Xuyi Wang / wolfSSL

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wolfcrypt/src/ge_low_mem.c@7:481bce714567, 2017-05-02 (annotated)

Committer:
wolfSSL
Date:
Tue May 02 08:44:47 2017 +0000
Revision:
7:481bce714567
wolfSSL3.10.2

Who changed what in which revision?

UserRevisionLine numberNew contents of line
wolfSSL 7:481bce714567 1 /* ge_low_mem.c
wolfSSL 7:481bce714567 2 *
wolfSSL 7:481bce714567 3 * Copyright (C) 2006-2016 wolfSSL Inc.
wolfSSL 7:481bce714567 4 *
wolfSSL 7:481bce714567 5 * This file is part of wolfSSL.
wolfSSL 7:481bce714567 6 *
wolfSSL 7:481bce714567 7 * wolfSSL is free software; you can redistribute it and/or modify
wolfSSL 7:481bce714567 8 * it under the terms of the GNU General Public License as published by
wolfSSL 7:481bce714567 9 * the Free Software Foundation; either version 2 of the License, or
wolfSSL 7:481bce714567 10 * (at your option) any later version.
wolfSSL 7:481bce714567 11 *
wolfSSL 7:481bce714567 12 * wolfSSL is distributed in the hope that it will be useful,
wolfSSL 7:481bce714567 13 * but WITHOUT ANY WARRANTY; without even the implied warranty of
wolfSSL 7:481bce714567 14 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
wolfSSL 7:481bce714567 15 * GNU General Public License for more details.
wolfSSL 7:481bce714567 16 *
wolfSSL 7:481bce714567 17 * You should have received a copy of the GNU General Public License
wolfSSL 7:481bce714567 18 * along with this program; if not, write to the Free Software
wolfSSL 7:481bce714567 19 * Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1335, USA
wolfSSL 7:481bce714567 20 */
wolfSSL 7:481bce714567 21
wolfSSL 7:481bce714567 22
wolfSSL 7:481bce714567 23 /* Based from Daniel Beer's public domain work. */
wolfSSL 7:481bce714567 24
wolfSSL 7:481bce714567 25 #ifdef HAVE_CONFIG_H
wolfSSL 7:481bce714567 26 #include <config.h>
wolfSSL 7:481bce714567 27 #endif
wolfSSL 7:481bce714567 28
wolfSSL 7:481bce714567 29 #include <wolfssl/wolfcrypt/settings.h>
wolfSSL 7:481bce714567 30
wolfSSL 7:481bce714567 31 #if defined(CURVED25519_SMALL) /* use slower code that takes less memory */
wolfSSL 7:481bce714567 32 #if defined(HAVE_ED25519)
wolfSSL 7:481bce714567 33
wolfSSL 7:481bce714567 34 #include <wolfssl/wolfcrypt/ge_operations.h>
wolfSSL 7:481bce714567 35 #include <wolfssl/wolfcrypt/error-crypt.h>
wolfSSL 7:481bce714567 36 #ifdef NO_INLINE
wolfSSL 7:481bce714567 37 #include <wolfssl/wolfcrypt/misc.h>
wolfSSL 7:481bce714567 38 #else
wolfSSL 7:481bce714567 39 #define WOLFSSL_MISC_INCLUDED
wolfSSL 7:481bce714567 40 #include <wolfcrypt/src/misc.c>
wolfSSL 7:481bce714567 41 #endif
wolfSSL 7:481bce714567 42
wolfSSL 7:481bce714567 43 void ed25519_smult(ge_p3 *r, const ge_p3 *a, const byte *e);
wolfSSL 7:481bce714567 44 void ed25519_add(ge_p3 *r, const ge_p3 *a, const ge_p3 *b);
wolfSSL 7:481bce714567 45 void ed25519_double(ge_p3 *r, const ge_p3 *a);
wolfSSL 7:481bce714567 46
wolfSSL 7:481bce714567 47
wolfSSL 7:481bce714567 48 static const byte ed25519_order[F25519_SIZE] = {
wolfSSL 7:481bce714567 49 0xed, 0xd3, 0xf5, 0x5c, 0x1a, 0x63, 0x12, 0x58,
wolfSSL 7:481bce714567 50 0xd6, 0x9c, 0xf7, 0xa2, 0xde, 0xf9, 0xde, 0x14,
wolfSSL 7:481bce714567 51 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
wolfSSL 7:481bce714567 52 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x10
wolfSSL 7:481bce714567 53 };
wolfSSL 7:481bce714567 54
wolfSSL 7:481bce714567 55 /*Arithmetic modulo the group order m = 2^252 +
wolfSSL 7:481bce714567 56 27742317777372353535851937790883648493 =
wolfSSL 7:481bce714567 57 7237005577332262213973186563042994240857116359379907606001950938285454250989 */
