Damien Miller | 8a56dc2 | 2013-12-18 17:48:11 +1100 | [diff] [blame] | 1 | /* $OpenBSD: fe25519.c,v 1.3 2013/12/09 11:03:45 markus Exp $ */ |
Damien Miller | 5be9d9e | 2013-12-07 11:24:01 +1100 | [diff] [blame] | 2 | |
Damien Miller | 8a56dc2 | 2013-12-18 17:48:11 +1100 | [diff] [blame] | 3 | /* |
| 4 | * Public Domain, Authors: Daniel J. Bernstein, Niels Duif, Tanja Lange, |
| 5 | * Peter Schwabe, Bo-Yin Yang. |
| 6 | * Copied from supercop-20130419/crypto_sign/ed25519/ref/fe25519.c |
| 7 | */ |
Damien Miller | 5be9d9e | 2013-12-07 11:24:01 +1100 | [diff] [blame] | 8 | |
| 9 | #define WINDOWSIZE 1 /* Should be 1,2, or 4 */ |
| 10 | #define WINDOWMASK ((1<<WINDOWSIZE)-1) |
| 11 | |
| 12 | #include "fe25519.h" |
| 13 | |
| 14 | static crypto_uint32 equal(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ |
| 15 | { |
| 16 | crypto_uint32 x = a ^ b; /* 0: yes; 1..65535: no */ |
| 17 | x -= 1; /* 4294967295: yes; 0..65534: no */ |
| 18 | x >>= 31; /* 1: yes; 0: no */ |
| 19 | return x; |
| 20 | } |
| 21 | |
| 22 | static crypto_uint32 ge(crypto_uint32 a,crypto_uint32 b) /* 16-bit inputs */ |
| 23 | { |
| 24 | unsigned int x = a; |
| 25 | x -= (unsigned int) b; /* 0..65535: yes; 4294901761..4294967295: no */ |
| 26 | x >>= 31; /* 0: yes; 1: no */ |
| 27 | x ^= 1; /* 1: yes; 0: no */ |
| 28 | return x; |
| 29 | } |
| 30 | |
| 31 | static crypto_uint32 times19(crypto_uint32 a) |
| 32 | { |
| 33 | return (a << 4) + (a << 1) + a; |
| 34 | } |
| 35 | |
| 36 | static crypto_uint32 times38(crypto_uint32 a) |
| 37 | { |
| 38 | return (a << 5) + (a << 2) + (a << 1); |
| 39 | } |
| 40 | |
| 41 | static void reduce_add_sub(fe25519 *r) |
| 42 | { |
| 43 | crypto_uint32 t; |
| 44 | int i,rep; |
| 45 | |
| 46 | for(rep=0;rep<4;rep++) |
| 47 | { |
| 48 | t = r->v[31] >> 7; |
| 49 | r->v[31] &= 127; |
| 50 | t = times19(t); |
| 51 | r->v[0] += t; |
| 52 | for(i=0;i<31;i++) |
| 53 | { |
| 54 | t = r->v[i] >> 8; |
| 55 | r->v[i+1] += t; |
| 56 | r->v[i] &= 255; |
| 57 | } |
| 58 | } |
| 59 | } |
| 60 | |
| 61 | static void reduce_mul(fe25519 *r) |
| 62 | { |
| 63 | crypto_uint32 t; |
| 64 | int i,rep; |
| 65 | |
| 66 | for(rep=0;rep<2;rep++) |
| 67 | { |
| 68 | t = r->v[31] >> 7; |
| 69 | r->v[31] &= 127; |
| 70 | t = times19(t); |
| 71 | r->v[0] += t; |
| 72 | for(i=0;i<31;i++) |
| 73 | { |
| 74 | t = r->v[i] >> 8; |
| 75 | r->v[i+1] += t; |
| 76 | r->v[i] &= 255; |
| 77 | } |
| 78 | } |
| 79 | } |
| 80 | |
| 81 | /* reduction modulo 2^255-19 */ |
| 82 | void fe25519_freeze(fe25519 *r) |
| 83 | { |
| 84 | int i; |
| 85 | crypto_uint32 m = equal(r->v[31],127); |
| 86 | for(i=30;i>0;i--) |
| 87 | m &= equal(r->v[i],255); |
| 88 | m &= ge(r->v[0],237); |
| 89 | |
| 90 | m = -m; |
| 91 | |
| 92 | r->v[31] -= m&127; |
| 93 | for(i=30;i>0;i--) |
| 94 | r->v[i] -= m&255; |
| 95 | r->v[0] -= m&237; |
| 96 | } |
