_ 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         uint16_t x1[18], x2[18], x3[18], z2[18], z3[18];
 183         uint16_t a[18], aa[18], b[18], bb[18];
 184         uint16_t c[18], d[18], e[18], da[18], cb[18];
 185         unsigned char k[32];
 186         uint32_t swap;
 187         int i;
 188
 189         (void)curve;
 190
 191         /*
 192          * Points are encoded over exactly 32 bytes. Multipliers must fit
 193          * in 32 bytes as well.
 194          * RFC 7748 mandates that the high bit of the last point byte must
 195          * be ignored/cleared.
 196          */
 197         if (Glen != 32 || kblen > 32) {
 198                 return 0;
 199         }
 200         G[31] &= 0x7F;
 201
 202         /*
 203          * Byteswap the point encoding, because it uses little-endian, and
 204          * the generic decoding routine uses big-endian.
 205          */
 206         byteswap(G);
 207
 208         /*
 209          * Initialise variables x1, x2, z2, x3 and z3. We set all of them
 210          * into Montgomery representation.
 211          */
 212         br_i15_decode_reduce(a, G, 32, C255_P);
 213         br_i15_montymul(x1, a, C255_R2, C255_P, P0I);
 214         memcpy(x3, x1, sizeof x1);
 215         br_i15_zero(z2, C255_P[0]);
 216         memcpy(x2, z2, sizeof z2);
 217         x2[1] = 19;
 218         memcpy(z3, x2, sizeof x2);
 219
 220         memcpy(k, kb, kblen);
 221         memset(k + kblen, 0, (sizeof k) - kblen);
 222         k[0] &= 0xF8;
 223         k[31] &= 0x7F;
 224         k[31] |= 0x40;
 225
 226         /* obsolete
 227         print_int_mont("x1", x1);
 228         */
 229
 230         swap = 0;
 231         for (i = 254; i >= 0; i --) {
 232                 uint32_t kt;
 233
 234                 kt = (k[i >> 3] >> (i & 7)) & 1;
 235                 swap ^= kt;
 236                 cswap(x2, x3, swap);
 237                 cswap(z2, z3, swap);
 238                 swap = kt;
 239
 240                 /* obsolete
 241                 print_int_mont("x2", x2);
 242                 print_int_mont("z2", z2);
 243                 print_int_mont("x3", x3);
 244                 print_int_mont("z3", z3);
 245                 */
 246
 247                 c255_add(a, x2, z2);
 248                 c255_mul(aa, a, a);
 249                 c255_sub(b, x2, z2);
 250                 c255_mul(bb, b, b);
 251                 c255_sub(e, aa, bb);
 252                 c255_add(c, x3, z3);
 253                 c255_sub(d, x3, z3);
 254                 c255_mul(da, d, a);
 255                 c255_mul(cb, c, b);
 256
 257                 /* obsolete
 258                 print_int_mont("a ", a);
 259                 print_int_mont("aa", aa);
 260                 print_int_mont("b ", b);
 261                 print_int_mont("bb", bb);
 262                 print_int_mont("e ", e);
 263                 print_int_mont("c ", c);
 264                 print_int_mont("d ", d);
 265                 print_int_mont("da", da);
 266                 print_int_mont("cb", cb);
 267                 */
 268
 269                 c255_add(x3, da, cb);
 270                 c255_mul(x3, x3, x3);
 271                 c255_sub(z3, da, cb);
 272                 c255_mul(z3, z3, z3);
 273                 c255_mul(z3, z3, x1);
 274                 c255_mul(x2, aa, bb);
 275                 c255_mul(z2, C255_A24, e);
 276                 c255_add(z2, z2, aa);
 277                 c255_mul(z2, e, z2);
 278
 279                 /* obsolete
 280                 print_int_mont("x2", x2);
 281                 print_int_mont("z2", z2);
 282                 print_int_mont("x3", x3);
 283                 print_int_mont("z3", z3);
 284                 */
 285         }
 286         cswap(x2, x3, swap);
 287         cswap(z2, z3, swap);
 288
 289         /*
 290          * Inverse z2 with a modular exponentiation. This is a simple
 291          * square-and-multiply algorithm; we mutualise most non-squarings
 292          * since the exponent contains almost only ones.
 293          */
 294         memcpy(a, z2, sizeof z2);
 295         for (i = 0; i < 15; i ++) {
 296                 c255_mul(a, a, a);
 297                 c255_mul(a, a, z2);
 298         }
 299         memcpy(b, a, sizeof a);
 300         for (i = 0; i < 14; i ++) {
 301                 int j;
 302
 303                 for (j = 0; j < 16; j ++) {
 304                         c255_mul(b, b, b);
 305                 }
 306                 c255_mul(b, b, a);
 307         }
 308         for (i = 14; i >= 0; i --) {
 309                 c255_mul(b, b, b);
 310                 if ((0xFFEB >> i) & 1) {
 311                         c255_mul(b, z2, b);
 312                 }
 313         }
 314         c255_mul(x2, x2, b);
 315         br_i15_from_monty(x2, C255_P, P0I);
 316         br_i15_encode(G, 32, x2);
 317         byteswap(G);
 318         return 1;
 319 }
 320
 321 static size_t
 322 api_mulgen(unsigned char *R,
 323         const unsigned char *x, size_t xlen, int curve)
 324 {
 325         const unsigned char *G;
 326         size_t Glen;
 327
 328         G = api_generator(curve, &Glen);
 329         memcpy(R, G, Glen);
 330         api_mul(R, Glen, x, xlen, curve);
 331         return Glen;
 332 }
 333
 334 static uint32_t
 335 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
 336         const unsigned char *x, size_t xlen,
 337         const unsigned char *y, size_t ylen, int curve)
 338 {
 339         /*
 340          * We don't implement this method, since it is used for ECDSA
 341          * only, and there is no ECDSA over Curve25519 (which instead
 342          * uses EdDSA).
 343          */
 344         (void)A;
 345         (void)B;
 346         (void)len;
 347         (void)x;
 348         (void)xlen;
 349         (void)y;
 350         (void)ylen;
 351         (void)curve;
 352         return 0;
 353 }
 354
 355 /* see bearssl_ec.h */
 356 const br_ec_impl br_ec_c25519_i15 = {
 357         (uint32_t)0x20000000,
 358         &api_generator,
 359         &api_order,
 360         &api_xoff,
 361         &api_mul,
 362         &api_mulgen,
 363         &api_muladd
 364 };