Xuyi Wang
/
wolfSSL
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Diff: wolfcrypt/src/fe_operations.c
- Revision:
- 17:ff9d1e86ad5f
- Parent:
- 16:048e5e270a58
--- a/wolfcrypt/src/fe_operations.c Tue Nov 19 14:32:16 2019 +0000
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,1437 +0,0 @@
-/* fe_operations.c
- *
- * Copyright (C) 2006-2017 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 <config.h>
-#endif
-
-#include <wolfssl/wolfcrypt/settings.h>
-
-#if defined(HAVE_CURVE25519) || defined(HAVE_ED25519)
-#if !defined(CURVE25519_SMALL) || !defined(ED25519_SMALL) /* run when not defined to use small memory math */
-
-#include <wolfssl/wolfcrypt/fe_operations.h>
-#include <stdint.h>
-
-#ifdef NO_INLINE
- #include <wolfssl/wolfcrypt/misc.h>
-#else
- #define WOLFSSL_MISC_INCLUDED
- #include <wolfcrypt/src/misc.c>
-#endif
-
-#ifdef CURVED25519_X64
-#include "fe_x25519_x64.i"
-#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.
-*/
-
-uint64_t load_3(const unsigned char *in)
-{
- uint64_t result;
- result = (uint64_t) in[0];
- result |= ((uint64_t) in[1]) << 8;
- result |= ((uint64_t) in[2]) << 16;
- return result;
-}
-
-
-uint64_t load_4(const unsigned char *in)
-{
- uint64_t result;
- result = (uint64_t) in[0];
- result |= ((uint64_t) in[1]) << 8;
- result |= ((uint64_t) in[2]) << 16;
- result |= ((uint64_t) in[3]) << 24;
- return result;
-}
-#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()
-{
-}
-#endif
-
-#if defined(HAVE_CURVE25519) && !defined(CURVE25519_SMALL) && \
- !defined(FREESCALE_LTC_ECC)
-int curve25519(byte* q, byte* n, byte* p)
-{
-#if 0
- unsigned char e[32];
-#endif
- fe x1;
- fe x2;
- fe z2;
- fe x3;
- fe z3;
- fe tmp0;
- fe tmp1;
- int pos;
- unsigned int swap;
- unsigned int b;
-
- /* 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)
-{
- 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] = (int32_t)h0;
- h[1] = (int32_t)h1;
- h[2] = (int32_t)h2;
- h[3] = (int32_t)h3;
- h[4] = (int32_t)h4;
- h[5] = (int32_t)h5;
- h[6] = (int32_t)h6;
- h[7] = (int32_t)h7;
- h[8] = (int32_t)h8;
- h[9] = (int32_t)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)
-{
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t g0 = g[0];
- int32_t g1 = g[1];
- int32_t g2 = g[2];
- int32_t g3 = g[3];
- int32_t g4 = g[4];
- int32_t g5 = g[5];
- int32_t g6 = g[6];
- int32_t g7 = g[7];
- int32_t g8 = g[8];
- int32_t g9 = g[9];
- int32_t h0 = f0 + g0;
- int32_t h1 = f1 + g1;
- int32_t h2 = f2 + g2;
- int32_t h3 = f3 + g3;
- int32_t h4 = f4 + g4;
- int32_t h5 = f5 + g5;
- int32_t h6 = f6 + g6;
- int32_t h7 = f7 + g7;
- int32_t h8 = f8 + g8;
- int32_t h9 = f9 + g9;
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-
-/*
-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.