wolfSSL 7:481bce714567 58
wolfSSL 7:481bce714567 59 static const word32 m[32] = {
wolfSSL 7:481bce714567 60 0xED,0xD3,0xF5,0x5C,0x1A,0x63,0x12,0x58,0xD6,0x9C,0xF7,0xA2,0xDE,0xF9,
wolfSSL 7:481bce714567 61 0xDE,0x14,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
wolfSSL 7:481bce714567 62 0x00,0x00,0x00,0x10
wolfSSL 7:481bce714567 63 };
wolfSSL 7:481bce714567 64
wolfSSL 7:481bce714567 65 static const word32 mu[33] = {
wolfSSL 7:481bce714567 66 0x1B,0x13,0x2C,0x0A,0xA3,0xE5,0x9C,0xED,0xA7,0x29,0x63,0x08,0x5D,0x21,
wolfSSL 7:481bce714567 67 0x06,0x21,0xEB,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
wolfSSL 7:481bce714567 68 0xFF,0xFF,0xFF,0xFF,0x0F
wolfSSL 7:481bce714567 69 };
wolfSSL 7:481bce714567 70
wolfSSL 7:481bce714567 71
wolfSSL 7:481bce714567 72 int ge_compress_key(byte* out, const byte* xIn, const byte* yIn,
wolfSSL 7:481bce714567 73 word32 keySz)
wolfSSL 7:481bce714567 74 {
wolfSSL 7:481bce714567 75 byte tmp[F25519_SIZE];
wolfSSL 7:481bce714567 76 byte parity;
wolfSSL 7:481bce714567 77 byte pt[32];
wolfSSL 7:481bce714567 78 int i;
wolfSSL 7:481bce714567 79
wolfSSL 7:481bce714567 80 fe_copy(tmp, xIn);
wolfSSL 7:481bce714567 81 parity = (tmp[0] & 1) << 7;
wolfSSL 7:481bce714567 82
wolfSSL 7:481bce714567 83 fe_copy(pt, yIn);
wolfSSL 7:481bce714567 84 pt[31] |= parity;
wolfSSL 7:481bce714567 85
wolfSSL 7:481bce714567 86 for(i = 0; i < 32; i++) {
wolfSSL 7:481bce714567 87 out[32-i-1] = pt[i];
wolfSSL 7:481bce714567 88 }
wolfSSL 7:481bce714567 89 (void)keySz;
wolfSSL 7:481bce714567 90 return 0;
wolfSSL 7:481bce714567 91 }
wolfSSL 7:481bce714567 92
wolfSSL 7:481bce714567 93
wolfSSL 7:481bce714567 94 static word32 lt(word32 a,word32 b) /* 16-bit inputs */
wolfSSL 7:481bce714567 95 {
wolfSSL 7:481bce714567 96 unsigned int x = a;
wolfSSL 7:481bce714567 97 x -= (unsigned int) b; /* 0..65535: no; 4294901761..4294967295: yes */
wolfSSL 7:481bce714567 98 x >>= 31; /* 0: no; 1: yes */
wolfSSL 7:481bce714567 99 return x;
wolfSSL 7:481bce714567 100 }
wolfSSL 7:481bce714567 101
wolfSSL 7:481bce714567 102
wolfSSL 7:481bce714567 103 /* Reduce coefficients of r before calling reduce_add_sub */
wolfSSL 7:481bce714567 104 static void reduce_add_sub(word32 *r)
wolfSSL 7:481bce714567 105 {
wolfSSL 7:481bce714567 106 word32 pb = 0;
wolfSSL 7:481bce714567 107 word32 b;
wolfSSL 7:481bce714567 108 word32 mask;
wolfSSL 7:481bce714567 109 int i;
wolfSSL 7:481bce714567 110 unsigned char t[32];
wolfSSL 7:481bce714567 111
wolfSSL 7:481bce714567 112 for(i=0;i<32;i++)
wolfSSL 7:481bce714567 113 {
wolfSSL 7:481bce714567 114 pb += m[i];
wolfSSL 7:481bce714567 115 b = lt(r[i],pb);
wolfSSL 7:481bce714567 116 t[i] = r[i]-pb+(b<<8);
wolfSSL 7:481bce714567 117 pb = b;
wolfSSL 7:481bce714567 118 }
wolfSSL 7:481bce714567 119 mask = b - 1;
wolfSSL 7:481bce714567 120 for(i=0;i<32;i++)
wolfSSL 7:481bce714567 121 r[i] ^= mask & (r[i] ^ t[i]);
wolfSSL 7:481bce714567 122 }
wolfSSL 7:481bce714567 123
wolfSSL 7:481bce714567 124
wolfSSL 7:481bce714567 125 /* Reduce coefficients of x before calling barrett_reduce */
wolfSSL 7:481bce714567 126 static void barrett_reduce(word32* r, word32 x[64])
wolfSSL 7:481bce714567 127 {
wolfSSL 7:481bce714567 128 /* See HAC, Alg. 14.42 */
wolfSSL 7:481bce714567 129 int i,j;
wolfSSL 7:481bce714567 130 word32 q2[66];
wolfSSL 7:481bce714567 131 word32 *q3 = q2 + 33;
wolfSSL 7:481bce714567 132 word32 r1[33];
wolfSSL 7:481bce714567 133 word32 r2[33];
wolfSSL 7:481bce714567 134 word32 carry;
wolfSSL 7:481bce714567 135 word32 pb = 0;
wolfSSL 7:481bce714567 136 word32 b;
wolfSSL 7:481bce714567 137
wolfSSL 7:481bce714567 138 for (i = 0;i < 66;++i) q2[i] = 0;
