_ Git - BearSSL/blob - src/ec/ec_c25519_i31.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^(31k) for the smallest k such that R >= p)
  31  */
  32
  33 static const uint32_t C255_P[] = {
  34         0x00000107,
  35         0x7FFFFFED, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF,
  36         0x7FFFFFFF, 0x7FFFFFFF, 0x7FFFFFFF, 0x0000007F
  37 };
  38
  39 #define P0I   0x286BCA1B
  40
  41 static const uint32_t C255_R2[] = {
  42         0x00000107,
  43         0x00000000, 0x02D20000, 0x00000000, 0x00000000, 0x00000000,
  44         0x00000000, 0x00000000, 0x00000000, 0x00000000
  45 };
  46
  47 static const uint32_t C255_A24[] = {
  48         0x00000107,
  49         0x53000000, 0x0000468B, 0x00000000, 0x00000000, 0x00000000,
  50         0x00000000, 0x00000000, 0x00000000, 0x00000000
  51 };
  52
  53 /* obsolete
  54 #include <stdio.h>
  55 #include <stdlib.h>
  56 static void
  57 print_int_mont(const char *name, const uint32_t *x)
  58 {
  59         uint32_t y[10];
  60         unsigned char tmp[32];
  61         size_t u;
  62
  63         printf("%s = ", name);
  64         memcpy(y, x, sizeof y);
  65         br_i31_from_monty(y, C255_P, P0I);
  66         br_i31_encode(tmp, sizeof tmp, y);
  67         for (u = 0; u < sizeof tmp; u ++) {
  68                 printf("%02X", tmp[u]);
  69         }
  70         printf("\n");
  71 }
  72 */
  73
  74 static const unsigned char GEN[] = {
  75         0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  76         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  77         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  78         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
  79 };
  80
  81 static const unsigned char ORDER[] = {
  82         0x7F, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
  83         0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
  84         0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF,
  85         0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF, 0xFF
  86 };
  87
  88 static const unsigned char *
  89 api_generator(int curve, size_t *len)
  90 {
  91         (void)curve;
  92         *len = 32;
  93         return GEN;
  94 }
  95
  96 static const unsigned char *
  97 api_order(int curve, size_t *len)
  98 {
  99         (void)curve;
 100         *len = 32;
 101         return ORDER;
 102 }
 103
 104 static size_t
 105 api_xoff(int curve, size_t *len)
 106 {
 107         (void)curve;
 108         *len = 32;
 109         return 0;
 110 }
 111
 112 static void
 113 cswap(uint32_t *a, uint32_t *b, uint32_t ctl)
 114 {
 115         int i;
 116
 117         ctl = -ctl;
 118         for (i = 0; i < 10; i ++) {
 119                 uint32_t aw, bw, tw;
 120
 121                 aw = a[i];
 122                 bw = b[i];
 123                 tw = ctl & (aw ^ bw);
 124                 a[i] = aw ^ tw;
 125                 b[i] = bw ^ tw;
 126         }
 127 }
 128
 129 static void
 130 c255_add(uint32_t *d, const uint32_t *a, const uint32_t *b)
 131 {
 132         uint32_t ctl;
 133         uint32_t t[10];
 134
 135         memcpy(t, a, sizeof t);
 136         ctl = br_i31_add(t, b, 1);
 137         ctl |= NOT(br_i31_sub(t, C255_P, 0));
 138         br_i31_sub(t, C255_P, ctl);
 139         memcpy(d, t, sizeof t);
 140 }
 141
 142 static void
 143 c255_sub(uint32_t *d, const uint32_t *a, const uint32_t *b)
 144 {
 145         uint32_t t[10];
 146
 147         memcpy(t, a, sizeof t);
 148         br_i31_add(t, C255_P, br_i31_sub(t, b, 1));
 149         memcpy(d, t, sizeof t);
 150 }
 151
 152 static void
 153 c255_mul(uint32_t *d, const uint32_t *a, const uint32_t *b)
 154 {
 155         uint32_t t[10];
 156
 157         br_i31_montymul(t, a, b, C255_P, P0I);
 158         memcpy(d, t, sizeof t);
 159 }
 160
 161 static void
 162 byteswap(unsigned char *G)
 163 {
 164         int i;
 165
 166         for (i = 0; i < 16; i ++) {
 167                 unsigned char t;
 168
 169                 t = G[i];
 170                 G[i] = G[31 - i];
 171                 G[31 - i] = t;
 172         }
 173 }
 174
 175 static uint32_t
 176 api_mul(unsigned char *G, size_t Glen,
 177         const unsigned char *kb, size_t kblen, int curve)
 178 {
 179         uint32_t x1[10], x2[10], x3[10], z2[10], z3[10];
 180         uint32_t a[10], aa[10], b[10], bb[10];
 181         uint32_t c[10], d[10], e[10], da[10], cb[10];
 182         unsigned char k[32];
 183         uint32_t swap;
 184         int i;
 185
 186         (void)curve;
 187
 188         /*
 189          * Points are encoded over exactly 32 bytes. Multipliers must fit
 190          * in 32 bytes as well.