-*/
-
-void fe_tobytes(unsigned char *s,const fe h)
-{
- int32_t h0 = h[0];
- int32_t h1 = h[1];
- int32_t h2 = h[2];
- int32_t h3 = h[3];
- int32_t h4 = h[4];
- int32_t h5 = h[5];
- int32_t h6 = h[6];
- int32_t h7 = h[7];
- int32_t h8 = h[8];
- int32_t h9 = h[9];
- int32_t q;
- int32_t carry0;
- int32_t carry1;
- int32_t carry2;
- int32_t carry3;
- int32_t carry4;
- int32_t carry5;
- int32_t carry6;
- int32_t carry7;
- int32_t carry8;
- int32_t carry9;
-
- q = (19 * h9 + (((int32_t) 1) << 24)) >> 25;
- q = (h0 + q) >> 26;
- q = (h1 + q) >> 25;
- q = (h2 + q) >> 26;
- q = (h3 + q) >> 25;
- q = (h4 + q) >> 26;
- q = (h5 + q) >> 25;
- q = (h6 + q) >> 26;
- q = (h7 + q) >> 25;
- q = (h8 + q) >> 26;
- q = (h9 + q) >> 25;
-
- /* Goal: Output h-(2^255-19)q, which is between 0 and 2^255-20. */
- h0 += 19 * q;
- /* Goal: Output h-2^255 q, which is between 0 and 2^255-20. */
-
- carry0 = h0 >> 26; h1 += carry0; h0 -= carry0 << 26;
- carry1 = h1 >> 25; h2 += carry1; h1 -= carry1 << 25;
- carry2 = h2 >> 26; h3 += carry2; h2 -= carry2 << 26;
- carry3 = h3 >> 25; h4 += carry3; h3 -= carry3 << 25;
- carry4 = h4 >> 26; h5 += carry4; h4 -= carry4 << 26;
- carry5 = h5 >> 25; h6 += carry5; h5 -= carry5 << 25;
- carry6 = h6 >> 26; h7 += carry6; h6 -= carry6 << 26;
- carry7 = h7 >> 25; h8 += carry7; h7 -= carry7 << 25;
- carry8 = h8 >> 26; h9 += carry8; h8 -= carry8 << 26;
- carry9 = h9 >> 25; h9 -= carry9 << 25;
- /* h10 = carry9 */
-
- /*
- Goal: Output h0+...+2^255 h10-2^255 q, which is between 0 and 2^255-20.
- Have h0+...+2^230 h9 between 0 and 2^255-1;
- evidently 2^255 h10-2^255 q = 0.
- Goal: Output h0+...+2^230 h9.
- */
-
- s[0] = (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)
-{
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t g0 = g[0];
- int32_t g1 = g[1];
- int32_t g2 = g[2];
- int32_t g3 = g[3];
- int32_t g4 = g[4];
- int32_t g5 = g[5];
- int32_t g6 = g[6];
- int32_t g7 = g[7];
- int32_t g8 = g[8];
- int32_t g9 = g[9];
- int32_t h0 = f0 - g0;
- int32_t h1 = f1 - g1;
- int32_t h2 = f2 - g2;
- int32_t h3 = f3 - g3;
- int32_t h4 = f4 - g4;
- int32_t h5 = f5 - g5;
- int32_t h6 = f6 - g6;
- int32_t h7 = f7 - g7;
- int32_t h8 = f8 - g8;
- int32_t h9 = f9 - g9;
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-
-#if defined(HAVE_CURVE25519) || \
- (defined(HAVE_ED25519) && !defined(ED25519_SMALL))
-/*
-Ignores top bit of h.
-*/
-
-void fe_frombytes(fe h,const unsigned char *s)
-{
- 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] = (int32_t)h0;
- h[1] = (int32_t)h1;
- h[2] = (int32_t)h2;
- h[3] = (int32_t)h3;
- h[4] = (int32_t)h4;
- h[5] = (int32_t)h5;
- h[6] = (int32_t)h6;
- h[7] = (int32_t)h7;
- h[8] = (int32_t)h8;
- h[9] = (int32_t)h9;
-}
-#endif
-
-
-void fe_invert(fe out,const fe z)
-{
- fe t0;
- fe t1;
- fe t2;
- fe t3;
- int i;
-
- /* 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)
-{
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- h[0] = f0;
- h[1] = f1;
- h[2] = f2;
- h[3] = f3;
- h[4] = f4;
- h[5] = f5;
- h[6] = f6;
- h[7] = f7;
- h[8] = f8;
- h[9] = f9;
-}
-
-
-/*
-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)
-{
- 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] = (int32_t)h0;