wolfSSL 7:481bce714567 139 for (i = 0;i < 33;++i) r2[i] = 0;
wolfSSL 7:481bce714567 140
wolfSSL 7:481bce714567 141 for(i=0;i<33;i++)
wolfSSL 7:481bce714567 142 for(j=0;j<33;j++)
wolfSSL 7:481bce714567 143 if(i+j >= 31) q2[i+j] += mu[i]*x[j+31];
wolfSSL 7:481bce714567 144 carry = q2[31] >> 8;
wolfSSL 7:481bce714567 145 q2[32] += carry;
wolfSSL 7:481bce714567 146 carry = q2[32] >> 8;
wolfSSL 7:481bce714567 147 q2[33] += carry;
wolfSSL 7:481bce714567 148
wolfSSL 7:481bce714567 149 for(i=0;i<33;i++)r1[i] = x[i];
wolfSSL 7:481bce714567 150 for(i=0;i<32;i++)
wolfSSL 7:481bce714567 151 for(j=0;j<33;j++)
wolfSSL 7:481bce714567 152 if(i+j < 33) r2[i+j] += m[i]*q3[j];
wolfSSL 7:481bce714567 153
wolfSSL 7:481bce714567 154 for(i=0;i<32;i++)
wolfSSL 7:481bce714567 155 {
wolfSSL 7:481bce714567 156 carry = r2[i] >> 8;
wolfSSL 7:481bce714567 157 r2[i+1] += carry;
wolfSSL 7:481bce714567 158 r2[i] &= 0xff;
wolfSSL 7:481bce714567 159 }
wolfSSL 7:481bce714567 160
wolfSSL 7:481bce714567 161 for(i=0;i<32;i++)
wolfSSL 7:481bce714567 162 {
wolfSSL 7:481bce714567 163 pb += r2[i];
wolfSSL 7:481bce714567 164 b = lt(r1[i],pb);
wolfSSL 7:481bce714567 165 r[i] = r1[i]-pb+(b<<8);
wolfSSL 7:481bce714567 166 pb = b;
wolfSSL 7:481bce714567 167 }
wolfSSL 7:481bce714567 168
wolfSSL 7:481bce714567 169 /* XXX: Can it really happen that r<0?, See HAC, Alg 14.42, Step 3
wolfSSL 7:481bce714567 170 * r is an unsigned type.
wolfSSL 7:481bce714567 171 * If so: Handle it here!
wolfSSL 7:481bce714567 172 */
wolfSSL 7:481bce714567 173
wolfSSL 7:481bce714567 174 reduce_add_sub(r);
wolfSSL 7:481bce714567 175 reduce_add_sub(r);
wolfSSL 7:481bce714567 176 }
wolfSSL 7:481bce714567 177
wolfSSL 7:481bce714567 178
wolfSSL 7:481bce714567 179 void sc_reduce(unsigned char x[64])
wolfSSL 7:481bce714567 180 {
wolfSSL 7:481bce714567 181 int i;
wolfSSL 7:481bce714567 182 word32 t[64];
wolfSSL 7:481bce714567 183 word32 r[32];
wolfSSL 7:481bce714567 184 for(i=0;i<64;i++) t[i] = x[i];
wolfSSL 7:481bce714567 185 barrett_reduce(r, t);
wolfSSL 7:481bce714567 186 for(i=0;i<32;i++) x[i] = (r[i] & 0xFF);
wolfSSL 7:481bce714567 187 }
wolfSSL 7:481bce714567 188
wolfSSL 7:481bce714567 189
wolfSSL 7:481bce714567 190 void sc_muladd(byte* out, const byte* a, const byte* b, const byte* c)
wolfSSL 7:481bce714567 191 {
wolfSSL 7:481bce714567 192
wolfSSL 7:481bce714567 193 byte s[32];
wolfSSL 7:481bce714567 194 byte e[64];
wolfSSL 7:481bce714567 195
wolfSSL 7:481bce714567 196 XMEMSET(e, 0, sizeof(e));
wolfSSL 7:481bce714567 197 XMEMCPY(e, b, 32);
wolfSSL 7:481bce714567 198
wolfSSL 7:481bce714567 199 /* Obtain e */
wolfSSL 7:481bce714567 200 sc_reduce(e);
wolfSSL 7:481bce714567 201
wolfSSL 7:481bce714567 202 /* Compute s = ze + k */
wolfSSL 7:481bce714567 203 fprime_mul(s, a, e, ed25519_order);
wolfSSL 7:481bce714567 204 fprime_add(s, c, ed25519_order);
wolfSSL 7:481bce714567 205
wolfSSL 7:481bce714567 206 XMEMCPY(out, s, 32);
wolfSSL 7:481bce714567 207 }
wolfSSL 7:481bce714567 208
wolfSSL 7:481bce714567 209
wolfSSL 7:481bce714567 210 /* Base point is (numbers wrapped):
wolfSSL 7:481bce714567 211 *
wolfSSL 7:481bce714567 212 * x = 151122213495354007725011514095885315114
wolfSSL 7:481bce714567 213 * 54012693041857206046113283949847762202
wolfSSL 7:481bce714567 214 * y = 463168356949264781694283940034751631413
wolfSSL 7:481bce714567 215 * 07993866256225615783033603165251855960
wolfSSL 7:481bce714567 216 *
wolfSSL 7:481bce714567 217 * y is derived by transforming the original Montgomery base (u=9). x
wolfSSL 7:481bce714567 218 * is the corresponding positive coordinate for the new curve equation.