| 97 | |
| 98 | void fe25519_unpack(fe25519 *r, const unsigned char x[32]) |
| 99 | { |
| 100 | int i; |
| 101 | for(i=0;i<32;i++) r->v[i] = x[i]; |
| 102 | r->v[31] &= 127; |
| 103 | } |
| 104 | |
| 105 | /* Assumes input x being reduced below 2^255 */ |
| 106 | void fe25519_pack(unsigned char r[32], const fe25519 *x) |
| 107 | { |
| 108 | int i; |
| 109 | fe25519 y = *x; |
| 110 | fe25519_freeze(&y); |
| 111 | for(i=0;i<32;i++) |
| 112 | r[i] = y.v[i]; |
| 113 | } |
| 114 | |
| 115 | int fe25519_iszero(const fe25519 *x) |
| 116 | { |
| 117 | int i; |
| 118 | int r; |
| 119 | fe25519 t = *x; |
| 120 | fe25519_freeze(&t); |
| 121 | r = equal(t.v[0],0); |
| 122 | for(i=1;i<32;i++) |
| 123 | r &= equal(t.v[i],0); |
| 124 | return r; |
| 125 | } |
| 126 | |
| 127 | int fe25519_iseq_vartime(const fe25519 *x, const fe25519 *y) |
| 128 | { |
| 129 | int i; |
| 130 | fe25519 t1 = *x; |
| 131 | fe25519 t2 = *y; |
| 132 | fe25519_freeze(&t1); |
| 133 | fe25519_freeze(&t2); |
| 134 | for(i=0;i<32;i++) |
| 135 | if(t1.v[i] != t2.v[i]) return 0; |
| 136 | return 1; |
| 137 | } |
| 138 | |
| 139 | void fe25519_cmov(fe25519 *r, const fe25519 *x, unsigned char b) |
| 140 | { |
| 141 | int i; |
| 142 | crypto_uint32 mask = b; |
| 143 | mask = -mask; |
| 144 | for(i=0;i<32;i++) r->v[i] ^= mask & (x->v[i] ^ r->v[i]); |
| 145 | } |
| 146 | |
| 147 | unsigned char fe25519_getparity(const fe25519 *x) |
| 148 | { |
| 149 | fe25519 t = *x; |
| 150 | fe25519_freeze(&t); |
| 151 | return t.v[0] & 1; |
| 152 | } |
| 153 | |
| 154 | void fe25519_setone(fe25519 *r) |
| 155 | { |
| 156 | int i; |
| 157 | r->v[0] = 1; |
| 158 | for(i=1;i<32;i++) r->v[i]=0; |
| 159 | } |
| 160 | |
| 161 | void fe25519_setzero(fe25519 *r) |
| 162 | { |
| 163 | int i; |
| 164 | for(i=0;i<32;i++) r->v[i]=0; |
| 165 | } |
| 166 | |
| 167 | void fe25519_neg(fe25519 *r, const fe25519 *x) |
| 168 | { |
| 169 | fe25519 t; |
| 170 | int i; |
| 171 | for(i=0;i<32;i++) t.v[i]=x->v[i]; |
| 172 | fe25519_setzero(r); |
| 173 | fe25519_sub(r, r, &t); |
| 174 | } |
| 175 | |
| 176 | void fe25519_add(fe25519 *r, const fe25519 *x, const fe25519 *y) |
| 177 | { |
| 178 | int i; |
| 179 | for(i=0;i<32;i++) r->v[i] = x->v[i] + y->v[i]; |
| 180 | reduce_add_sub(r); |
| 181 | } |
| 182 | |
| 183 | void fe25519_sub(fe25519 *r, const fe25519 *x, const fe25519 *y) |
| 184 | { |
| 185 | int i; |
| 186 | crypto_uint32 t[32]; |
| 187 | t[0] = x->v[0] + 0x1da; |
| 188 | t[31] = x->v[31] + 0xfe; |
| 189 | for(i=1;i<31;i++) t[i] = x->v[i] + 0x1fe; |
| 190 | for(i=0;i<32;i++) r->v[i] = t[i] - y->v[i]; |
| 191 | reduce_add_sub(r); |
| 192 | } |
| 193 | |
| 194 | void fe25519_mul(fe25519 *r, const fe25519 *x, const fe25519 *y) |
| 195 | { |
| 196 | int i,j; |
| 197 | crypto_uint32 t[63]; |
| 198 | for(i=0;i<63;i++)t[i] = 0; |
| 199 | |
| 200 | for(i=0;i<32;i++) |
