
| s4 += s16 * 666643; |
| s5 += s16 * 470296; |
| s6 += s16 * 654183; |
| s7 -= s16 * 997805; |
| s8 += s16 * 136657; |
| s9 -= s16 * 683901; |
| s16 = 0; |
| |
| s3 += s15 * 666643; |
| s4 += s15 * 470296; |
| s5 += s15 * 654183; |
| s6 -= s15 * 997805; |
| s7 += s15 * 136657; |
| s8 -= s15 * 683901; |
| s15 = 0; |
| |
| s2 += s14 * 666643; |
| s3 += s14 * 470296; |
| s4 += s14 * 654183; |
| s5 -= s14 * 997805; |
| s6 += s14 * 136657; |
| s7 -= s14 * 683901; |
| s14 = 0; |
| |
| s1 += s13 * 666643; |
| s2 += s13 * 470296; |
| s3 += s13 * 654183; |
| s4 -= s13 * 997805; |
| s5 += s13 * 136657; |
| s6 -= s13 * 683901; |
| s13 = 0; |
| |
| 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; |
| 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; |
| |
| 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; |
| |
| /* hush warnings after setting values to 0 */ |
| (void)s12; |
| (void)s13; |
| (void)s14; |
| (void)s15; |
| (void)s16; |
| (void)s17; |
| (void)s18; |
| (void)s19; |
| (void)s20; |
| (void)s21; |
| (void)s22; |
| (void)s23; |
| } |
| |
| |
| /* |
| 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] = (ab+c) mod l |
| where l = 2^252 + 27742317777372353535851937790883648493. |
| */ |
| void sc_muladd(byte* s, const byte* a, const byte* b, const byte* 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; |
| s23 = 0; |
| |
| s10 += s22 * 666643; |
| s11 += s22 * 470296; |
| s12 += s22 * 654183; |
| s13 -= s22 * 997805; |
| s14 += s22 * 136657; |
| s15 -= s22 * 683901; |
| s22 = 0; |
| |
| s9 += s21 * 666643; |
| s10 += s21 * 470296; |
| s11 += s21 * 654183; |
| s12 -= s21 * 997805; |
| s13 += s21 * 136657; |
| s14 -= s21 * 683901; |
| s21 = 0; |
| |
| s8 += s20 * 666643; |
| s9 += s20 * 470296; |
| s10 += s20 * 654183; |
| s11 -= s20 * 997805; |
| s12 += s20 * 136657; |
| s13 -= s20 * 683901; |
| s20 = 0; |
| |
| s7 += s19 * 666643; |
| s8 += s19 * 470296; |
| s9 += s19 * 654183; |
| s10 -= s19 * 997805; |
| s11 += s19 * 136657; |
| s12 -= s19 * 683901; |
| s19 = 0; |
| |
| s6 += s18 * 666643; |
| s7 += s18 * 470296; |
| s8 += s18 * 654183; |
| s9 -= s18 * 997805; |
| s10 += s18 * 136657; |
| s11 -= s18 * 683901; |
| s18 = 0; |
| |
| 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; |
| s17 = 0; |
| |
| s4 += s16 * 666643; |
| s5 += s16 * 470296; |
| s6 += s16 * 654183; |
| s7 -= s16 * 997805; |
| s8 += s16 * 136657; |
| s9 -= s16 * 683901; |
| s16 = 0; |
| |
| s3 += s15 * 666643; |
| s4 += s15 * 470296; |
| s5 += s15 * 654183; |
| s6 -= s15 * 997805; |
| s7 += s15 * 136657; |
| s8 -= s15 * 683901; |
| s15 = 0; |
| |
| s2 += s14 * 666643; |
| s3 += s14 * 470296; |
| s4 += s14 * 654183; |
| s5 -= s14 * 997805; |
| s6 += s14 * 136657; |
| s7 -= s14 * 683901; |
| s14 = 0; |
| |
| s1 += s13 * 666643; |
| s2 += s13 * 470296; |
| s3 += s13 * 654183; |
| s4 -= s13 * 997805; |
| s5 += s13 * 136657; |
| s6 -= s13 * 683901; |
| s13 = 0; |
| |
| 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; |
| 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; |
| |
| 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; |
| |
| /* hush warnings after setting values to 0 */ |
| (void)s12; |
| (void)s13; |
| (void)s14; |
| (void)s15; |
| (void)s16; |
| (void)s17; |
| (void)s18; |
| (void)s19; |
| (void)s20; |
| (void)s21; |
| (void)s22; |
| (void)s23; |
| } |