wolfSSL 7:481bce714567 219 * t is x*y.
wolfSSL 7:481bce714567 220 */
wolfSSL 7:481bce714567 221 const ge_p3 ed25519_base = {
wolfSSL 7:481bce714567 222 {
wolfSSL 7:481bce714567 223 0x1a, 0xd5, 0x25, 0x8f, 0x60, 0x2d, 0x56, 0xc9,
wolfSSL 7:481bce714567 224 0xb2, 0xa7, 0x25, 0x95, 0x60, 0xc7, 0x2c, 0x69,
wolfSSL 7:481bce714567 225 0x5c, 0xdc, 0xd6, 0xfd, 0x31, 0xe2, 0xa4, 0xc0,
wolfSSL 7:481bce714567 226 0xfe, 0x53, 0x6e, 0xcd, 0xd3, 0x36, 0x69, 0x21
wolfSSL 7:481bce714567 227 },
wolfSSL 7:481bce714567 228 {
wolfSSL 7:481bce714567 229 0x58, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
wolfSSL 7:481bce714567 230 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
wolfSSL 7:481bce714567 231 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66,
wolfSSL 7:481bce714567 232 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66, 0x66
wolfSSL 7:481bce714567 233 },
wolfSSL 7:481bce714567 234 {1, 0},
wolfSSL 7:481bce714567 235 {
wolfSSL 7:481bce714567 236 0xa3, 0xdd, 0xb7, 0xa5, 0xb3, 0x8a, 0xde, 0x6d,
wolfSSL 7:481bce714567 237 0xf5, 0x52, 0x51, 0x77, 0x80, 0x9f, 0xf0, 0x20,
wolfSSL 7:481bce714567 238 0x7d, 0xe3, 0xab, 0x64, 0x8e, 0x4e, 0xea, 0x66,
wolfSSL 7:481bce714567 239 0x65, 0x76, 0x8b, 0xd7, 0x0f, 0x5f, 0x87, 0x67
wolfSSL 7:481bce714567 240 },
wolfSSL 7:481bce714567 241
wolfSSL 7:481bce714567 242 };
wolfSSL 7:481bce714567 243
wolfSSL 7:481bce714567 244
wolfSSL 7:481bce714567 245 const ge_p3 ed25519_neutral = {
wolfSSL 7:481bce714567 246 {0},
wolfSSL 7:481bce714567 247 {1, 0},
wolfSSL 7:481bce714567 248 {1, 0},
wolfSSL 7:481bce714567 249 {0},
wolfSSL 7:481bce714567 250
wolfSSL 7:481bce714567 251 };
wolfSSL 7:481bce714567 252
wolfSSL 7:481bce714567 253
wolfSSL 7:481bce714567 254 static const byte ed25519_d[F25519_SIZE] = {
wolfSSL 7:481bce714567 255 0xa3, 0x78, 0x59, 0x13, 0xca, 0x4d, 0xeb, 0x75,
wolfSSL 7:481bce714567 256 0xab, 0xd8, 0x41, 0x41, 0x4d, 0x0a, 0x70, 0x00,
wolfSSL 7:481bce714567 257 0x98, 0xe8, 0x79, 0x77, 0x79, 0x40, 0xc7, 0x8c,
wolfSSL 7:481bce714567 258 0x73, 0xfe, 0x6f, 0x2b, 0xee, 0x6c, 0x03, 0x52
wolfSSL 7:481bce714567 259 };
wolfSSL 7:481bce714567 260
wolfSSL 7:481bce714567 261
wolfSSL 7:481bce714567 262 /* k = 2d */
wolfSSL 7:481bce714567 263 static const byte ed25519_k[F25519_SIZE] = {
wolfSSL 7:481bce714567 264 0x59, 0xf1, 0xb2, 0x26, 0x94, 0x9b, 0xd6, 0xeb,
wolfSSL 7:481bce714567 265 0x56, 0xb1, 0x83, 0x82, 0x9a, 0x14, 0xe0, 0x00,
wolfSSL 7:481bce714567 266 0x30, 0xd1, 0xf3, 0xee, 0xf2, 0x80, 0x8e, 0x19,
wolfSSL 7:481bce714567 267 0xe7, 0xfc, 0xdf, 0x56, 0xdc, 0xd9, 0x06, 0x24
wolfSSL 7:481bce714567 268 };
wolfSSL 7:481bce714567 269
wolfSSL 7:481bce714567 270
wolfSSL 7:481bce714567 271 void ed25519_add(ge_p3 *r,
wolfSSL 7:481bce714567 272 const ge_p3 *p1, const ge_p3 *p2)
wolfSSL 7:481bce714567 273 {
wolfSSL 7:481bce714567 274 /* Explicit formulas database: add-2008-hwcd-3
wolfSSL 7:481bce714567 275 *
wolfSSL 7:481bce714567 276 * source 2008 Hisil--Wong--Carter--Dawson,
wolfSSL 7:481bce714567 277 * http://eprint.iacr.org/2008/522, Section 3.1
wolfSSL 7:481bce714567 278 * appliesto extended-1
wolfSSL 7:481bce714567 279 * parameter k
wolfSSL 7:481bce714567 280 * assume k = 2 d