| 201 | for(j=0;j<32;j++) |
| 202 | t[i+j] += x->v[i] * y->v[j]; |
| 203 | |
| 204 | for(i=32;i<63;i++) |
| 205 | r->v[i-32] = t[i-32] + times38(t[i]); |
| 206 | r->v[31] = t[31]; /* result now in r[0]...r[31] */ |
| 207 | |
| 208 | reduce_mul(r); |
| 209 | } |
| 210 | |
| 211 | void fe25519_square(fe25519 *r, const fe25519 *x) |
| 212 | { |
| 213 | fe25519_mul(r, x, x); |
| 214 | } |
| 215 | |
| 216 | void fe25519_invert(fe25519 *r, const fe25519 *x) |
| 217 | { |
| 218 | fe25519 z2; |
| 219 | fe25519 z9; |
| 220 | fe25519 z11; |
| 221 | fe25519 z2_5_0; |
| 222 | fe25519 z2_10_0; |
| 223 | fe25519 z2_20_0; |
| 224 | fe25519 z2_50_0; |
| 225 | fe25519 z2_100_0; |
| 226 | fe25519 t0; |
| 227 | fe25519 t1; |
| 228 | int i; |
| 229 | |
| 230 | /* 2 */ fe25519_square(&z2,x); |
| 231 | /* 4 */ fe25519_square(&t1,&z2); |
| 232 | /* 8 */ fe25519_square(&t0,&t1); |
| 233 | /* 9 */ fe25519_mul(&z9,&t0,x); |
| 234 | /* 11 */ fe25519_mul(&z11,&z9,&z2); |
| 235 | /* 22 */ fe25519_square(&t0,&z11); |
| 236 | /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t0,&z9); |
| 237 | |
| 238 | /* 2^6 - 2^1 */ fe25519_square(&t0,&z2_5_0); |
| 239 | /* 2^7 - 2^2 */ fe25519_square(&t1,&t0); |
| 240 | /* 2^8 - 2^3 */ fe25519_square(&t0,&t1); |
| 241 | /* 2^9 - 2^4 */ fe25519_square(&t1,&t0); |
| 242 | /* 2^10 - 2^5 */ fe25519_square(&t0,&t1); |
| 243 | /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t0,&z2_5_0); |
| 244 | |
| 245 | /* 2^11 - 2^1 */ fe25519_square(&t0,&z2_10_0); |
| 246 | /* 2^12 - 2^2 */ fe25519_square(&t1,&t0); |
| 247 | /* 2^20 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
| 248 | /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t1,&z2_10_0); |
| 249 | |
| 250 | /* 2^21 - 2^1 */ fe25519_square(&t0,&z2_20_0); |
| 251 | /* 2^22 - 2^2 */ fe25519_square(&t1,&t0); |
| 252 | /* 2^40 - 2^20 */ for (i = 2;i < 20;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
| 253 | /* 2^40 - 2^0 */ fe25519_mul(&t0,&t1,&z2_20_0); |
| 254 | |
| 255 | /* 2^41 - 2^1 */ fe25519_square(&t1,&t0); |
| 256 | /* 2^42 - 2^2 */ fe25519_square(&t0,&t1); |
| 257 | /* 2^50 - 2^10 */ for (i = 2;i < 10;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } |
| 258 | /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t0,&z2_10_0); |
| 259 | |
| 260 | /* 2^51 - 2^1 */ fe25519_square(&t0,&z2_50_0); |
| 261 | /* 2^52 - 2^2 */ fe25519_square(&t1,&t0); |
| 262 | /* 2^100 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
| 263 | /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t1,&z2_50_0); |
| 264 | |
| 265 | /* 2^101 - 2^1 */ fe25519_square(&t1,&z2_100_0); |
| 266 | /* 2^102 - 2^2 */ fe25519_square(&t0,&t1); |
| 267 | /* 2^200 - 2^100 */ for (i = 2;i < 100;i += 2) { fe25519_square(&t1,&t0); fe25519_square(&t0,&t1); } |
| 268 | /* 2^200 - 2^0 */ fe25519_mul(&t1,&t0,&z2_100_0); |
| 269 | |
