/* fe_operations.c * * Copyright (C) 2006-2022 wolfSSL Inc. * * This file is part of wolfSSL. * * 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 02110-1335, USA */ /* Based On Daniel J Bernstein's curve25519 Public Domain ref10 work. */ #ifdef HAVE_CONFIG_H #include #endif #include #if defined(HAVE_CURVE25519) || defined(HAVE_ED25519) #if !defined(CURVE25519_SMALL) || !defined(ED25519_SMALL) /* run when not defined to use small memory math */ #include #ifdef NO_INLINE #include #else #define WOLFSSL_MISC_INCLUDED #include #endif #ifdef CURVED25519_X64 /* Assembly code in fe_x25519_asm.* */ #elif defined(WOLFSSL_ARMASM) /* Assembly code in fe_armv[78]_x25519.* */ #elif defined(CURVED25519_128BIT) #include "fe_x25519_128.i" #else #if defined(HAVE_CURVE25519) || \ (defined(HAVE_ED25519) && !defined(ED25519_SMALL)) /* 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. */ word64 load_3(const unsigned char *in) { word64 result; result = (word64) in[0]; result |= ((word64) in[1]) << 8; result |= ((word64) in[2]) << 16; return result; } word64 load_4(const unsigned char *in) { word64 result; result = (word64) in[0]; result |= ((word64) in[1]) << 8; result |= ((word64) in[2]) << 16; result |= ((word64) in[3]) << 24; return result; } #endif /* h = 1 */ void fe_1(fe h) { h[0] = 1; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } /* h = 0 */ void fe_0(fe h) { h[0] = 0; h[1] = 0; h[2] = 0; h[3] = 0; h[4] = 0; h[5] = 0; h[6] = 0; h[7] = 0; h[8] = 0; h[9] = 0; } #if ((defined(HAVE_CURVE25519) && !defined(CURVE25519_SMALL)) || \ (defined(HAVE_ED25519) && !defined(ED25519_SMALL))) && \ !defined(FREESCALE_LTC_ECC) /* to be Complementary to fe_low_mem.c */ void fe_init(void) { } #endif #if defined(HAVE_CURVE25519) && !defined(CURVE25519_SMALL) && \ !defined(FREESCALE_LTC_ECC) int curve25519(byte* q, const byte* n, const byte* p) { #if 0 unsigned char e[32]; #endif fe x1 = {0}; fe x2 = {0}; fe z2 = {0}; fe x3 = {0}; fe z3 = {0}; fe tmp0 = {0}; fe tmp1 = {0}; int pos = 0; unsigned int swap = 0; unsigned int b = 0; /* Clamp already done during key generation and import */ #if 0 { unsigned int i; for (i = 0;i < 32;++i) e[i] = n[i]; e[0] &= 248; e[31] &= 127; e[31] |= 64; } #endif fe_frombytes(x1,p); fe_1(x2); fe_0(z2); fe_copy(x3,x1); fe_1(z3); swap = 0; for (pos = 254;pos >= 0;--pos) { #if 0 b = e[pos / 8] >> (pos & 7); #else b = n[pos / 8] >> (pos & 7); #endif b &= 1; swap ^= b; fe_cswap(x2,x3,swap); fe_cswap(z2,z3,swap); swap = b; /* montgomery */ fe_sub(tmp0,x3,z3); fe_sub(tmp1,x2,z2); fe_add(x2,x2,z2); fe_add(z2,x3,z3); fe_mul(z3,tmp0,x2); fe_mul(z2,z2,tmp1); fe_sq(tmp0,tmp1); fe_sq(tmp1,x2); fe_add(x3,z3,z2); fe_sub(z2,z3,z2); fe_mul(x2,tmp1,tmp0); fe_sub(tmp1,tmp1,tmp0); fe_sq(z2,z2); fe_mul121666(z3,tmp1); fe_sq(x3,x3); fe_add(tmp0,tmp0,z3); fe_mul(z3,x1,z2); fe_mul(z2,tmp1,tmp0); } fe_cswap(x2,x3,swap); fe_cswap(z2,z3,swap); fe_invert(z2,z2); fe_mul(x2,x2,z2); fe_tobytes(q,x2); return 0; } #endif /* HAVE_CURVE25519 && !CURVE25519_SMALL && !FREESCALE_LTC_ECC */ /* 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. */ void fe_sq(fe h,const fe f) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 f0_2 = 2 * f0; sword32 f1_2 = 2 * f1; sword32 f2_2 = 2 * f2; sword32 f3_2 = 2 * f3; sword32 f4_2 = 2 * f4; sword32 f5_2 = 2 * f5; sword32 f6_2 = 2 * f6; sword32 f7_2 = 2 * f7; sword32 f5_38 = 38 * f5; /* 1.959375*2^30 */ sword32 f6_19 = 19 * f6; /* 1.959375*2^30 */ sword32 f7_38 = 38 * f7; /* 1.959375*2^30 */ sword32 f8_19 = 19 * f8; /* 1.959375*2^30 */ sword32 f9_38 = 38 * f9; /* 1.959375*2^30 */ sword64 f0f0 = f0 * (sword64) f0; sword64 f0f1_2 = f0_2 * (sword64) f1; sword64 f0f2_2 = f0_2 * (sword64) f2; sword64 f0f3_2 = f0_2 * (sword64) f3; sword64 f0f4_2 = f0_2 * (sword64) f4; sword64 f0f5_2 = f0_2 * (sword64) f5; sword64 f0f6_2 = f0_2 * (sword64) f6; sword64 f0f7_2 = f0_2 * (sword64) f7; sword64 f0f8_2 = f0_2 * (sword64) f8; sword64 f0f9_2 = f0_2 * (sword64) f9; sword64 f1f1_2 = f1_2 * (sword64) f1; sword64 f1f2_2 = f1_2 * (sword64) f2; sword64 f1f3_4 = f1_2 * (sword64) f3_2; sword64 f1f4_2 = f1_2 * (sword64) f4; sword64 f1f5_4 = f1_2 * (sword64) f5_2; sword64 f1f6_2 = f1_2 * (sword64) f6; sword64 f1f7_4 = f1_2 * (sword64) f7_2; sword64 f1f8_2 = f1_2 * (sword64) f8; sword64 f1f9_76 = f1_2 * (sword64) f9_38; sword64 f2f2 = f2 * (sword64) f2; sword64 f2f3_2 = f2_2 * (sword64) f3; sword64 f2f4_2 = f2_2 * (sword64) f4; sword64 f2f5_2 = f2_2 * (sword64) f5; sword64 f2f6_2 = f2_2 * (sword64) f6; sword64 f2f7_2 = f2_2 * (sword64) f7; sword64 f2f8_38 = f2_2 * (sword64) f8_19; sword64 f2f9_38 = f2 * (sword64) f9_38; sword64 f3f3_2 = f3_2 * (sword64) f3; sword64 f3f4_2 = f3_2 * (sword64) f4; sword64 f3f5_4 = f3_2 * (sword64) f5_2; sword64 f3f6_2 = f3_2 * (sword64) f6; sword64 f3f7_76 = f3_2 * (sword64) f7_38; sword64 f3f8_38 = f3_2 * (sword64) f8_19; sword64 f3f9_76 = f3_2 * (sword64) f9_38; sword64 f4f4 = f4 * (sword64) f4; sword64 f4f5_2 = f4_2 * (sword64) f5; sword64 f4f6_38 = f4_2 * (sword64) f6_19; sword64 f4f7_38 = f4 * (sword64) f7_38; sword64 f4f8_38 = f4_2 * (sword64) f8_19; sword64 f4f9_38 = f4 * (sword64) f9_38; sword64 f5f5_38 = f5 * (sword64) f5_38; sword64 f5f6_38 = f5_2 * (sword64) f6_19; sword64 f5f7_76 = f5_2 * (sword64) f7_38; sword64 f5f8_38 = f5_2 * (sword64) f8_19; sword64 f5f9_76 = f5_2 * (sword64) f9_38; sword64 f6f6_19 = f6 * (sword64) f6_19; sword64 f6f7_38 = f6 * (sword64) f7_38; sword64 f6f8_38 = f6_2 * (sword64) f8_19; sword64 f6f9_38 = f6 * (sword64) f9_38; sword64 f7f7_38 = f7 * (sword64) f7_38; sword64 f7f8_38 = f7_2 * (sword64) f8_19; sword64 f7f9_76 = f7_2 * (sword64) f9_38; sword64 f8f8_19 = f8 * (sword64) f8_19; sword64 f8f9_38 = f8 * (sword64) f9_38; sword64 f9f9_38 = f9 * (sword64) f9_38; sword64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; sword64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; sword64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; sword64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; sword64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; sword64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; sword64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; sword64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; sword64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; sword64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; sword64 carry0; sword64 carry1; sword64 carry2; sword64 carry3; sword64 carry4; sword64 carry5; sword64 carry6; sword64 carry7; sword64 carry8; sword64 carry9; carry0 = (h0 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (sword64) (1UL<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (sword64) (1UL<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (sword64) (1UL<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (sword64) (1UL<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (sword64) (1UL<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (sword64) (1UL<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (sword64) (1UL<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (sword64) (1UL<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (sword64) (1UL<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (sword64) (1UL<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = (sword32)h0; h[1] = (sword32)h1; h[2] = (sword32)h2; h[3] = (sword32)h3; h[4] = (sword32)h4; h[5] = (sword32)h5; h[6] = (sword32)h6; h[7] = (sword32)h7; h[8] = (sword32)h8; h[9] = (sword32)h9; } /* 