wolfSSL 7:481bce714567 281 * compute A = (Y1-X1)(Y2-X2)
wolfSSL 7:481bce714567 282 * compute B = (Y1+X1)(Y2+X2)
wolfSSL 7:481bce714567 283 * compute C = T1 k T2
wolfSSL 7:481bce714567 284 * compute D = Z1 2 Z2
wolfSSL 7:481bce714567 285 * compute E = B - A
wolfSSL 7:481bce714567 286 * compute F = D - C
wolfSSL 7:481bce714567 287 * compute G = D + C
wolfSSL 7:481bce714567 288 * compute H = B + A
wolfSSL 7:481bce714567 289 * compute X3 = E F
wolfSSL 7:481bce714567 290 * compute Y3 = G H
wolfSSL 7:481bce714567 291 * compute T3 = E H
wolfSSL 7:481bce714567 292 * compute Z3 = F G
wolfSSL 7:481bce714567 293 */
wolfSSL 7:481bce714567 294 byte a[F25519_SIZE];
wolfSSL 7:481bce714567 295 byte b[F25519_SIZE];
wolfSSL 7:481bce714567 296 byte c[F25519_SIZE];
wolfSSL 7:481bce714567 297 byte d[F25519_SIZE];
wolfSSL 7:481bce714567 298 byte e[F25519_SIZE];
wolfSSL 7:481bce714567 299 byte f[F25519_SIZE];
wolfSSL 7:481bce714567 300 byte g[F25519_SIZE];
wolfSSL 7:481bce714567 301 byte h[F25519_SIZE];
wolfSSL 7:481bce714567 302
wolfSSL 7:481bce714567 303 /* A = (Y1-X1)(Y2-X2) */
wolfSSL 7:481bce714567 304 fe_sub(c, p1->Y, p1->X);
wolfSSL 7:481bce714567 305 fe_sub(d, p2->Y, p2->X);
wolfSSL 7:481bce714567 306 fe_mul__distinct(a, c, d);
wolfSSL 7:481bce714567 307
wolfSSL 7:481bce714567 308 /* B = (Y1+X1)(Y2+X2) */
wolfSSL 7:481bce714567 309 fe_add(c, p1->Y, p1->X);
wolfSSL 7:481bce714567 310 fe_add(d, p2->Y, p2->X);
wolfSSL 7:481bce714567 311 fe_mul__distinct(b, c, d);
wolfSSL 7:481bce714567 312
wolfSSL 7:481bce714567 313 /* C = T1 k T2 */
wolfSSL 7:481bce714567 314 fe_mul__distinct(d, p1->T, p2->T);
wolfSSL 7:481bce714567 315 fe_mul__distinct(c, d, ed25519_k);
wolfSSL 7:481bce714567 316
wolfSSL 7:481bce714567 317 /* D = Z1 2 Z2 */
wolfSSL 7:481bce714567 318 fe_mul__distinct(d, p1->Z, p2->Z);
wolfSSL 7:481bce714567 319 fe_add(d, d, d);
wolfSSL 7:481bce714567 320
wolfSSL 7:481bce714567 321 /* E = B - A */
wolfSSL 7:481bce714567 322 fe_sub(e, b, a);
wolfSSL 7:481bce714567 323
wolfSSL 7:481bce714567 324 /* F = D - C */
wolfSSL 7:481bce714567 325 fe_sub(f, d, c);
wolfSSL 7:481bce714567 326
wolfSSL 7:481bce714567 327 /* G = D + C */
wolfSSL 7:481bce714567 328 fe_add(g, d, c);
wolfSSL 7:481bce714567 329
wolfSSL 7:481bce714567 330 /* H = B + A */
wolfSSL 7:481bce714567 331 fe_add(h, b, a);
wolfSSL 7:481bce714567 332
wolfSSL 7:481bce714567 333 /* X3 = E F */
wolfSSL 7:481bce714567 334 fe_mul__distinct(r->X, e, f);
wolfSSL 7:481bce714567 335
wolfSSL 7:481bce714567 336 /* Y3 = G H */
wolfSSL 7:481bce714567 337 fe_mul__distinct(r->Y, g, h);
wolfSSL 7:481bce714567 338
wolfSSL 7:481bce714567 339 /* T3 = E H */
wolfSSL 7:481bce714567 340 fe_mul__distinct(r->T, e, h);
wolfSSL 7:481bce714567 341
wolfSSL 7:481bce714567 342 /* Z3 = F G */
wolfSSL 7:481bce714567 343 fe_mul__distinct(r->Z, f, g);
wolfSSL 7:481bce714567 344 }
wolfSSL 7:481bce714567 345
wolfSSL 7:481bce714567 346
wolfSSL 7:481bce714567 347 void ed25519_double(ge_p3 *r, const ge_p3 *p)
wolfSSL 7:481bce714567 348 {
wolfSSL 7:481bce714567 349 /* Explicit formulas database: dbl-2008-hwcd
wolfSSL 7:481bce714567 350 *
wolfSSL 7:481bce714567 351 * source 2008 Hisil--Wong--Carter--Dawson,