| |
| |
| int ge_compress_key(byte* out, const byte* xIn, const byte* yIn, word32 keySz) |
| { |
| fe x,y,z; |
| ge_p3 g; |
| byte bArray[keySz]; |
| word32 i; |
| |
| fe_0(x); |
| fe_0(y); |
| fe_1(z); |
| fe_frombytes(x, xIn); |
| fe_frombytes(y, yIn); |
| |
| fe_copy(g.X, x); |
| fe_copy(g.Y, y); |
| fe_copy(g.Z, z); |
| |
| ge_p3_tobytes(bArray, &g); |
| |
| for (i = 0; i < keySz; i++) { |
| out[keySz - 1 - i] = bArray[i]; |
| } |
| |
| return 0; |
| } |
| |
| |
| /* |
| r = p + q |
| */ |
| 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); |
| } |
| |
| |
| /* ge_scalar mult base */ |
| 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 cmov(ge_precomp *t,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); |
| } |
| |
| |
| /* base[i][j] = (j+1)*256^i*B */ |
| static ge_precomp base[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 }, |
| }, |
| { |
| { -15157904,7134312,8639287,-2814877,-7235688,10421742,564065,5336097,6750977,-14521026 }, |
| { 11836410,-3979488,26297894,16080799,23455045,15735944,1695823,-8819122,8169720,16220347 }, |
| { -18115838,8653647,17578566,-6092619,-8025777,-16012763,-11144307,-2627664,-5990708,-14166033 }, |
| }, |
| { |
| { -23308498,-10968312,15213228,-10081214,-30853605,-11050004,27884329,2847284,2655861,1738395 }, |
| { -27537433,-14253021,-25336301,-8002780,-9370762,8129821,21651608,-3239336,-19087449,-11005278 }, |
| { 1533110,3437855,23735889,459276,29970501,11335377,26030092,5821408,10478196,8544890 }, |
| }, |
| { |
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| { |
| { -2444496,-149937,29348902,8186665,1873760,12489863,-30934579,-7839692,-7852844,-8138429 }, |
| { -15236356,-15433509,7766470,746860,26346930,-10221762,-27333451,10754588,-9431476,5203576 }, |
| { 31834314,14135496,-770007,5159118,20917671,-16768096,-7467973,-7337524,31809243,7347066 }, |
| }, |
| { |
| { -9606723,-11874240,20414459,13033986,13716524,-11691881,19797970,-12211255,15192876,-2087490 }, |
| { -12663563,-2181719,1168162,-3804809,26747877,-14138091,10609330,12694420,33473243,-13382104 }, |
| { 33184999,11180355,15832085,-11385430,-1633671,225884,15089336,-11023903,-6135662,14480053 }, |
| }, |
| { |
| { 31308717,-5619998,31030840,-1897099,15674547,-6582883,5496208,13685227,27595050,8737275 }, |
| { -20318852,-15150239,10933843,-16178022,8335352,-7546022,-31008351,-12610604,26498114,66511 }, |
| { 22644454,-8761729,-16671776,4884562,-3105614,-13559366,30540766,-4286747,-13327787,-7515095 }, |
| }, |
| { |
| { -28017847,9834845,18617207,-2681312,-3401956,-13307506,8205540,13585437,-17127465,15115439 }, |
| { 23711543,-672915,31206561,-8362711,6164647,-9709987,-33535882,-1426096,8236921,16492939 }, |
| { -23910559,-13515526,-26299483,-4503841,25005590,-7687270,19574902,10071562,6708380,-6222424 }, |
| }, |
| { |
| { 2101391,-4930054,19702731,2367575,-15427167,1047675,5301017,9328700,29955601,-11678310 }, |
| { 3096359,9271816,-21620864,-15521844,-14847996,-7592937,-25892142,-12635595,-9917575,6216608 }, |
| { -32615849,338663,-25195611,2510422,-29213566,-13820213,24822830,-6146567,-26767480,7525079 }, |
| }, |
| { |
| { -23066649,-13985623,16133487,-7896178,-3389565,778788,-910336,-2782495,-19386633,11994101 }, |
| { 21691500,-13624626,-641331,-14367021,3285881,-3483596,-25064666,9718258,-7477437,13381418 }, |