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. */ void fe_add(fe h,const fe f,const fe g) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 g0 = g[0]; sword32 g1 = g[1]; sword32 g2 = g[2]; sword32 g3 = g[3]; sword32 g4 = g[4]; sword32 g5 = g[5]; sword32 g6 = g[6]; sword32 g7 = g[7]; sword32 g8 = g[8]; sword32 g9 = g[9]; sword32 h0 = f0 + g0; sword32 h1 = f1 + g1; sword32 h2 = f2 + g2; sword32 h3 = f3 + g3; sword32 h4 = f4 + g4; sword32 h5 = f5 + g5; sword32 h6 = f6 + g6; sword32 h7 = f7 + g7; sword32 h8 = f8 + g8; sword32 h9 = f9 + g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* Preconditions: |h| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Write p=2^255-19; q=floor(h/p). Basic claim: q = floor(2^(-255)(h + 19 2^(-25)h9 + 2^(-1))). Proof: Have |h|<=p so |q|<=1 so |19^2 2^(-255) q|<1/4. Also have |h-2^230 h9|<2^231 so |19 2^(-255)(h-2^230 h9)|<1/4. Write y=2^(-1)-19^2 2^(-255)q-19 2^(-255)(h-2^230 h9). Then 0> 25; q = (h0 + q) >> 26; q = (h1 + q) >> 25; q = (h2 + q) >> 26; q = (h3 + q) >> 25; q = (h4 + q) >> 26; q = (h5 + q) >> 25; q = (h6 + q) >> 26; q = (h7 + q) >> 25; q = (h8 + q) >> 26; q = (h9 + q) >> 25; /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */ h0 += 19 * q; /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */ carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26; carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25; carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26; carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25; carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26; carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25; carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26; carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25; carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = h9 >> 25; h9 -= carry9 << 25; /* h10 = carry9 */ /* Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20. Have h0+...+2^230 h9 between 0 and 2^255-1; evidently 2^255 h10-2^255 q = 0. Goal: Output h0+...+2^230 h9. */ s[0] = (byte)(h0 >> 0); s[1] = (byte)(h0 >> 8); s[2] = (byte)(h0 >> 16); s[3] = (byte)((h0 >> 24) | (h1 << 2)); s[4] = (byte)(h1 >> 6); s[5] = (byte)(h1 >> 14); s[6] = (byte)((h1 >> 22) | (h2 << 3)); s[7] = (byte)(h2 >> 5); s[8] = (byte)(h2 >> 13); s[9] = (byte)((h2 >> 21) | (h3 << 5)); s[10] = (byte)(h3 >> 3); s[11] = (byte)(h3 >> 11); s[12] = (byte)((h3 >> 19) | (h4 << 6)); s[13] = (byte)(h4 >> 2); s[14] = (byte)(h4 >> 10); s[15] = (byte)(h4 >> 18); s[16] = (byte)(h5 >> 0); s[17] = (byte)(h5 >> 8); s[18] = (byte)(h5 >> 16); s[19] = (byte)((h5 >> 24) | (h6 << 1)); s[20] = (byte)(h6 >> 7); s[21] = (byte)(h6 >> 15); s[22] = (byte)((h6 >> 23) | (h7 << 3)); s[23] = (byte)(h7 >> 5); s[24] = (byte)(h7 >> 13); s[25] = (byte)((h7 >> 21) | (h8 << 4)); s[26] = (byte)(h8 >> 4); s[27] = (byte)(h8 >> 12); s[28] = (byte)((h8 >> 20) | (h9 << 6)); s[29] = (byte)(h9 >> 2); s[30] = (byte)(h9 >> 10); s[31] = (byte)(h9 >> 18); } /* 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. */ void fe_sub(fe h,const fe f,const fe g) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 g0 = g[0]; sword32 g1 = g[1]; sword32 g2 = g[2]; sword32 g3 = g[3]; sword32 g4 = g[4]; sword32 g5 = g[5]; sword32 g6 = g[6]; sword32 g7 = g[7]; sword32 g8 = g[8]; sword32 g9 = g[9]; sword32 h0 = f0 - g0; sword32 h1 = f1 - g1; sword32 h2 = f2 - g2; sword32 h3 = f3 - g3; sword32 h4 = f4 - g4; sword32 h5 = f5 - g5; sword32 h6 = f6 - g6; sword32 h7 = f7 - g7; sword32 h8 = f8 - g8; sword32 h9 = f9 - g9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } #if defined(HAVE_CURVE25519) || \ (defined(HAVE_ED25519) && !defined(ED25519_SMALL)) /* Ignores top bit of h. */ void fe_frombytes(fe h,const unsigned char *s) { sword64 h0 = load_4(s); sword64 h1 = load_3(s + 4) << 6; sword64 h2 = load_3(s + 7) << 5; sword64 h3 = load_3(s + 10) << 3; sword64 h4 = load_3(s + 13) << 2; sword64 h5 = load_4(s + 16); sword64 h6 = load_3(s + 20) << 7; sword64 h7 = load_3(s + 23) << 5; sword64 h8 = load_3(s + 26) << 4; sword64 h9 = (load_3(s + 29) & 8388607) << 2; sword64 carry0; sword64 carry1; sword64 carry2; sword64 carry3; sword64 carry4; sword64 carry5; sword64 carry6; sword64 carry7; sword64 carry8; sword64 carry9; carry9 = (h9 + (sword64) (1UL<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (sword64) (1UL<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (sword64) (1UL<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (sword64) (1UL<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (sword64) (1UL<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (sword64) (1UL<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (sword64) (1UL<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (sword64) (1UL<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (sword64) (1UL<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; h[0] = (sword32)h0; h[1] = (sword32)h1; h[2] = (sword32)h2; h[3] = (sword32)h3; h[4] = (sword32)h4; h[5] = (sword32)h5; h[6] = (sword32)h6; h[7] = (sword32)h7; h[8] = (sword32)h8; h[9] = (sword32)h9; } #endif void fe_invert(fe out,const fe z) { fe t0 = {0}; fe t1 = {0}; fe t2 = {0}; fe t3 = {0}; int i = 0; /* pow225521 */ 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); return; } /* h = f */ void fe_copy(fe h,const fe f) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; h[0] = f0; h[1] = f1; h[2] = f2; h[3] = f3; h[4] = f4; h[5] = f5; h[6] = f6; h[7] = f7; h[8] = f8; h[9] = f9; } /* 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. */ void fe_mul(fe h,const fe f,const fe g) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 g0 = g[0]; sword32 g1 = g[1]; sword32 g2 = g[2]; sword32 g3 = g[3]; sword32 g4 = g[4]; sword32 g5 = g[5]; sword32 g6 = g[6]; sword32 g7 = g[7]; sword32 g8 = g[8]; sword32 g9 = g[9]; sword32 g1_19 = 19 * g1; /* 1.959375*2^29 */ sword32 g2_19 = 19 * g2; /* 1.959375*2^30; still ok */ sword32 g3_19 = 19 * g3; sword32 g4_19 = 19 * g4; sword32 g5_19 = 19 * g5; sword32 g6_19 = 19 * g6; sword32 g7_19 = 19 * g7; sword32 g8_19 = 19 * g8; sword32 g9_19 = 19 * g9; sword32 f1_2 = 2 * f1; sword32 f3_2 = 2 * f3; sword32 f5_2 = 2 * f5; sword32 f7_2 = 2 * f7; sword32 f9_2 = 2 * f9; sword64 f0g0 = f0 * (sword64) g0; sword64 f0g1 = f0 * (sword64) g1; sword64 f0g2 = f0 * (sword64) g2; sword64 f0g3 = f0 * (sword64) g3; sword64 f0g4 = f0 * (sword64) g4; sword64 f0g5 = f0 * (sword64) g5; sword64 f0g6 = f0 * (sword64) g6; sword64 f0g7 = f0 * (sword64) g7; sword64 f0g8 = f0 * (sword64) g8; sword64 f0g9 = f0 * (sword64) g9; sword64 f1g0 = f1 * (sword64) g0; sword64 f1g1_2 = f1_2 * (sword64) g1; sword64 f1g2 = f1 * (sword64) g2; sword64 f1g3_2 = f1_2 * (sword64) g3; sword64 f1g4 = f1 * (sword64) g4; sword64 f1g5_2 = f1_2 * (sword64) g5; sword64 f1g6 = f1 * (sword64) g6; sword64 f1g7_2 = f1_2 * (sword64) g7; sword64 f1g8 = f1 * (sword64) g8; sword64 f1g9_38 = f1_2 * (sword64) g9_19; sword64 f2g0 = f2 * (sword64) g0; sword64 f2g1 = f2 * (sword64) g1; sword64 f2g2 = f2 * (sword64) g2; sword64 f2g3 = f2 * (sword64) g3; sword64 f2g4 = f2 * (sword64) g4; sword64 f2g5 = f2 * (sword64) g5; sword64 f2g6 = f2 * (sword64) g6; sword64 f2g7 = f2 * (sword64) g7; sword64 f2g8_19 = f2 * (sword64) g8_19; sword64 f2g9_19 = f2 * (sword64) g9_19; sword64 f3g0 = f3 * (sword64) g0; sword64 f3g1_2 = f3_2 * (sword64) g1; sword64 f3g2 = f3 * (sword64) g2; sword64 f3g3_2 = f3_2 * (sword64) g3; sword64 f3g4 = f3 * (sword64) g4; sword64 f3g5_2 = f3_2 * (sword64) g5; sword64 f3g6 = f3 * (sword64) g6; sword64 f3g7_38 = f3_2 * (sword64) g7_19; sword64 f3g8_19 = f3 * (sword64) g8_19; sword64 f3g9_38 = f3_2 * (sword64) g9_19; sword64 f4g0 = f4 * (sword64) g0; sword64 f4g1 = f4 * (sword64) g1; sword64 f4g2 = f4 * (sword64) g2; sword64 f4g3 = f4 * (sword64) g3; sword64 f4g4 = f4 * (sword64) g4; sword64 f4g5 = f4 * (sword64) g5; sword64 f4g6_19 = f4 * (sword64) g6_19; sword64 f4g7_19 = f4 * (sword64) g7_19; sword64 f4g8_19 = f4 * (sword64) g8_19; sword64 f4g9_19 = f4 * (sword64) g9_19; sword64 f5g0 = f5 * (sword64) g0; sword64 f5g1_2 = f5_2 * (sword64) g1; sword64 f5g2 = f5 * (sword64) g2; sword64 f5g3_2 = f5_2 * (sword64) g3; sword64 f5g4 = f5 * (sword64) g4; sword64 f5g5_38 = f5_2 * (sword64) g5_19; sword64 f5g6_19 = f5 * (sword64) g6_19; sword64 f5g7_38 = f5_2 * (sword64) g7_19; sword64 f5g8_19 = f5 * (sword64) g8_19; sword64 f5g9_38 = f5_2 * (sword64) g9_19; sword64 f6g0 = f6 * (sword64) g0; sword64 f6g1 = f6 * (sword64) g1; sword64 f6g2 = f6 * (sword64) g2; sword64 f6g3 = f6 * (sword64) g3; sword64 f6g4_19 = f6 * (sword64) g4_19; sword64 f6g5_19 = f6 * (sword64) g5_19; sword64 f6g6_19 = f6 * (sword64) g6_19; sword64 f6g7_19 = f6 * (sword64) g7_19; sword64 f6g8_19 = f6 * (sword64) g8_19; sword64 f6g9_19 = f6 * (sword64) g9_19; sword64 f7g0 = f7 * (sword64) g0; sword64 f7g1_2 = f7_2 * (sword64) g1; sword64 f7g2 = f7 * (sword64) g2; sword64 f7g3_38 = f7_2 * (sword64) g3_19; sword64 f7g4_19 = f7 * (sword64) g4_19; sword64 f7g5_38 = f7_2 * (sword64) g5_19; sword64 f7g6_19 = f7 * (sword64) g6_19; sword64 f7g7_38 = f7_2 * (sword64) g7_19; sword64 f7g8_19 = f7 * (sword64) g8_19; sword64 f7g9_38 = f7_2 * (sword64) g9_19; sword64 f8g0 = f8 * (sword64) g0; sword64 f8g1 = f8 * (sword64) g1; sword64 f8g2_19 = f8 * (sword64) g2_19; sword64 f8g3_19 = f8 * (sword64) g3_19; sword64 f8g4_19 = f8 * (sword64) g4_19; sword64 f8g5_19 = f8 * (sword64) g5_19; sword64 f8g6_19 = f8 * (sword64) g6_19; sword64 f8g7_19 = f8 * (sword64) g7_19; sword64 f8g8_19 = f8 * (sword64) g8_19; sword64 f8g9_19 = f8 * (sword64) g9_19; sword64 f9g0 = f9 * (sword64) g0; sword64 f9g1_38 = f9_2 * (sword64) g1_19; sword64 f9g2_19 = f9 * (sword64) g2_19; sword64 f9g3_38 = f9_2 * (sword64) g3_19; sword64 f9g4_19 = f9 * (sword64) g4_19; sword64 f9g5_38 = f9_2 * (sword64) g5_19; sword64 f9g6_19 = f9 * (sword64) g6_19; sword64 f9g7_38 = f9_2 * (sword64) g7_19; sword64 f9g8_19 = f9 * (sword64) g8_19; sword64 f9g9_38 = f9_2 * (sword64) g9_19; sword64 h0 = f0g0+f1g9_38+f2g8_19+f3g7_38+f4g6_19+f5g5_38+f6g4_19+f7g3_38+f8g2_19+f9g1_38; sword64 h1 = f0g1+f1g0 +f2g9_19+f3g8_19+f4g7_19+f5g6_19+f6g5_19+f7g4_19+f8g3_19+f9g2_19; sword64 h2 = f0g2+f1g1_2 +f2g0 +f3g9_38+f4g8_19+f5g7_38+f6g6_19+f7g5_38+f8g4_19+f9g3_38; sword64 h3 = f0g3+f1g2 +f2g1 +f3g0 +f4g9_19+f5g8_19+f6g7_19+f7g6_19+f8g5_19+f9g4_19; sword64 h4 = f0g4+f1g3_2 +f2g2 +f3g1_2 +f4g0 +f5g9_38+f6g8_19+f7g7_38+f8g6_19+f9g5_38; sword64 h5 = f0g5+f1g4 +f2g3 +f3g2 +f4g1 +f5g0 +f6g9_19+f7g8_19+f8g7_19+f9g6_19; sword64 h6 = f0g6+f1g5_2 +f2g4 +f3g3_2 +f4g2 +f5g1_2 +f6g0 +f7g9_38+f8g8_19+f9g7_38; sword64 h7 = f0g7+f1g6 +f2g5 +f3g4 +f4g3 +f5g2 +f6g1 +f7g0 +f8g9_19+f9g8_19; sword64 