 191          * RFC 7748 mandates that the high bit of the last point byte must
 192          * be ignored/cleared.
 193          */
 194         if (Glen != 32 || kblen > 32) {
 195                 return 0;
 196         }
 197         G[31] &= 0x7F;
 198
 199         /*
 200          * Byteswap the point encoding, because it uses little-endian, and
 201          * the generic decoding routine uses big-endian.
 202          */
 203         byteswap(G);
 204
 205         /*
 206          * Decode the point ('u' coordinate). This should be reduced
 207          * modulo p, but we prefer to avoid the dependency on
 208          * br_i31_decode_reduce(). Instead, we use br_i31_decode_mod()
 209          * with a synthetic modulus of value 2^255 (this must work
 210          * since G was truncated to 255 bits), then use a conditional
 211          * subtraction. We use br_i31_decode_mod() and not
 212          * br_i31_decode(), because the ec_prime_i31 implementation uses
 213          * the former but not the latter.
 214          *    br_i31_decode_reduce(a, G, 32, C255_P);
 215          */
 216         br_i31_zero(b, 0x108);
 217         b[9] = 0x0100;
 218         br_i31_decode_mod(a, G, 32, b);
 219         a[0] = 0x107;
 220         br_i31_sub(a, C255_P, NOT(br_i31_sub(a, C255_P, 0)));
 221
 222         /*
 223          * Initialise variables x1, x2, z2, x3 and z3. We set all of them
 224          * into Montgomery representation.
 225          */
 226         br_i31_montymul(x1, a, C255_R2, C255_P, P0I);
 227         memcpy(x3, x1, sizeof x1);
 228         br_i31_zero(z2, C255_P[0]);
 229         memcpy(x2, z2, sizeof z2);
 230         x2[1] = 0x13000000;
 231         memcpy(z3, x2, sizeof x2);
 232
 233         memcpy(k, kb, kblen);
 234         memset(k + kblen, 0, (sizeof k) - kblen);
 235         k[0] &= 0xF8;
 236         k[31] &= 0x7F;
 237         k[31] |= 0x40;
 238
 239         /* obsolete
 240         print_int_mont("x1", x1);
 241         */
 242
 243         swap = 0;
 244         for (i = 254; i >= 0; i --) {
 245                 uint32_t kt;
 246
 247                 kt = (k[i >> 3] >> (i & 7)) & 1;
 248                 swap ^= kt;
 249                 cswap(x2, x3, swap);
 250                 cswap(z2, z3, swap);
 251                 swap = kt;
 252
 253                 /* obsolete
 254                 print_int_mont("x2", x2);
 255                 print_int_mont("z2", z2);
 256                 print_int_mont("x3", x3);
 257                 print_int_mont("z3", z3);
 258                 */
 259
 260                 c255_add(a, x2, z2);
 261                 c255_mul(aa, a, a);
 262                 c255_sub(b, x2, z2);
 263                 c255_mul(bb, b, b);
 264                 c255_sub(e, aa, bb);
 265                 c255_add(c, x3, z3);
 266                 c255_sub(d, x3, z3);
 267                 c255_mul(da, d, a);
 268                 c255_mul(cb, c, b);
 269
 270                 /* obsolete
 271                 print_int_mont("a ", a);
 272                 print_int_mont("aa", aa);
 273                 print_int_mont("b ", b);
 274                 print_int_mont("bb", bb);
 275                 print_int_mont("e ", e);
 276                 print_int_mont("c ", c);
 277                 print_int_mont("d ", d);
 278                 print_int_mont("da", da);
 279                 print_int_mont("cb", cb);
 280                 */
 281