| { 18445390,-4202236,14979846,11622458,-1727110,-3582980,23111648,-6375247,28535282,15779576 }, |
| }, |
| { |
| { 30098053,3089662,-9234387,16662135,-21306940,11308411,-14068454,12021730,9955285,-16303356 }, |
| { 9734894,-14576830,-7473633,-9138735,2060392,11313496,-18426029,9924399,20194861,13380996 }, |
| { -26378102,-7965207,-22167821,15789297,-18055342,-6168792,-1984914,15707771,26342023,10146099 }, |
| }, |
| }, |
| { |
| { |
| { -26016874,-219943,21339191,-41388,19745256,-2878700,-29637280,2227040,21612326,-545728 }, |
| { -13077387,1184228,23562814,-5970442,-20351244,-6348714,25764461,12243797,-20856566,11649658 }, |
| { -10031494,11262626,27384172,2271902,26947504,-15997771,39944,6114064,33514190,2333242 }, |
| }, |
| { |
| { -21433588,-12421821,8119782,7219913,-21830522,-9016134,-6679750,-12670638,24350578,-13450001 }, |
| { -4116307,-11271533,-23886186,4843615,-30088339,690623,-31536088,-10406836,8317860,12352766 }, |
| { 18200138,-14475911,-33087759,-2696619,-23702521,-9102511,-23552096,-2287550,20712163,6719373 }, |
| }, |
| { |
| { 26656208,6075253,-7858556,1886072,-28344043,4262326,11117530,-3763210,26224235,-3297458 }, |
| { -17168938,-14854097,-3395676,-16369877,-19954045,14050420,21728352,9493610,18620611,-16428628 }, |
| { -13323321,13325349,11432106,5964811,18609221,6062965,-5269471,-9725556,-30701573,-16479657 }, |
| }, |
| { |
| { -23860538,-11233159,26961357,1640861,-32413112,-16737940,12248509,-5240639,13735342,1934062 }, |
| { 25089769,6742589,17081145,-13406266,21909293,-16067981,-15136294,-3765346,-21277997,5473616 }, |
| { 31883677,-7961101,1083432,-11572403,22828471,13290673,-7125085,12469656,29111212,-5451014 }, |
| }, |
| { |
| { 24244947,-15050407,-26262976,2791540,-14997599,16666678,24367466,6388839,-10295587,452383 }, |
| { -25640782,-3417841,5217916,16224624,19987036,-4082269,-24236251,-5915248,15766062,8407814 }, |
| { -20406999,13990231,15495425,16395525,5377168,15166495,-8917023,-4388953,-8067909,2276718 }, |
| }, |
| { |
| { 30157918,12924066,-17712050,9245753,19895028,3368142,-23827587,5096219,22740376,-7303417 }, |
| { 2041139,-14256350,7783687,13876377,-25946985,-13352459,24051124,13742383,-15637599,13295222 }, |
| { 33338237,-8505733,12532113,7977527,9106186,-1715251,-17720195,-4612972,-4451357,-14669444 }, |
| }, |
| { |
| { -20045281,5454097,-14346548,6447146,28862071,1883651,-2469266,-4141880,7770569,9620597 }, |
| { 23208068,7979712,33071466,8149229,1758231,-10834995,30945528,-1694323,-33502340,-14767970 }, |
| { 1439958,-16270480,-1079989,-793782,4625402,10647766,-5043801,1220118,30494170,-11440799 }, |
| }, |
| { |
| { -5037580,-13028295,-2970559,-3061767,15640974,-6701666,-26739026,926050,-1684339,-13333647 }, |
| { 13908495,-3549272,30919928,-6273825,-21521863,7989039,9021034,9078865,3353509,4033511 }, |
| { -29663431,-15113610,32259991,-344482,24295849,-12912123,23161163,8839127,27485041,7356032 }, |
| }, |
| }, |
| { |
| { |
| { 9661027,705443,11980065,-5370154,-1628543,14661173,-6346142,2625015,28431036,-16771834 }, |
| { -23839233,-8311415,-25945511,7480958,-17681669,-8354183,-22545972,14150565,15970762,4099461 }, |
| { 29262576,16756590,26350592,-8793563,8529671,-11208050,13617293,-9937143,11465739,8317062 }, |
| }, |
| { |
| { -25493081,-6962928,32500200,-9419051,-23038724,-2302222,14898637,3848455,20969334,-5157516 }, |