h8 = f0g8+f1g7_2 +f2g6 +f3g5_2 +f4g4 +f5g3_2 +f6g2 +f7g1_2 +f8g0 +f9g9_38; sword64 h9 = f0g9+f1g8 +f2g7 +f3g6 +f4g5 +f5g4 +f6g3 +f7g2 +f8g1 +f9g0 ; sword64 carry0; sword64 carry1; sword64 carry2; sword64 carry3; sword64 carry4; sword64 carry5; sword64 carry6; sword64 carry7; sword64 carry8; sword64 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 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (sword64) (1UL<<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 + (sword64) (1UL<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (sword64) (1UL<<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 + (sword64) (1UL<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (sword64) (1UL<<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 + (sword64) (1UL<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (sword64) (1UL<<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 + (sword64) (1UL<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (sword64) (1UL<<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 + (sword64) (1UL<<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 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; /* |h0| <= 2^25; from now on fits into int32 unchanged */ /* |h1| <= 1.01*2^24 */ h[0] = (sword32)h0; h[1] = (sword32)h1; h[2] = (sword32)h2; h[3] = (sword32)h3; h[4] = (sword32)h4; h[5] = (sword32)h5; h[6] = (sword32)h6; h[7] = (sword32)h7; h[8] = (sword32)h8; h[9] = (sword32)h9; } /* Replace (f,g) with (g,f) if b == 1; replace (f,g) with (f,g) if b == 0. Preconditions: b in {0,1}. */ void fe_cswap(fe f, fe g, int b) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 g0 = g[0]; sword32 g1 = g[1]; sword32 g2 = g[2]; sword32 g3 = g[3]; sword32 g4 = g[4]; sword32 g5 = g[5]; sword32 g6 = g[6]; sword32 g7 = g[7]; sword32 g8 = g[8]; sword32 g9 = g[9]; sword32 x0 = f0 ^ g0; sword32 x1 = f1 ^ g1; sword32 x2 = f2 ^ g2; sword32 x3 = f3 ^ g3; sword32 x4 = f4 ^ g4; sword32 x5 = f5 ^ g5; sword32 x6 = f6 ^ g6; sword32 x7 = f7 ^ g7; sword32 x8 = f8 ^ g8; sword32 x9 = f9 ^ g9; b = -b; x0 &= b; x1 &= b; x2 &= b; x3 &= b; x4 &= b; x5 &= b; x6 &= b; x7 &= b; x8 &= b; x9 &= b; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; g[0] = g0 ^ x0; g[1] = g1 ^ x1; g[2] = g2 ^ x2; g[3] = g3 ^ x3; g[4] = g4 ^ x4; g[5] = g5 ^ x5; g[6] = g6 ^ x6; g[7] = g7 ^ x7; g[8] = g8 ^ x8; g[9] = g9 ^ x9; } /* h = f * 121666 Can overlap h with f. Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. Postconditions: |h| bounded by 1.1*2^25,1.1*2^24,1.1*2^25,1.1*2^24,etc. */ void fe_mul121666(fe h,fe f) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword64 h0 = f0 * (sword64) 121666; sword64 h1 = f1 * (sword64) 121666; sword64 h2 = f2 * (sword64) 121666; sword64 h3 = f3 * (sword64) 121666; sword64 h4 = f4 * (sword64) 121666; sword64 h5 = f5 * (sword64) 121666; sword64 h6 = f6 * (sword64) 121666; sword64 h7 = f7 * (sword64) 121666; sword64 h8 = f8 * (sword64) 121666; sword64 h9 = f9 * (sword64) 121666; sword64 carry0; sword64 carry1; sword64 carry2; sword64 carry3; sword64 carry4; sword64 carry5; sword64 carry6; sword64 carry7; sword64 carry8; sword64 carry9; carry9 = (h9 + (sword64) (1UL<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry1 = (h1 + (sword64) (1UL<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry3 = (h3 + (sword64) (1UL<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry5 = (h5 + (sword64) (1UL<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry7 = (h7 + (sword64) (1UL<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry0 = (h0 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry2 = (h2 + (sword64) (1UL<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry4 = (h4 + (sword64) (1UL<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry6 = (h6 + (sword64) (1UL<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry8 = (h8 + (sword64) (1UL<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; h[0] = (sword32)h0; h[1] = (sword32)h1; h[2] = (sword32)h2; h[3] = (sword32)h3; h[4] = (sword32)h4; h[5] = (sword32)h5; h[6] = (sword32)h6; h[7] = (sword32)h7; h[8] = (sword32)h8; h[9] = (sword32)h9; } /* 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. */ void fe_sq2(fe h,const fe f) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 f0_2 = 2 * f0; sword32 f1_2 = 2 * f1; sword32 f2_2 = 2 * f2; sword32 f3_2 = 2 * f3; sword32 f4_2 = 2 * f4; sword32 f5_2 = 2 * f5; sword32 f6_2 = 2 * f6; sword32 f7_2 = 2 * f7; sword32 f5_38 = 38 * f5; /* 1.959375*2^30 */ sword32 f6_19 = 19 * f6; /* 1.959375*2^30 */ sword32 f7_38 = 38 * f7; /* 1.959375*2^30 */ sword32 f8_19 = 19 * f8; /* 1.959375*2^30 */ sword32 f9_38 = 38 * f9; /* 1.959375*2^30 */ sword64 f0f0 = f0 * (sword64) f0; sword64 f0f1_2 = f0_2 * (sword64) f1; sword64 f0f2_2 = f0_2 * (sword64) f2; sword64 f0f3_2 = f0_2 * (sword64) f3; sword64 f0f4_2 = f0_2 * (sword64) f4; sword64 f0f5_2 = f0_2 * (sword64) f5; sword64 f0f6_2 = f0_2 * (sword64) f6; sword64 f0f7_2 = f0_2 * (sword64) f7; sword64 f0f8_2 = f0_2 * (sword64) f8; sword64 f0f9_2 = f0_2 * (sword64) f9; sword64 f1f1_2 = f1_2 * (sword64) f1; sword64 f1f2_2 = f1_2 * (sword64) f2; sword64 f1f3_4 = f1_2 * (sword64) f3_2; sword64 f1f4_2 = f1_2 * (sword64) f4; sword64 f1f5_4 = f1_2 * (sword64) f5_2; sword64 f1f6_2 = f1_2 * (sword64) f6; sword64 f1f7_4 = f1_2 * (sword64) f7_2; sword64 f1f8_2 = f1_2 * (sword64) f8; sword64 f1f9_76 = f1_2 * (sword64) f9_38; sword64 f2f2 = f2 * (sword64) f2; sword64 f2f3_2 = f2_2 * (sword64) f3; sword64 f2f4_2 = f2_2 * (sword64) f4; sword64 f2f5_2 = f2_2 * (sword64) f5; sword64 f2f6_2 = f2_2 * (sword64) f6; sword64 f2f7_2 = f2_2 * (sword64) f7; sword64 f2f8_38 = f2_2 * (sword64) f8_19; sword64 f2f9_38 = f2 * (sword64) f9_38; sword64 f3f3_2 = f3_2 * (sword64) f3; sword64 f3f4_2 = f3_2 * (sword64) f4; sword64 f3f5_4 = f3_2 * (sword64) f5_2; sword64 f3f6_2 = f3_2 * (sword64) f6; sword64 f3f7_76 = f3_2 * (sword64) f7_38; sword64 f3f8_38 = f3_2 * (sword64) f8_19; sword64 f3f9_76 = f3_2 * (sword64) f9_38; sword64 f4f4 = f4 * (sword64) f4; sword64 f4f5_2 = f4_2 * (sword64) f5; sword64 f4f6_38 = f4_2 * (sword64) f6_19; sword64 f4f7_38 = f4 * (sword64) f7_38; sword64 f4f8_38 = f4_2 * (sword64) f8_19; sword64 f4f9_38 = f4 * (sword64) f9_38; sword64 f5f5_38 = f5 * (sword64) f5_38; sword64 f5f6_38 = f5_2 * (sword64) f6_19; sword64 f5f7_76 = f5_2 * (sword64) f7_38; sword64 f5f8_38 = f5_2 * (sword64) f8_19; sword64 f5f9_76 = f5_2 * (sword64) f9_38; sword64 f6f6_19 = f6 * (sword64) f6_19; sword64 f6f7_38 = f6 * (sword64) f7_38; sword64 f6f8_38 = f6_2 * (sword64) f8_19; sword64 f6f9_38 = f6 * (sword64) f9_38; sword64 f7f7_38 = f7 * (sword64) f7_38; sword64 f7f8_38 = f7_2 * (sword64) f8_19; sword64 f7f9_76 = f7_2 * (sword64) f9_38; sword64 f8f8_19 = f8 * (sword64) f8_19; sword64 f8f9_38 = f8 * (sword64) f9_38; sword64 f9f9_38 = f9 * (sword64) f9_38; sword64 h0 = f0f0 +f1f9_76+f2f8_38+f3f7_76+f4f6_38+f5f5_38; sword64 h1 = f0f1_2+f2f9_38+f3f8_38+f4f7_38+f5f6_38; sword64 h2 = f0f2_2+f1f1_2 +f3f9_76+f4f8_38+f5f7_76+f6f6_19; sword64 h3 = f0f3_2+f1f2_2 +f4f9_38+f5f8_38+f6f7_38; sword64 h4 = f0f4_2+f1f3_4 +f2f2 +f5f9_76+f6f8_38+f7f7_38; sword64 h5 = f0f5_2+f1f4_2 +f2f3_2 +f6f9_38+f7f8_38; sword64 h6 = f0f6_2+f1f5_4 +f2f4_2 +f3f3_2 +f7f9_76+f8f8_19; sword64 