_ 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 static const uint16_t C255_A24[] = {
  50         0x0110,
  51         0x45D3, 0x0046, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
  52         0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000, 0x0000,
  53         0x0000
  54 };
  55
  56 static const unsigned char GEN[] = {
  57         0x09, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  58         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  59         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  60         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00
  61 };
  62
  63 static const unsigned char ORDER[] = {
  64         0x10, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  65         0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00, 0x00,
  66         0x14, 0xDE, 0xF9, 0xDE, 0xA2, 0xF7, 0x9C, 0xD6,
  67         0x58, 0x12, 0x63, 0x1A, 0x5C, 0xF5, 0xD3, 0xED
  68 };
  69
  70 static const unsigned char *
  71 api_generator(int curve, size_t *len)
  72 {
  73         (void)curve;
  74         *len = 32;
  75         return GEN;
  76 }
  77
  78 static const unsigned char *
  79 api_order(int curve, size_t *len)
  80 {
  81         (void)curve;
  82         *len = 32;
  83         return ORDER;
  84 }
  85
  86 static void
  87 cswap(uint16_t *a, uint16_t *b, uint32_t ctl)
  88 {
  89         int i;
  90
  91         ctl = -ctl;
  92         for (i = 0; i < 18; i ++) {
  93                 uint32_t aw, bw, tw;
  94
  95                 aw = a[i];
  96                 bw = b[i];
  97                 tw = ctl & (aw ^ bw);
  98                 a[i] = aw ^ tw;
  99                 b[i] = bw ^ tw;
 100         }
 101 }
 102
 103 static void
 104 c255_add(uint16_t *d, const uint16_t *a, const uint16_t *b)
 105 {
 106         uint32_t ctl;
 107         uint16_t t[18];
 108
 109         memcpy(t, a, sizeof t);
 110         ctl = br_i15_add(t, b, 1);
 111         ctl |= NOT(br_i15_sub(t, C255_P, 0));
 112         br_i15_sub(t, C255_P, ctl);
 113         memcpy(d, t, sizeof t);
 114 }
 115
 116 static void
 117 c255_sub(uint16_t *d, const uint16_t *a, const uint16_t *b)
 118 {
 119         uint16_t t[18];
 120
 121         memcpy(t, a, sizeof t);
 122         br_i15_add(t, C255_P, br_i15_sub(t, b, 1));
 123         memcpy(d, t, sizeof t);
 124 }
 125
 126 static void
 127 c255_mul(uint16_t *d, const uint16_t *a, const uint16_t *b)
 128 {
 129         uint16_t t[18];
 130
 131         br_i15_montymul(t, a, b, C255_P, P0I);
 132         memcpy(d, t, sizeof t);
 133 }
 134
 135 static void
 136 byteswap(unsigned char *G)
 137 {
 138         int i;
 139
 140         for (i = 0; i < 16; i ++) {
 141                 unsigned char t;
 142
 143                 t = G[i];
 144                 G[i] = G[31 - i];
 145                 G[31 - i] = t;
 146         }
 147 }
 148
 149 static uint32_t
 150 api_mul(unsigned char *G, size_t Glen,
 151         const unsigned char *kb, size_t kblen, int curve)
 152 {
 153         uint16_t x1[18], x2[18], x3[18], z2[18], z3[18];
 154         uint16_t a[18], aa[18], b[18], bb[18];
 155         uint16_t c[18], d[18], e[18], da[18], cb[18];
 156         unsigned char k[32];
 157         uint32_t swap;
 158         int i;
 159
 160         (void)curve;
 161
 162         /*
 163          * Points are encoded over exactly 32 bytes. Multipliers must fit
 164          * in 32 bytes as well.
 165          * RFC 7748 mandates that the high bit of the last point byte must
 166          * be ignored/cleared.
 167          */
 168         if (Glen != 32 || kblen > 32) {
 169                 return 0;
 170         }
 171         G[31] &= 0x7F;
 172
 173         /*
 174          * Byteswap the point encoding, because it uses little-endian, and
 175          * the generic decoding routine uses big-endian.
 176          */
 177         byteswap(G);
 178
 179         /*
 180          * Initialise variables x1, x2, z2, x3 and z3. We set all of them
 181          * into Montgomery representation.