| { -20384450,-14347713,-18336405,13884722,-33039454,2842114,-21610826,-3649888,11177095,14989547 }, |
| { -24496721,-11716016,16959896,2278463,12066309,10137771,13515641,2581286,-28487508,9930240 }, |
| }, |
| { |
| { -17751622,-2097826,16544300,-13009300,-15914807,-14949081,18345767,-13403753,16291481,-5314038 }, |
| { -33229194,2553288,32678213,9875984,8534129,6889387,-9676774,6957617,4368891,9788741 }, |
| { 16660756,7281060,-10830758,12911820,20108584,-8101676,-21722536,-8613148,16250552,-11111103 }, |
| }, |
| { |
| { -19765507,2390526,-16551031,14161980,1905286,6414907,4689584,10604807,-30190403,4782747 }, |
| { -1354539,14736941,-7367442,-13292886,7710542,-14155590,-9981571,4383045,22546403,437323 }, |
| { 31665577,-12180464,-16186830,1491339,-18368625,3294682,27343084,2786261,-30633590,-14097016 }, |
| }, |
| { |
| { -14467279,-683715,-33374107,7448552,19294360,14334329,-19690631,2355319,-19284671,-6114373 }, |
| { 15121312,-15796162,6377020,-6031361,-10798111,-12957845,18952177,15496498,-29380133,11754228 }, |
| { -2637277,-13483075,8488727,-14303896,12728761,-1622493,7141596,11724556,22761615,-10134141 }, |
| }, |
| { |
| { 16918416,11729663,-18083579,3022987,-31015732,-13339659,-28741185,-12227393,32851222,11717399 }, |
| { 11166634,7338049,-6722523,4531520,-29468672,-7302055,31474879,3483633,-1193175,-4030831 }, |
| { -185635,9921305,31456609,-13536438,-12013818,13348923,33142652,6546660,-19985279,-3948376 }, |
| }, |
| { |
| { -32460596,11266712,-11197107,-7899103,31703694,3855903,-8537131,-12833048,-30772034,-15486313 }, |
| { -18006477,12709068,3991746,-6479188,-21491523,-10550425,-31135347,-16049879,10928917,3011958 }, |
| { -6957757,-15594337,31696059,334240,29576716,14796075,-30831056,-12805180,18008031,10258577 }, |
| }, |
| { |
| { -22448644,15655569,7018479,-4410003,-30314266,-1201591,-1853465,1367120,25127874,6671743 }, |
| { 29701166,-14373934,-10878120,9279288,-17568,13127210,21382910,11042292,25838796,4642684 }, |
| { -20430234,14955537,-24126347,8124619,-5369288,-5990470,30468147,-13900640,18423289,4177476 }, |
| }, |
| }, |
| } ; |
| |
| |
| static void ge_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); |
| cmov(t,&base[pos][0],equal(babs,1)); |
| cmov(t,&base[pos][1],equal(babs,2)); |
| cmov(t,&base[pos][2],equal(babs,3)); |
| cmov(t,&base[pos][3],equal(babs,4)); |
| cmov(t,&base[pos][4],equal(babs,5)); |
| cmov(t,&base[pos][5],equal(babs,6)); |
| cmov(t,&base[pos][6],equal(babs,7)); |
| cmov(t,&base[pos][7],equal(babs,8)); |
| fe_copy(minust.yplusx,t->yminusx); |
| fe_copy(minust.yminusx,t->yplusx); |
| fe_neg(minust.xy2d,t->xy2d); |
| cmov(t,&minust,bnegative); |
| } |
| |
| |
| /* |
| h = a * B |
| where a = a[0]+256*a[1]+...+256^31 a[31] |
| B is the Ed25519 base point (x,4/5) with x positive. |
| |
| Preconditions: |
| a[31] <= 127 |
| */ |
| void ge_scalarmult_base(ge_p3 *h,const unsigned char *a) |
| { |
| signed char e[64]; |
| signed char carry; |
| ge_p1p1 r; |
| ge_p2 s; |
| ge_precomp t; |
| int i; |
| |
| for (i = 0;i < 32;++i) { |
| e[2 * i + 0] = (a[i] >> 0) & 15; |
| e[2 * i + 1] = (a[i] >> 4) & 15; |
| } |
| /* each e[i] is between 0 and 15 */ |
| /* e[63] is between 0 and 7 */ |
| |
| carry = 0; |
| for (i = 0;i < 63;++i) { |
| e[i] += carry; |
| carry = e[i] + 8; |
| carry >>= 4; |
| e[i] -= carry << 4; |
| } |
| e[63] += carry; |
