_ Git - BearSSL/blob - src/ec/ec_c25519_i15.c

   1 /*
   2  * Copyright (c) 2017 Thomas Pornin <pornin@bolet.org>
   3  *
   4  * Permission is hereby granted, free of charge, to any person obtaining
   5  * a copy of this software and associated documentation files (the
   6  * "Software"), to deal in the Software without restriction, including
   7  * without limitation the rights to use, copy, modify, merge, publish,
   8  * distribute, sublicense, and/or sell copies of the Software, and to
   9  * permit persons to whom the Software is furnished to do so, subject to
  10  * the following conditions:
  11  *
  12  * The above copyright notice and this permission notice shall be
  13  * included in all copies or substantial portions of the Software.
  14  *
  15  * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,
  16  * EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF
  17  * MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND
  18  * NONINFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS
  19  * BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN
  20  * ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
  21  * CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
  22  * SOFTWARE.
  23  */
  24
  25 #include "inner.h"
  26
  27 /*
  28  * Parameters for the field:
  29  *   - field modulus p = 2^255-19
  30  *   - R^2 mod p (R = 2^(15k) for the smallest k such that R >= p)
  31  */
  32
  33 static const uint16_t C255_P[] = {
  34         0x0110,
  35         0x7FED, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
  36         0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF, 0x7FFF,
  37         0x7FFF
  38 };
  39
  40 #define P0I   0x4A1B
  41
  42 static const uint16_t C255_R2[] = {
  43         0x0110,
  44         0x0169, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
  45         0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
  46         0x0000
  47 };
  48
  49 /* obsolete
  50 #include <stdio.h>
  51 #include <stdlib.h>
  52 static void
  53 print_int_mont(const char *name, const uint16_t *x)
  54 {
  55         uint16_t y[18];
  56         unsigned char tmp[32];
  57         size_t u;
  58
  59         printf("%s = ", name);
  60         memcpy(y, x, sizeof y);
  61         br_i15_from_monty(y, C255_P, P0I);
  62         br_i15_encode(tmp, sizeof tmp, y);
  63         for (u = 0; u < sizeof tmp; u ++) {
  64                 printf("%02X", tmp[u]);
  65         }
  66         printf("\n");
  67 }
  68 */
  69
  70 static const uint16_t C255_A24[] = {
  71         0x0110,
  72         0x45D3, 0x0046, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
  73         0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
  74         0x0000
  75 };
  76
  77 static const unsigned char GEN[] = {
  78         0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  79         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  80         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  81         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
  82 };
  83
  84 static const unsigned char ORDER[] = {
  85         0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
  86         0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
  87         0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
  88         0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
  89 };
  90
  91 static const unsigned char *
  92 api_generator(int curve, size_t *len)
  93 {
  94         (void)curve;
  95         *len = 32;
  96         return GEN;
  97 }
  98
  99 static const unsigned char *
 100 api_order(int curve, size_t *len)
 101 {
 102         (void)curve;
 103         *len = 32;
 104         return ORDER;
 105 }
 106
 107 static size_t
 108 api_xoff(int curve, size_t *len)
 109 {
 110         (void)curve;
 111         *len = 32;
 112         return 0;
 113 }
 114
 115 static void
 116 cswap(uint16_t *a, uint16_t *b, uint32_t ctl)
 117 {
 118         int i;
 119
 120         ctl = -ctl;
 121         for (i = 0; i < 18; i ++) {
 122                 uint32_t aw, bw, tw;
 123
 124                 aw = a[i];
 125                 bw = b[i];
 126                 tw = ctl & (aw ^ bw);
 127                 a[i] = aw ^ tw;
 128                 b[i] = bw ^ tw;
 129         }
 130 }
 131
 132 static void
 133 c255_add(uint16_t *d, const uint16_t *a, const uint16_t *b)
 134 {
 135         uint32_t ctl;
 136         uint16_t t[18];
 137
 138         memcpy(t, a, sizeof t);
 139         ctl = br_i15_add(t, b, 1);
 140         ctl |= NOT(br_i15_sub(t, C255_P, 0));
 141         br_i15_sub(t, C255_P, ctl);
 142         memcpy(d, t, sizeof t);
 143 }
 144
 145 static void
 146 c255_sub(uint16_t *d, const uint16_t *a, const uint16_t *b)
 147 {
 148         uint16_t t[18];
 149
 150         memcpy(t, a, sizeof t);
 151         br_i15_add(t, C255_P, br_i15_sub(t, b, 1));
 152         memcpy(d, t, sizeof t);
 153 }
 154
 155 static void
 156 c255_mul(uint16_t *d, const uint16_t *a, const uint16_t *b)
 157 {
 158         uint16_t t[18];
 159
 160         br_i15_montymul(t, a, b, C255_P, P0I);
 161         memcpy(d, t, sizeof t);
 162 }
 163
 164 static void
 165 byteswap(unsigned char *G)
 166 {
 167         int i;
 168
 169         for (i = 0; i < 16; i ++) {
 170                 unsigned char t;
 171
 172                 t = G[i];
 173                 G[i] = G[31 - i];
 174                 G[31 - i] = t;
 175         }
 176 }
 177
 178 static uint32_t
 179 api_mul(unsigned char *G, size_t Glen,
 180         const unsigned char *kb, size_t kblen, int curve)
 181 {
 182 #define ILEN   (18 * sizeof(uint16_t))
 183
 184         /*
 185          * The a[] and b[] arrays have an extra word to allow for
 186          * decoding without using br_i15_decode_reduce().