wolfSSL 7:481bce714567 352 * http://eprint.iacr.org/2008/522, Section 3.3
wolfSSL 7:481bce714567 353 * compute A = X1^2
wolfSSL 7:481bce714567 354 * compute B = Y1^2
wolfSSL 7:481bce714567 355 * compute C = 2 Z1^2
wolfSSL 7:481bce714567 356 * compute D = a A
wolfSSL 7:481bce714567 357 * compute E = (X1+Y1)^2-A-B
wolfSSL 7:481bce714567 358 * compute G = D + B
wolfSSL 7:481bce714567 359 * compute F = G - C
wolfSSL 7:481bce714567 360 * compute H = D - B
wolfSSL 7:481bce714567 361 * compute X3 = E F
wolfSSL 7:481bce714567 362 * compute Y3 = G H
wolfSSL 7:481bce714567 363 * compute T3 = E H
wolfSSL 7:481bce714567 364 * compute Z3 = F G
wolfSSL 7:481bce714567 365 */
wolfSSL 7:481bce714567 366 byte a[F25519_SIZE];
wolfSSL 7:481bce714567 367 byte b[F25519_SIZE];
wolfSSL 7:481bce714567 368 byte c[F25519_SIZE];
wolfSSL 7:481bce714567 369 byte e[F25519_SIZE];
wolfSSL 7:481bce714567 370 byte f[F25519_SIZE];
wolfSSL 7:481bce714567 371 byte g[F25519_SIZE];
wolfSSL 7:481bce714567 372 byte h[F25519_SIZE];
wolfSSL 7:481bce714567 373
wolfSSL 7:481bce714567 374 /* A = X1^2 */
wolfSSL 7:481bce714567 375 fe_mul__distinct(a, p->X, p->X);
wolfSSL 7:481bce714567 376
wolfSSL 7:481bce714567 377 /* B = Y1^2 */
wolfSSL 7:481bce714567 378 fe_mul__distinct(b, p->Y, p->Y);
wolfSSL 7:481bce714567 379
wolfSSL 7:481bce714567 380 /* C = 2 Z1^2 */
wolfSSL 7:481bce714567 381 fe_mul__distinct(c, p->Z, p->Z);
wolfSSL 7:481bce714567 382 fe_add(c, c, c);
wolfSSL 7:481bce714567 383
wolfSSL 7:481bce714567 384 /* D = a A (alter sign) */
wolfSSL 7:481bce714567 385 /* E = (X1+Y1)^2-A-B */
wolfSSL 7:481bce714567 386 fe_add(f, p->X, p->Y);
wolfSSL 7:481bce714567 387 fe_mul__distinct(e, f, f);
wolfSSL 7:481bce714567 388 fe_sub(e, e, a);
wolfSSL 7:481bce714567 389 fe_sub(e, e, b);
wolfSSL 7:481bce714567 390
wolfSSL 7:481bce714567 391 /* G = D + B */
wolfSSL 7:481bce714567 392 fe_sub(g, b, a);
wolfSSL 7:481bce714567 393
wolfSSL 7:481bce714567 394 /* F = G - C */
wolfSSL 7:481bce714567 395 fe_sub(f, g, c);
wolfSSL 7:481bce714567 396
wolfSSL 7:481bce714567 397 /* H = D - B */
wolfSSL 7:481bce714567 398 fe_neg(h, b);
wolfSSL 7:481bce714567 399 fe_sub(h, h, a);
wolfSSL 7:481bce714567 400
wolfSSL 7:481bce714567 401 /* X3 = E F */
wolfSSL 7:481bce714567 402 fe_mul__distinct(r->X, e, f);
wolfSSL 7:481bce714567 403
wolfSSL 7:481bce714567 404 /* Y3 = G H */
wolfSSL 7:481bce714567 405 fe_mul__distinct(r->Y, g, h);
wolfSSL 7:481bce714567 406
wolfSSL 7:481bce714567 407 /* T3 = E H */
wolfSSL 7:481bce714567 408 fe_mul__distinct(r->T, e, h);
wolfSSL 7:481bce714567 409
wolfSSL 7:481bce714567 410 /* Z3 = F G */
wolfSSL 7:481bce714567 411 fe_mul__distinct(r->Z, f, g);
wolfSSL 7:481bce714567 412 }
wolfSSL 7:481bce714567 413
wolfSSL 7:481bce714567 414
wolfSSL 7:481bce714567 415 void ed25519_smult(ge_p3 *r_out, const ge_p3 *p, const byte *e)
wolfSSL 7:481bce714567 416 {
wolfSSL 7:481bce714567 417 ge_p3 r;
wolfSSL 7:481bce714567 418 int i;
wolfSSL 7:481bce714567 419
wolfSSL 7:481bce714567 420 XMEMCPY(&r, &ed25519_neutral, sizeof(r));
wolfSSL 7:481bce714567 421
wolfSSL 7:481bce714567 422 for (i = 255; i >= 0; i--) {
wolfSSL 7:481bce714567 423 const byte bit = (e[i >> 3] >> (i & 7)) & 1;