| /* each e[i] is between -8 and 8 */ |
| |
| ge_p3_0(h); |
| for (i = 1;i < 64;i += 2) { |
| ge_select(&t,i / 2,e[i]); |
| ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); |
| } |
| |
| ge_p3_dbl(&r,h); ge_p1p1_to_p2(&s,&r); |
| ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); |
| ge_p2_dbl(&r,&s); ge_p1p1_to_p2(&s,&r); |
| ge_p2_dbl(&r,&s); ge_p1p1_to_p3(h,&r); |
| |
| for (i = 0;i < 64;i += 2) { |
| ge_select(&t,i / 2,e[i]); |
| ge_madd(&r,h,&t); ge_p1p1_to_p3(h,&r); |
| } |
| } |
| |
| |
| /* ge double scalar mult */ |
| static void slide(signed char *r,const unsigned char *a) |
| { |
| int i; |
| int b; |
| int k; |
| |
| for (i = 0;i < 256;++i) |
| r[i] = 1 & (a[i >> 3] >> (i & 7)); |
| |
| for (i = 0;i < 256;++i) |
| if (r[i]) { |
| for (b = 1;b <= 6 && i + b < 256;++b) { |
| if (r[i + b]) { |
| if (r[i] + (r[i + b] << b) <= 15) { |
| r[i] += r[i + b] << b; r[i + b] = 0; |
| } else if (r[i] - (r[i + b] << b) >= -15) { |
| r[i] -= r[i + b] << b; |
| for (k = i + b;k < 256;++k) { |
| if (!r[k]) { |
| r[k] = 1; |
| break; |
| } |
| r[k] = 0; |
| } |
| } else |
| break; |
| } |
| } |
| } |
| } |
| |
| |
| static ge_precomp Bi[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 }, |
| }, |
| { |
| { 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 }, |
| }, |
| { |
| { 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 }, |
| }, |
| { |
| { 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 }, |
| }, |
| { |
| { -22518993,-6692182,14201702,-8745502,-23510406,8844726,18474211,-1361450,-13062696,13821877 }, |
| { -6455177,-7839871,3374702,-4740862,-27098617,-10571707,31655028,-7212327,18853322,-14220951 }, |
| { 4566830,-12963868,-28974889,-12240689,-7602672,-2830569,-8514358,-10431137,2207753,-3209784 }, |
| }, |
| { |
| { -25154831,-4185821,29681144,7868801,-6854661,-9423865,-12437364,-663000,-31111463,-16132436 }, |
| { 25576264,-2703214,7349804,-11814844,16472782,9300885,3844789,15725684,171356,6466918 }, |
| { 23103977,13316479,9739013,-16149481,817875,-15038942,8965339,-14088058,-30714912,16193877 }, |
| }, |
| { |
| { -33521811,3180713,-2394130,14003687,-16903474,-16270840,17238398,4729455,-18074513,9256800 }, |
| { -25182317,-4174131,32336398,5036987,-21236817,11360617,22616405,9761698,-19827198,630305 }, |
| { -13720693,2639453,-24237460,-7406481,9494427,-5774029,-6554551,-15960994,-2449256,-14291300 }, |
| }, |
| { |
| { -3151181,-5046075,9282714,6866145,-31907062,-863023,-18940575,15033784,25105118,-7894876 }, |
| { -24326370,15950226,-31801215,-14592823,-11662737,-5090925,1573892,-2625887,2198790,-15804619 }, |
| { -3099351,10324967,-2241613,7453183,-5446979,-2735503,-13812022,-16236442,-32461234,-12290683 }, |
| }, |
| } ; |
| |
| |
| /* |
| 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. |
| */ |
| int ge_double_scalarmult_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_cached Ai[8]; /* A,3A,5A,7A,9A,11A,13A,15A */ |
| ge_p1p1 t; |
| ge_p3 u; |
| ge_p3 A2; |
| int i; |
| |
| slide(aslide,a); |
| slide(bslide,b); |
| |
| ge_p3_to_cached(&Ai[0],A); |
| ge_p3_dbl(&t,A); ge_p1p1_to_p3(&A2,&t); |
| ge_add(&t,&A2,&Ai[0]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[1],&u); |
| ge_add(&t,&A2,&Ai[1]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[2],&u); |
| ge_add(&t,&A2,&Ai[2]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[3],&u); |