 187          */
 188         uint16_t x1[18], x2[18], x3[18], z2[18], z3[18];
 189         uint16_t a[19], aa[18], b[19], bb[18];
 190         uint16_t c[18], d[18], e[18], da[18], cb[18];
 191         unsigned char k[32];
 192         uint32_t swap;
 193         int i;
 194
 195         (void)curve;
 196
 197         /*
 198          * Points are encoded over exactly 32 bytes. Multipliers must fit
 199          * in 32 bytes as well.
 200          * RFC 7748 mandates that the high bit of the last point byte must
 201          * be ignored/cleared.
 202          */
 203         if (Glen != 32 || kblen > 32) {
 204                 return 0;
 205         }
 206         G[31] &= 0x7F;
 207
 208         /*
 209          * Byteswap the point encoding, because it uses little-endian, and
 210          * the generic decoding routine uses big-endian.
 211          */
 212         byteswap(G);
 213
 214         /*
 215          * Decode the point ('u' coordinate). This should be reduced
 216          * modulo p, but we prefer to avoid the dependency on
 217          * br_i15_decode_reduce(). Instead, we use br_i15_decode_mod()
 218          * with a synthetic modulus of value 2^255 (this must work
 219          * since G was truncated to 255 bits), then use a conditional
 220          * subtraction. We use br_i15_decode_mod() and not
 221          * br_i15_decode(), because the ec_prime_i15 implementation uses
 222          * the former but not the latter.
 223          *    br_i15_decode_reduce(a, G, 32, C255_P);
 224          */
 225         br_i15_zero(b, 0x111);
 226         b[18] = 1;
 227         br_i15_decode_mod(a, G, 32, b);
 228         a[0] = 0x110;
 229         br_i15_sub(a, C255_P, NOT(br_i15_sub(a, C255_P, 0)));
 230
 231         /*
 232          * Initialise variables x1, x2, z2, x3 and z3. We set all of them
 233          * into Montgomery representation.
 234          */
 235         br_i15_montymul(x1, a, C255_R2, C255_P, P0I);
 236         memcpy(x3, x1, ILEN);
 237         br_i15_zero(z2, C255_P[0]);
 238         memcpy(x2, z2, ILEN);
 239         x2[1] = 19;
 240         memcpy(z3, x2, ILEN);
 241
 242         memset(k, 0, (sizeof k) - kblen);
 243         memcpy(k + (sizeof k) - kblen, kb, kblen);
 244         k[31] &= 0xF8;
 245         k[0] &= 0x7F;
 246         k[0] |= 0x40;
 247
 248         /* obsolete
 249         print_int_mont("x1", x1);
 250         */
 251
 252         swap = 0;
 253         for (i = 254; i >= 0; i --) {
 254                 uint32_t kt;
 255
 256                 kt = (k[31 - (i >> 3)] >> (i & 7)) & 1;
 257                 swap ^= kt;
 258                 cswap(x2, x3, swap);
 259                 cswap(z2, z3, swap);
 260                 swap = kt;
 261
 262                 /* obsolete
 263                 print_int_mont("x2", x2);
 264                 print_int_mont("z2", z2);
 265                 print_int_mont("x3", x3);
 266                 print_int_mont("z3", z3);
 267                 */
 268
 269                 c255_add(a, x2, z2);
 270                 c255_mul(aa, a, a);
 271                 c255_sub(b, x2, z2);
 272                 c255_mul(bb, b, b);
 273                 c255_sub(e, aa, bb);
 274                 c255_add(c, x3, z3);
 275                 c255_sub(d, x3, z3);
 276                 c255_mul(da, d, a);
 277                 c255_mul(cb, c, b);
 278
 279                 /* obsolete
 280                 print_int_mont("a ", a);
 281                 print_int_mont("aa", aa);
 282                 print_int_mont("b ", b);
 283                 print_int_mont("bb", bb);
 284                 print_int_mont("e ", e);