 182          */
 183         br_i15_decode_reduce(a, G, 32, C255_P);
 184         br_i15_montymul(x1, a, C255_R2, C255_P, P0I);
 185         memcpy(x3, x1, sizeof x1);
 186         br_i15_zero(z2, C255_P[0]);
 187         memcpy(x2, z2, sizeof z2);
 188         x2[1] = 19;
 189         memcpy(z3, x2, sizeof x2);
 190
 191         memcpy(k, kb, kblen);
 192         memset(k + kblen, 0, (sizeof k) - kblen);
 193         k[0] &= 0xF8;
 194         k[31] &= 0x7F;
 195         k[31] |= 0x40;
 196
 197         swap = 0;
 198         for (i = 254; i >= 0; i --) {
 199                 uint32_t kt;
 200
 201                 kt = (k[i >> 3] >> (i & 7)) & 1;
 202                 swap ^= kt;
 203                 cswap(x2, x3, swap);
 204                 cswap(z2, z3, swap);
 205                 swap = kt;
 206
 207                 c255_add(a, x2, z2);
 208                 c255_mul(aa, a, a);
 209                 c255_sub(b, x2, z2);
 210                 c255_mul(bb, b, b);
 211                 c255_sub(e, aa, bb);
 212                 c255_add(c, x3, z3);
 213                 c255_sub(d, x3, z3);
 214                 c255_mul(da, d, a);
 215                 c255_mul(cb, c, b);
 216                 c255_add(x3, da, cb);
 217                 c255_mul(x3, x3, x3);
 218                 c255_sub(z3, da, cb);
 219                 c255_mul(z3, z3, z3);
 220                 c255_mul(z3, z3, x1);
 221                 c255_mul(x2, aa, bb);
 222                 c255_mul(z2, C255_A24, e);
 223                 c255_add(z2, z2, aa);
 224                 c255_mul(z2, e, z2);
 225         }
 226         cswap(x2, x3, swap);
 227         cswap(z2, z3, swap);
 228
 229         /*
 230          * Inverse z2 with a modular exponentiation. This is a simple
 231          * square-and-multiply algorithm; we mutualise most non-squarings
 232          * since the exponent contains almost only ones.
 233          */
 234         memcpy(a, z2, sizeof z2);
 235         for (i = 0; i < 15; i ++) {
 236                 c255_mul(a, a, a);
 237                 c255_mul(a, a, z2);
 238         }
 239         memcpy(b, a, sizeof a);
 240         for (i = 0; i < 14; i ++) {
 241                 int j;
 242
 243                 for (j = 0; j < 16; j ++) {
 244                         c255_mul(b, b, b);
 245                 }
 246                 c255_mul(b, b, a);
 247         }
 248         for (i = 14; i >= 0; i --) {
 249                 c255_mul(b, b, b);
 250                 if ((0xFFEB >> i) & 1) {
 251                         c255_mul(b, z2, b);
 252                 }
 253         }
 254         c255_mul(x2, x2, b);
 255         br_i15_from_monty(x2, C255_P, P0I);
 256         br_i15_encode(G, 32, x2);
 257         byteswap(G);
 258         return 1;
 259 }
 260
 261 static size_t
 262 api_mulgen(unsigned char *R,
 263         const unsigned char *x, size_t xlen, int curve)
 264 {
 265         const unsigned char *G;
 266         size_t Glen;
 267
 268         G = api_generator(curve, &Glen);
 269         memcpy(R, G, Glen);
 270         api_mul(R, Glen, x, xlen, curve);
 271         return Glen;
 272 }
 273
 274 static uint32_t
 275 api_muladd(unsigned char *A, const unsigned char *B, size_t len,
 276         const unsigned char *x, size_t xlen,
 277         const unsigned char *y, size_t ylen, int curve)
 278 {
 279         /*
 280          * We don't implement this method, since it is used for ECDSA
 281          * only, and there is no ECDSA over Curve25519 (which instead
 282          * uses EdDSA).
 283          */
 284         (void)A;
 285         (void)B;
 286         (void)len;
 287         (void)x;
 288         (void)xlen;
 289         (void)y;
 290         (void)ylen;
 291         (void)curve;
 292         return 0;
 293 }
 294
 295 /* see bearssl_ec.h */
 296 const br_ec_impl br_ec_c25519_i15 = {
 297         (uint32_t)0x20000000,
 298         &api_generator,
 299         &api_order,
 300         &api_mul,
 301         &api_mulgen,
 302         &api_muladd
 303 };