wolfSSL 7:481bce714567 424 ge_p3 s;
wolfSSL 7:481bce714567 425
wolfSSL 7:481bce714567 426 ed25519_double(&r, &r);
wolfSSL 7:481bce714567 427 ed25519_add(&s, &r, p);
wolfSSL 7:481bce714567 428
wolfSSL 7:481bce714567 429 fe_select(r.X, r.X, s.X, bit);
wolfSSL 7:481bce714567 430 fe_select(r.Y, r.Y, s.Y, bit);
wolfSSL 7:481bce714567 431 fe_select(r.Z, r.Z, s.Z, bit);
wolfSSL 7:481bce714567 432 fe_select(r.T, r.T, s.T, bit);
wolfSSL 7:481bce714567 433 }
wolfSSL 7:481bce714567 434 XMEMCPY(r_out, &r, sizeof(r));
wolfSSL 7:481bce714567 435 }
wolfSSL 7:481bce714567 436
wolfSSL 7:481bce714567 437
wolfSSL 7:481bce714567 438 void ge_scalarmult_base(ge_p3 *R,const unsigned char *nonce)
wolfSSL 7:481bce714567 439 {
wolfSSL 7:481bce714567 440 ed25519_smult(R, &ed25519_base, nonce);
wolfSSL 7:481bce714567 441 }
wolfSSL 7:481bce714567 442
wolfSSL 7:481bce714567 443
wolfSSL 7:481bce714567 444 /* pack the point h into array s */
wolfSSL 7:481bce714567 445 void ge_p3_tobytes(unsigned char *s,const ge_p3 *h)
wolfSSL 7:481bce714567 446 {
wolfSSL 7:481bce714567 447 byte x[F25519_SIZE];
wolfSSL 7:481bce714567 448 byte y[F25519_SIZE];
wolfSSL 7:481bce714567 449 byte z1[F25519_SIZE];
wolfSSL 7:481bce714567 450 byte parity;
wolfSSL 7:481bce714567 451
wolfSSL 7:481bce714567 452 fe_inv__distinct(z1, h->Z);
wolfSSL 7:481bce714567 453 fe_mul__distinct(x, h->X, z1);
wolfSSL 7:481bce714567 454 fe_mul__distinct(y, h->Y, z1);
wolfSSL 7:481bce714567 455
wolfSSL 7:481bce714567 456 fe_normalize(x);
wolfSSL 7:481bce714567 457 fe_normalize(y);
wolfSSL 7:481bce714567 458
wolfSSL 7:481bce714567 459 parity = (x[0] & 1) << 7;
wolfSSL 7:481bce714567 460 fe_copy(s, y);
wolfSSL 7:481bce714567 461 fe_normalize(s);
wolfSSL 7:481bce714567 462 s[31] |= parity;
wolfSSL 7:481bce714567 463 }
wolfSSL 7:481bce714567 464
wolfSSL 7:481bce714567 465
wolfSSL 7:481bce714567 466 /* pack the point h into array s */
wolfSSL 7:481bce714567 467 void ge_tobytes(unsigned char *s,const ge_p2 *h)
wolfSSL 7:481bce714567 468 {
wolfSSL 7:481bce714567 469 byte x[F25519_SIZE];
wolfSSL 7:481bce714567 470 byte y[F25519_SIZE];
wolfSSL 7:481bce714567 471 byte z1[F25519_SIZE];
wolfSSL 7:481bce714567 472 byte parity;
wolfSSL 7:481bce714567 473
wolfSSL 7:481bce714567 474 fe_inv__distinct(z1, h->Z);
wolfSSL 7:481bce714567 475 fe_mul__distinct(x, h->X, z1);
wolfSSL 7:481bce714567 476 fe_mul__distinct(y, h->Y, z1);
wolfSSL 7:481bce714567 477
wolfSSL 7:481bce714567 478 fe_normalize(x);
wolfSSL 7:481bce714567 479 fe_normalize(y);
wolfSSL 7:481bce714567 480
wolfSSL 7:481bce714567 481 parity = (x[0] & 1) << 7;
wolfSSL 7:481bce714567 482 fe_copy(s, y);
wolfSSL 7:481bce714567 483 fe_normalize(s);
wolfSSL 7:481bce714567 484 s[31] |= parity;
wolfSSL 7:481bce714567 485 }
wolfSSL 7:481bce714567 486
wolfSSL 7:481bce714567 487
wolfSSL 7:481bce714567 488 /*
wolfSSL 7:481bce714567 489 Test if the public key can be uncompressed and negate it (-X,Y,Z,-T)
wolfSSL 7:481bce714567 490 return 0 on success
wolfSSL 7:481bce714567 491 */
wolfSSL 7:481bce714567 492 int ge_frombytes_negate_vartime(ge_p3 *p,const unsigned char *s)
wolfSSL 7:481bce714567 493 {
wolfSSL 7:481bce714567 494