 285                 print_int_mont("c ", c);
 286                 print_int_mont("d ", d);
 287                 print_int_mont("da", da);
 288                 print_int_mont("cb", cb);
 289                 */
 290
 291                 c255_add(x3, da, cb);
 292                 c255_mul(x3, x3, x3);
 293                 c255_sub(z3, da, cb);
 294                 c255_mul(z3, z3, z3);
 295                 c255_mul(z3, z3, x1);
 296                 c255_mul(x2, aa, bb);
 297                 c255_mul(z2, C255_A24, e);
 298                 c255_add(z2, z2, aa);
 299                 c255_mul(z2, e, z2);
 300
 301                 /* obsolete
 302                 print_int_mont("x2", x2);
 303                 print_int_mont("z2", z2);
 304                 print_int_mont("x3", x3);
 305                 print_int_mont("z3", z3);
 306                 */
 307         }
 308         cswap(x2, x3, swap);
 309         cswap(z2, z3, swap);
 310
 311         /*
 312          * Inverse z2 with a modular exponentiation. This is a simple
 313          * square-and-multiply algorithm; we mutualise most non-squarings
 314          * since the exponent contains almost only ones.
 315          */
 316         memcpy(a, z2, ILEN);
 317         for (i = 0; i < 15; i ++) {
 318                 c255_mul(a, a, a);
 319                 c255_mul(a, a, z2);
 320         }
 321         memcpy(b, a, ILEN);
 322         for (i = 0; i < 14; i ++) {
 323                 int j;
 324
 325                 for (j = 0; j < 16; j ++) {
 326                         c255_mul(b, b, b);
 327                 }
 328                 c255_mul(b, b, a);
 329         }
 330         for (i = 14; i >= 0; i --) {
 331                 c255_mul(b, b, b);
 332                 if ((0xFFEB >> i) & 1) {
 333                         c255_mul(b, z2, b);
 334                 }
 335         }
 336         c255_mul(b, x2, b);
 337
 338         /*
 339          * To avoid a dependency on br_i15_from_monty(), we use a
 340          * Montgomery multiplication with 1.
 341          *    memcpy(x2, b, ILEN);
 342          *    br_i15_from_monty(x2, C255_P, P0I);
 343          */
 344         br_i15_zero(a, C255_P[0]);
 345         a[1] = 1;
 346         br_i15_montymul(x2, a, b, C255_P, P0I);
 347
 348         br_i15_encode(G, 32, x2);
 349         byteswap(G);
 350         return 1;
 351
 352 #undef ILEN
 353 }
 354
 355 static size_t
 356 api_mulgen(unsigned char *R,
 357         const unsigned char *x, size_t xlen, int curve)
 358 {
 359         const unsigned char *G;
 360         size_t Glen;
 361
 362         G = api_generator(curve, &Glen);
 363         memcpy(R, G, Glen);
 364         api_mul(R, Glen, x, xlen, curve);
 365         return Glen;
 366 }
 367
 368 static uint32_t
 369 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
 370         const unsigned char *x, size_t xlen,
 371         const unsigned char *y, size_t ylen, int curve)
 372 {
 373         /*
 374          * We don't implement this method, since it is used for ECDSA
 375          * only, and there is no ECDSA over Curve25519 (which instead
 376          * uses EdDSA).
 377          */
 378         (void)A;
 379         (void)B;
 380         (void)len;
 381         (void)x;
 382         (void)xlen;
 383         (void)y;
 384         (void)ylen;
 385         (void)curve;
 386         return 0;
 387 }
 388
 389 /* see bearssl_ec.h */
 390 const br_ec_impl br_ec_c25519_i15 = {
 391         (uint32_t)0x20000000,
 392         &api_generator,
 393         &api_order,
 394         &api_xoff,
 395         &api_mul,
 396         &api_mulgen,
 397         &api_muladd
 398 };