| 270 | /* 2^201 - 2^1 */ fe25519_square(&t0,&t1); |
| 271 | /* 2^202 - 2^2 */ fe25519_square(&t1,&t0); |
| 272 | /* 2^250 - 2^50 */ for (i = 2;i < 50;i += 2) { fe25519_square(&t0,&t1); fe25519_square(&t1,&t0); } |
| 273 | /* 2^250 - 2^0 */ fe25519_mul(&t0,&t1,&z2_50_0); |
| 274 | |
| 275 | /* 2^251 - 2^1 */ fe25519_square(&t1,&t0); |
| 276 | /* 2^252 - 2^2 */ fe25519_square(&t0,&t1); |
| 277 | /* 2^253 - 2^3 */ fe25519_square(&t1,&t0); |
| 278 | /* 2^254 - 2^4 */ fe25519_square(&t0,&t1); |
| 279 | /* 2^255 - 2^5 */ fe25519_square(&t1,&t0); |
| 280 | /* 2^255 - 21 */ fe25519_mul(r,&t1,&z11); |
| 281 | } |
| 282 | |
| 283 | void fe25519_pow2523(fe25519 *r, const fe25519 *x) |
| 284 | { |
| 285 | fe25519 z2; |
| 286 | fe25519 z9; |
| 287 | fe25519 z11; |
| 288 | fe25519 z2_5_0; |
| 289 | fe25519 z2_10_0; |
| 290 | fe25519 z2_20_0; |
| 291 | fe25519 z2_50_0; |
| 292 | fe25519 z2_100_0; |
| 293 | fe25519 t; |
| 294 | int i; |
| 295 | |
| 296 | /* 2 */ fe25519_square(&z2,x); |
| 297 | /* 4 */ fe25519_square(&t,&z2); |
| 298 | /* 8 */ fe25519_square(&t,&t); |
| 299 | /* 9 */ fe25519_mul(&z9,&t,x); |
| 300 | /* 11 */ fe25519_mul(&z11,&z9,&z2); |
| 301 | /* 22 */ fe25519_square(&t,&z11); |
| 302 | /* 2^5 - 2^0 = 31 */ fe25519_mul(&z2_5_0,&t,&z9); |
| 303 | |
| 304 | /* 2^6 - 2^1 */ fe25519_square(&t,&z2_5_0); |
| 305 | /* 2^10 - 2^5 */ for (i = 1;i < 5;i++) { fe25519_square(&t,&t); } |
| 306 | /* 2^10 - 2^0 */ fe25519_mul(&z2_10_0,&t,&z2_5_0); |
| 307 | |
| 308 | /* 2^11 - 2^1 */ fe25519_square(&t,&z2_10_0); |
| 309 | /* 2^20 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } |
| 310 | /* 2^20 - 2^0 */ fe25519_mul(&z2_20_0,&t,&z2_10_0); |
| 311 | |
| 312 | /* 2^21 - 2^1 */ fe25519_square(&t,&z2_20_0); |
| 313 | /* 2^40 - 2^20 */ for (i = 1;i < 20;i++) { fe25519_square(&t,&t); } |
| 314 | /* 2^40 - 2^0 */ fe25519_mul(&t,&t,&z2_20_0); |
| 315 | |
| 316 | /* 2^41 - 2^1 */ fe25519_square(&t,&t); |
| 317 | /* 2^50 - 2^10 */ for (i = 1;i < 10;i++) { fe25519_square(&t,&t); } |
| 318 | /* 2^50 - 2^0 */ fe25519_mul(&z2_50_0,&t,&z2_10_0); |
| 319 | |
| 320 | /* 2^51 - 2^1 */ fe25519_square(&t,&z2_50_0); |
| 321 | /* 2^100 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } |
| 322 | /* 2^100 - 2^0 */ fe25519_mul(&z2_100_0,&t,&z2_50_0); |
| 323 | |
| 324 | /* 2^101 - 2^1 */ fe25519_square(&t,&z2_100_0); |
| 325 | /* 2^200 - 2^100 */ for (i = 1;i < 100;i++) { fe25519_square(&t,&t); } |
| 326 | /* 2^200 - 2^0 */ fe25519_mul(&t,&t,&z2_100_0); |
| 327 | |
| 328 | /* 2^201 - 2^1 */ fe25519_square(&t,&t); |
| 329 | /* 2^250 - 2^50 */ for (i = 1;i < 50;i++) { fe25519_square(&t,&t); } |
| 330 | /* 2^250 - 2^0 */ fe25519_mul(&t,&t,&z2_50_0); |
| 331 | |
| 332 | /* 2^251 - 2^1 */ fe25519_square(&t,&t); |
| 333 | /* 2^252 - 2^2 */ fe25519_square(&t,&t); |
| 334 | /* 2^252 - 3 */ fe25519_mul(r,&t,x); |
| 335 | } |