h7 = f0f7_2+f1f6_2 +f2f5_2 +f3f4_2 +f8f9_38; sword64 h8 = f0f8_2+f1f7_4 +f2f6_2 +f3f5_4 +f4f4 +f9f9_38; sword64 h9 = f0f9_2+f1f8_2 +f2f7_2 +f3f6_2 +f4f5_2; sword64 carry0; sword64 carry1; sword64 carry2; sword64 carry3; sword64 carry4; sword64 carry5; sword64 carry6; sword64 carry7; sword64 carry8; sword64 carry9; h0 += h0; h1 += h1; h2 += h2; h3 += h3; h4 += h4; h5 += h5; h6 += h6; h7 += h7; h8 += h8; h9 += h9; carry0 = (h0 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; carry4 = (h4 + (sword64) (1UL<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry1 = (h1 + (sword64) (1UL<<24)) >> 25; h2 += carry1; h1 -= carry1 << 25; carry5 = (h5 + (sword64) (1UL<<24)) >> 25; h6 += carry5; h5 -= carry5 << 25; carry2 = (h2 + (sword64) (1UL<<25)) >> 26; h3 += carry2; h2 -= carry2 << 26; carry6 = (h6 + (sword64) (1UL<<25)) >> 26; h7 += carry6; h6 -= carry6 << 26; carry3 = (h3 + (sword64) (1UL<<24)) >> 25; h4 += carry3; h3 -= carry3 << 25; carry7 = (h7 + (sword64) (1UL<<24)) >> 25; h8 += carry7; h7 -= carry7 << 25; carry4 = (h4 + (sword64) (1UL<<25)) >> 26; h5 += carry4; h4 -= carry4 << 26; carry8 = (h8 + (sword64) (1UL<<25)) >> 26; h9 += carry8; h8 -= carry8 << 26; carry9 = (h9 + (sword64) (1UL<<24)) >> 25; h0 += carry9 * 19; h9 -= carry9 << 25; carry0 = (h0 + (sword64) (1UL<<25)) >> 26; h1 += carry0; h0 -= carry0 << 26; h[0] = (sword32)h0; h[1] = (sword32)h1; h[2] = (sword32)h2; h[3] = (sword32)h3; h[4] = (sword32)h4; h[5] = (sword32)h5; h[6] = (sword32)h6; h[7] = (sword32)h7; h[8] = (sword32)h8; h[9] = (sword32)h9; } void fe_pow22523(fe out,const fe z) { fe t0 = {0}; fe t1 = {0}; fe t2 = {0}; int i = 0; 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); return; } /* 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. */ void fe_neg(fe h,const fe f) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 h0 = -f0; sword32 h1 = -f1; sword32 h2 = -f2; sword32 h3 = -f3; sword32 h4 = -f4; sword32 h5 = -f5; sword32 h6 = -f6; sword32 h7 = -f7; sword32 h8 = -f8; sword32 h9 = -f9; h[0] = h0; h[1] = h1; h[2] = h2; h[3] = h3; h[4] = h4; h[5] = h5; h[6] = h6; h[7] = h7; h[8] = h8; h[9] = h9; } /* Preconditions: |f| bounded by 1.1*2^26,1.1*2^25,1.1*2^26,1.1*2^25,etc. */ static const unsigned char zero[32] = {0}; int fe_isnonzero(const fe f) { unsigned char s[32]; fe_tobytes(s,f); return ConstantCompare(s,zero,32); } /* 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. */ int fe_isnegative(const fe f) { unsigned char s[32]; fe_tobytes(s,f); return s[0] & 1; } /* Replace (f,g) with (g,g) if b == 1; replace (f,g) with (f,g) if b == 0. Preconditions: b in {0,1}. */ void fe_cmov(fe f, const fe g, int b) { sword32 f0 = f[0]; sword32 f1 = f[1]; sword32 f2 = f[2]; sword32 f3 = f[3]; sword32 f4 = f[4]; sword32 f5 = f[5]; sword32 f6 = f[6]; sword32 f7 = f[7]; sword32 f8 = f[8]; sword32 f9 = f[9]; sword32 g0 = g[0]; sword32 g1 = g[1]; sword32 g2 = g[2]; sword32 g3 = g[3]; sword32 g4 = g[4]; sword32 g5 = g[5]; sword32 g6 = g[6]; sword32 g7 = g[7]; sword32 g8 = g[8]; sword32 g9 = g[9]; sword32 x0 = f0 ^ g0; sword32 x1 = f1 ^ g1; sword32 x2 = f2 ^ g2; sword32 x3 = f3 ^ g3; sword32 x4 = f4 ^ g4; sword32 x5 = f5 ^ g5; sword32 x6 = f6 ^ g6; sword32 x7 = f7 ^ g7; sword32 x8 = f8 ^ g8; sword32 x9 = f9 ^ g9; b = -b; x0 &= b; x1 &= b; x2 &= b; x3 &= b; x4 &= b; x5 &= b; x6 &= b; x7 &= b; x8 &= b; x9 &= b; f[0] = f0 ^ x0; f[1] = f1 ^ x1; f[2] = f2 ^ x2; f[3] = f3 ^ x3; f[4] = f4 ^ x4; f[5] = f5 ^ x5; f[6] = f6 ^ x6; f[7] = f7 ^ x7; f[8] = f8 ^ x8; f[9] = f9 ^ x9; } #endif #endif /* !CURVE25519_SMALL || !ED25519_SMALL */ #endif /* HAVE_CURVE25519 || HAVE_ED25519 */