| ge_add(&t,&A2,&Ai[3]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[4],&u); |
| ge_add(&t,&A2,&Ai[4]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[5],&u); |
| ge_add(&t,&A2,&Ai[5]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[6],&u); |
| ge_add(&t,&A2,&Ai[6]); ge_p1p1_to_p3(&u,&t); ge_p3_to_cached(&Ai[7],&u); |
| |
| ge_p2_0(r); |
| |
| for (i = 255;i >= 0;--i) { |
| if (aslide[i] || bslide[i]) break; |
| } |
| |
| for (;i >= 0;--i) { |
| ge_p2_dbl(&t,r); |
| |
| if (aslide[i] > 0) { |
| ge_p1p1_to_p3(&u,&t); |
| ge_add(&t,&u,&Ai[aslide[i]/2]); |
| } else if (aslide[i] < 0) { |
| ge_p1p1_to_p3(&u,&t); |
| ge_sub(&t,&u,&Ai[(-aslide[i])/2]); |
| } |
| |
| if (bslide[i] > 0) { |
| ge_p1p1_to_p3(&u,&t); |
| ge_madd(&t,&u,&Bi[bslide[i]/2]); |
| } else if (bslide[i] < 0) { |
| ge_p1p1_to_p3(&u,&t); |
| ge_msub(&t,&u,&Bi[(-bslide[i])/2]); |
| } |
| |
| ge_p1p1_to_p2(r,&t); |
| } |
| |
| return 0; |
| } |
| |
| |
| 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 |
| } ; |
| |
| |
| int ge_frombytes_negate_vartime(ge_p3 *h,const unsigned char *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; |
| } |
| |
| |
| /* ge madd */ |
| /* |
| r = p + q |
| */ |
| |
| 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); |
| } |
| |
| |
| /* ge msub */ |
| |
| /* |
| r = p - q |
| */ |
| |
| 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); |
| } |
| |
| |
| /* ge p1p1 to p2 */ |
| /* |
| r = p |
| */ |
| |
| extern 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); |
| } |
| |
| |
| /* ge p1p1 to p3 */ |
| |
| /* |
| r = p |
| */ |
| |
| extern 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); |
| } |
| |
| |
| /* ge p2 0 */ |
| |
| void ge_p2_0(ge_p2 *h) |
| { |
| fe_0(h->X); |
| fe_1(h->Y); |
| fe_1(h->Z); |
| } |
| |
| |
| /* ge p2 dbl */ |
| |
| /* |
| r = 2 * p |
| */ |
| |
| void ge_p2_dbl(ge_p1p1 *r,const ge_p2 *p) |
| { |
| fe t0; |
| fe_sq(r->X,p->X); |
| fe_sq(r->Z,p->Y); |
| fe_sq2(r->T,p->Z); |
| fe_add(r->Y,p->X,p->Y); |
| fe_sq(t0,r->Y); |
| fe_add(r->Y,r->Z,r->X); |
| fe_sub(r->Z,r->Z,r->X); |
| fe_sub(r->X,t0,r->Y); |
| fe_sub(r->T,r->T,r->Z); |
| } |
| |
| |
| /* ge p3 0 */ |
| |
| void ge_p3_0(ge_p3 *h) |
| { |
| fe_0(h->X); |
| fe_1(h->Y); |
| fe_1(h->Z); |
| fe_0(h->T); |
| } |
| |
| |
| /* ge p3 dble */ |
| |
| /* |
| r = 2 * p |
| */ |
| |
| 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); |
| } |
| |
| |
| /* ge p3 to cached */ |
| |
| /* |
| r = p |
| */ |
| |
| static const fe d2 = { |
| -21827239,-5839606,-30745221,13898782,229458, |
| 15978800,-12551817,-6495438,29715968,9444199 |
| } ; |
| |
| |
| extern 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); |
| } |
| |
| |
| /* ge p3 to p2 */ |
| /* |
| r = p |
| */ |
| |
| extern 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); |
| } |
| |
| |
| /* ge p3 tobytes */ |
| 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; |
| } |
| |
| |
| /* ge_precomp_0 */ |
| void ge_precomp_0(ge_precomp *h) |
| { |
| fe_1(h->yplusx); |
| fe_1(h->yminusx); |
| fe_0(h->xy2d); |
| } |
| |
| |
| /* ge_sub */ |
| /* |
| r = p - q |
| */ |
| |
| 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); |
| } |
| |
| |
| /* ge tobytes */ |
| 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; |
| } |
| #endif /* HAVE_ED25519 */ |
| |