 282                 c255_add(x3, da, cb);
 283                 c255_mul(x3, x3, x3);
 284                 c255_sub(z3, da, cb);
 285                 c255_mul(z3, z3, z3);
 286                 c255_mul(z3, z3, x1);
 287                 c255_mul(x2, aa, bb);
 288                 c255_mul(z2, C255_A24, e);
 289                 c255_add(z2, z2, aa);
 290                 c255_mul(z2, e, z2);
 291
 292                 /* obsolete
 293                 print_int_mont("x2", x2);
 294                 print_int_mont("z2", z2);
 295                 print_int_mont("x3", x3);
 296                 print_int_mont("z3", z3);
 297                 */
 298         }
 299         cswap(x2, x3, swap);
 300         cswap(z2, z3, swap);
 301
 302         /*
 303          * Inverse z2 with a modular exponentiation. This is a simple
 304          * square-and-multiply algorithm; we mutualise most non-squarings
 305          * since the exponent contains almost only ones.
 306          */
 307         memcpy(a, z2, sizeof z2);
 308         for (i = 0; i < 15; i ++) {
 309                 c255_mul(a, a, a);
 310                 c255_mul(a, a, z2);
 311         }
 312         memcpy(b, a, sizeof a);
 313         for (i = 0; i < 14; i ++) {
 314                 int j;
 315
 316                 for (j = 0; j < 16; j ++) {
 317                         c255_mul(b, b, b);
 318                 }
 319                 c255_mul(b, b, a);
 320         }
 321         for (i = 14; i >= 0; i --) {
 322                 c255_mul(b, b, b);
 323                 if ((0xFFEB >> i) & 1) {
 324                         c255_mul(b, z2, b);
 325                 }
 326         }
 327         c255_mul(b, x2, b);
 328
 329         /*
 330          * To avoid a dependency on br_i31_from_monty(), we use
 331          * a Montgomery multiplication with 1.
 332          *    memcpy(x2, b, sizeof b);
 333          *    br_i31_from_monty(x2, C255_P, P0I);
 334          */
 335         br_i31_zero(a, C255_P[0]);
 336         a[1] = 1;
 337         br_i31_montymul(x2, a, b, C255_P, P0I);
 338
 339         br_i31_encode(G, 32, x2);
 340         byteswap(G);
 341         return 1;
 342 }
 343
 344 static size_t
 345 api_mulgen(unsigned char *R,
 346         const unsigned char *x, size_t xlen, int curve)
 347 {
 348         const unsigned char *G;
 349         size_t Glen;
 350
 351         G = api_generator(curve, &Glen);
 352         memcpy(R, G, Glen);
 353         api_mul(R, Glen, x, xlen, curve);
 354         return Glen;
 355 }
 356
 357 static uint32_t
 358 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
 359         const unsigned char *x, size_t xlen,
 360         const unsigned char *y, size_t ylen, int curve)
 361 {
 362         /*
 363          * We don't implement this method, since it is used for ECDSA
 364          * only, and there is no ECDSA over Curve25519 (which instead
 365          * uses EdDSA).
 366          */
 367         (void)A;
 368         (void)B;
 369         (void)len;
 370         (void)x;
 371         (void)xlen;
 372         (void)y;
 373         (void)ylen;
 374         (void)curve;
 375         return 0;
 376 }
 377
 378 /* see bearssl_ec.h */
 379 const br_ec_impl br_ec_c25519_i31 = {
 380         (uint32_t)0x20000000,
 381         &api_generator,
 382         &api_order,
 383         &api_xoff,
 384         &api_mul,
 385         &api_mulgen,
 386         &api_muladd
 387 };