wolfSSL 7:481bce714567 495 byte parity;
wolfSSL 7:481bce714567 496 byte x[F25519_SIZE];
wolfSSL 7:481bce714567 497 byte y[F25519_SIZE];
wolfSSL 7:481bce714567 498 byte a[F25519_SIZE];
wolfSSL 7:481bce714567 499 byte b[F25519_SIZE];
wolfSSL 7:481bce714567 500 byte c[F25519_SIZE];
wolfSSL 7:481bce714567 501 int ret = 0;
wolfSSL 7:481bce714567 502
wolfSSL 7:481bce714567 503 /* unpack the key s */
wolfSSL 7:481bce714567 504 parity = s[31] >> 7;
wolfSSL 7:481bce714567 505 fe_copy(y, s);
wolfSSL 7:481bce714567 506 y[31] &= 127;
wolfSSL 7:481bce714567 507
wolfSSL 7:481bce714567 508 fe_mul__distinct(c, y, y);
wolfSSL 7:481bce714567 509 fe_mul__distinct(b, c, ed25519_d);
wolfSSL 7:481bce714567 510 fe_add(a, b, f25519_one);
wolfSSL 7:481bce714567 511 fe_inv__distinct(b, a);
wolfSSL 7:481bce714567 512 fe_sub(a, c, f25519_one);
wolfSSL 7:481bce714567 513 fe_mul__distinct(c, a, b);
wolfSSL 7:481bce714567 514 fe_sqrt(a, c);
wolfSSL 7:481bce714567 515 fe_neg(b, a);
wolfSSL 7:481bce714567 516 fe_select(x, a, b, (a[0] ^ parity) & 1);
wolfSSL 7:481bce714567 517
wolfSSL 7:481bce714567 518 /* test that x^2 is equal to c */
wolfSSL 7:481bce714567 519 fe_mul__distinct(a, x, x);
wolfSSL 7:481bce714567 520 fe_normalize(a);
wolfSSL 7:481bce714567 521 fe_normalize(c);
wolfSSL 7:481bce714567 522 ret |= ConstantCompare(a, c, F25519_SIZE);
wolfSSL 7:481bce714567 523
wolfSSL 7:481bce714567 524 /* project the key s onto p */
wolfSSL 7:481bce714567 525 fe_copy(p->X, x);
wolfSSL 7:481bce714567 526 fe_copy(p->Y, y);
wolfSSL 7:481bce714567 527 fe_load(p->Z, 1);
wolfSSL 7:481bce714567 528 fe_mul__distinct(p->T, x, y);
wolfSSL 7:481bce714567 529
wolfSSL 7:481bce714567 530 /* negate, the point becomes (-X,Y,Z,-T) */
wolfSSL 7:481bce714567 531 fe_neg(p->X,p->X);
wolfSSL 7:481bce714567 532 fe_neg(p->T,p->T);
wolfSSL 7:481bce714567 533
wolfSSL 7:481bce714567 534 return ret;
wolfSSL 7:481bce714567 535 }
wolfSSL 7:481bce714567 536
wolfSSL 7:481bce714567 537
wolfSSL 7:481bce714567 538 int ge_double_scalarmult_vartime(ge_p2* R, const unsigned char *h,
wolfSSL 7:481bce714567 539 const ge_p3 *inA,const unsigned char *sig)
wolfSSL 7:481bce714567 540 {
wolfSSL 7:481bce714567 541 ge_p3 p, A;
wolfSSL 7:481bce714567 542 int ret = 0;
wolfSSL 7:481bce714567 543
wolfSSL 7:481bce714567 544 XMEMCPY(&A, inA, sizeof(ge_p3));
wolfSSL 7:481bce714567 545
wolfSSL 7:481bce714567 546 /* find SB */
wolfSSL 7:481bce714567 547 ed25519_smult(&p, &ed25519_base, sig);
wolfSSL 7:481bce714567 548
wolfSSL 7:481bce714567 549 /* find H(R,A,M) * -A */
wolfSSL 7:481bce714567 550 ed25519_smult(&A, &A, h);
wolfSSL 7:481bce714567 551
wolfSSL 7:481bce714567 552 /* SB + -H(R,A,M)A */
wolfSSL 7:481bce714567 553 ed25519_add(&A, &p, &A);
wolfSSL 7:481bce714567 554
wolfSSL 7:481bce714567 555 fe_copy(R->X, A.X);
wolfSSL 7:481bce714567 556 fe_copy(R->Y, A.Y);
wolfSSL 7:481bce714567 557 fe_copy(R->Z, A.Z);
wolfSSL 7:481bce714567 558
wolfSSL 7:481bce714567 559 return ret;
wolfSSL 7:481bce714567 560 }
wolfSSL 7:481bce714567 561
wolfSSL 7:481bce714567 562 #endif /* HAVE_ED25519 */
wolfSSL 7:481bce714567 563 #endif /* CURVED25519_SMALL */
wolfSSL 7:481bce714567 564
wolfSSL 7:481bce714567 565