- h[1] = (int32_t)h1;
- h[2] = (int32_t)h2;
- h[3] = (int32_t)h3;
- h[4] = (int32_t)h4;
- h[5] = (int32_t)h5;
- h[6] = (int32_t)h6;
- h[7] = (int32_t)h7;
- h[8] = (int32_t)h8;
- h[9] = (int32_t)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)
-{
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t g0 = g[0];
- int32_t g1 = g[1];
- int32_t g2 = g[2];
- int32_t g3 = g[3];
- int32_t g4 = g[4];
- int32_t g5 = g[5];
- int32_t g6 = g[6];
- int32_t g7 = g[7];
- int32_t g8 = g[8];
- int32_t g9 = g[9];
- int32_t x0 = f0 ^ g0;
- int32_t x1 = f1 ^ g1;
- int32_t x2 = f2 ^ g2;
- int32_t x3 = f3 ^ g3;
- int32_t x4 = f4 ^ g4;
- int32_t x5 = f5 ^ g5;
- int32_t x6 = f6 ^ g6;
- int32_t x7 = f7 ^ g7;
- int32_t x8 = f8 ^ g8;
- int32_t x9 = f9 ^ g9;
- 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)
-{
- 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];
- int64_t h0 = f0 * (int64_t) 121666;
- int64_t h1 = f1 * (int64_t) 121666;
- int64_t h2 = f2 * (int64_t) 121666;
- int64_t h3 = f3 * (int64_t) 121666;
- int64_t h4 = f4 * (int64_t) 121666;
- int64_t h5 = f5 * (int64_t) 121666;
- int64_t h6 = f6 * (int64_t) 121666;
- int64_t h7 = f7 * (int64_t) 121666;
- int64_t h8 = f8 * (int64_t) 121666;
- int64_t h9 = f9 * (int64_t) 121666;
- 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] = (int32_t)h0;
- h[1] = (int32_t)h1;
- h[2] = (int32_t)h2;
- h[3] = (int32_t)h3;
- h[4] = (int32_t)h4;
- h[5] = (int32_t)h5;
- h[6] = (int32_t)h6;
- h[7] = (int32_t)h7;
- h[8] = (int32_t)h8;
- h[9] = (int32_t)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)
-{
- 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] = (int32_t)h0;
- h[1] = (int32_t)h1;
- h[2] = (int32_t)h2;
- h[3] = (int32_t)h3;
- h[4] = (int32_t)h4;
- h[5] = (int32_t)h5;
- h[6] = (int32_t)h6;
- h[7] = (int32_t)h7;
- h[8] = (int32_t)h8;
- h[9] = (int32_t)h9;
-}
-
-
-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);
-
- 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)
-{
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t h0 = -f0;
- int32_t h1 = -f1;
- int32_t h2 = -f2;
- int32_t h3 = -f3;
- int32_t h4 = -f4;
- int32_t h5 = -f5;
- int32_t h6 = -f6;
- int32_t h7 = -f7;
- int32_t h8 = -f8;
- int32_t h9 = -f9;
- h[0] = h0;
- h[1] = h1;
- h[2] = h2;
- h[3] = h3;
- h[4] = h4;
- h[5] = h5;
- h[6] = h6;
- h[7] = h7;
- h[8] = h8;
- h[9] = h9;
-}
-
-
-/*
-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)
-{
- int32_t f0 = f[0];
- int32_t f1 = f[1];
- int32_t f2 = f[2];
- int32_t f3 = f[3];
- int32_t f4 = f[4];
- int32_t f5 = f[5];
- int32_t f6 = f[6];
- int32_t f7 = f[7];
- int32_t f8 = f[8];
- int32_t f9 = f[9];
- int32_t g0 = g[0];
- int32_t g1 = g[1];
- int32_t g2 = g[2];
- int32_t g3 = g[3];
- int32_t g4 = g[4];
- int32_t g5 = g[5];
- int32_t g6 = g[6];
- int32_t g7 = g[7];
- int32_t g8 = g[8];
- int32_t g9 = g[9];
- int32_t x0 = f0 ^ g0;
- int32_t x1 = f1 ^ g1;
- int32_t x2 = f2 ^ g2;
- int32_t x3 = f3 ^ g3;
- int32_t x4 = f4 ^ g4;
- int32_t x5 = f5 ^ g5;
- int32_t x6 = f6 ^ g6;
- int32_t x7 = f7 ^ g7;
- int32_t x8 = f8 ^ g8;
- int32_t x9 = f9 ^ g9;
- 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 */
-