github.com/kisexp/xdchain@v0.0.0-20211206025815-490d6b732aa7/crypto/secp256k1/libsecp256k1/src/field_5x52_impl.h (about) 1 /********************************************************************** 2 * Copyright (c) 2013, 2014 Pieter Wuille * 3 * Distributed under the MIT software license, see the accompanying * 4 * file COPYING or http://www.opensource.org/licenses/mit-license.php.* 5 **********************************************************************/ 6 7 #ifndef _SECP256K1_FIELD_REPR_IMPL_H_ 8 #define _SECP256K1_FIELD_REPR_IMPL_H_ 9 10 #if defined HAVE_CONFIG_H 11 #include "libsecp256k1-config.h" 12 #endif 13 14 #include "util.h" 15 #include "num.h" 16 #include "field.h" 17 18 #if defined(USE_ASM_X86_64) 19 #include "field_5x52_asm_impl.h" 20 #else 21 #include "field_5x52_int128_impl.h" 22 #endif 23 24 /** Implements arithmetic modulo FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFF FFFFFFFE FFFFFC2F, 25 * represented as 5 uint64_t's in base 2^52. The values are allowed to contain >52 each. In particular, 26 * each FieldElem has a 'magnitude' associated with it. Internally, a magnitude M means each element 27 * is at most M*(2^53-1), except the most significant one, which is limited to M*(2^49-1). All operations 28 * accept any input with magnitude at most M, and have different rules for propagating magnitude to their 29 * output. 30 */ 31 32 #ifdef VERIFY 33 static void secp256k1_fe_verify(const secp256k1_fe *a) { 34 const uint64_t *d = a->n; 35 int m = a->normalized ? 1 : 2 * a->magnitude, r = 1; 36 /* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */ 37 r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m); 38 r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m); 39 r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m); 40 r &= (d[3] <= 0xFFFFFFFFFFFFFULL * m); 41 r &= (d[4] <= 0x0FFFFFFFFFFFFULL * m); 42 r &= (a->magnitude >= 0); 43 r &= (a->magnitude <= 2048); 44 if (a->normalized) { 45 r &= (a->magnitude <= 1); 46 if (r && (d[4] == 0x0FFFFFFFFFFFFULL) && ((d[3] & d[2] & d[1]) == 0xFFFFFFFFFFFFFULL)) { 47 r &= (d[0] < 0xFFFFEFFFFFC2FULL); 48 } 49 } 50 VERIFY_CHECK(r == 1); 51 } 52 #endif 53 54 static void secp256k1_fe_normalize(secp256k1_fe *r) { 55 uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; 56 57 /* Reduce t4 at the start so there will be at most a single carry from the first pass */ 58 uint64_t m; 59 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; 60 61 /* The first pass ensures the magnitude is 1, ... */ 62 t0 += x * 0x1000003D1ULL; 63 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; 64 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; 65 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; 66 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; 67 68 /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ 69 VERIFY_CHECK(t4 >> 49 == 0); 70 71 /* At most a single final reduction is needed; check if the value is >= the field characteristic */ 72 x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) 73 & (t0 >= 0xFFFFEFFFFFC2FULL)); 74 75 /* Apply the final reduction (for constant-time behaviour, we do it always) */ 76 t0 += x * 0x1000003D1ULL; 77 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; 78 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; 79 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; 80 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; 81 82 /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ 83 VERIFY_CHECK(t4 >> 48 == x); 84 85 /* Mask off the possible multiple of 2^256 from the final reduction */ 86 t4 &= 0x0FFFFFFFFFFFFULL; 87 88 r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; 89 90 #ifdef VERIFY 91 r->magnitude = 1; 92 r->normalized = 1; 93 secp256k1_fe_verify(r); 94 #endif 95 } 96 97 static void secp256k1_fe_normalize_weak(secp256k1_fe *r) { 98 uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; 99 100 /* Reduce t4 at the start so there will be at most a single carry from the first pass */ 101 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; 102 103 /* The first pass ensures the magnitude is 1, ... */ 104 t0 += x * 0x1000003D1ULL; 105 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; 106 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; 107 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; 108 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; 109 110 /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ 111 VERIFY_CHECK(t4 >> 49 == 0); 112 113 r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; 114 115 #ifdef VERIFY 116 r->magnitude = 1; 117 secp256k1_fe_verify(r); 118 #endif 119 } 120 121 static void secp256k1_fe_normalize_var(secp256k1_fe *r) { 122 uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; 123 124 /* Reduce t4 at the start so there will be at most a single carry from the first pass */ 125 uint64_t m; 126 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; 127 128 /* The first pass ensures the magnitude is 1, ... */ 129 t0 += x * 0x1000003D1ULL; 130 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; 131 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; m = t1; 132 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; m &= t2; 133 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; m &= t3; 134 135 /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ 136 VERIFY_CHECK(t4 >> 49 == 0); 137 138 /* At most a single final reduction is needed; check if the value is >= the field characteristic */ 139 x = (t4 >> 48) | ((t4 == 0x0FFFFFFFFFFFFULL) & (m == 0xFFFFFFFFFFFFFULL) 140 & (t0 >= 0xFFFFEFFFFFC2FULL)); 141 142 if (x) { 143 t0 += 0x1000003D1ULL; 144 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; 145 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; 146 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; 147 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; 148 149 /* If t4 didn't carry to bit 48 already, then it should have after any final reduction */ 150 VERIFY_CHECK(t4 >> 48 == x); 151 152 /* Mask off the possible multiple of 2^256 from the final reduction */ 153 t4 &= 0x0FFFFFFFFFFFFULL; 154 } 155 156 r->n[0] = t0; r->n[1] = t1; r->n[2] = t2; r->n[3] = t3; r->n[4] = t4; 157 158 #ifdef VERIFY 159 r->magnitude = 1; 160 r->normalized = 1; 161 secp256k1_fe_verify(r); 162 #endif 163 } 164 165 static int secp256k1_fe_normalizes_to_zero(secp256k1_fe *r) { 166 uint64_t t0 = r->n[0], t1 = r->n[1], t2 = r->n[2], t3 = r->n[3], t4 = r->n[4]; 167 168 /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ 169 uint64_t z0, z1; 170 171 /* Reduce t4 at the start so there will be at most a single carry from the first pass */ 172 uint64_t x = t4 >> 48; t4 &= 0x0FFFFFFFFFFFFULL; 173 174 /* The first pass ensures the magnitude is 1, ... */ 175 t0 += x * 0x1000003D1ULL; 176 t1 += (t0 >> 52); t0 &= 0xFFFFFFFFFFFFFULL; z0 = t0; z1 = t0 ^ 0x1000003D0ULL; 177 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; 178 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; 179 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; 180 z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; 181 182 /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ 183 VERIFY_CHECK(t4 >> 49 == 0); 184 185 return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); 186 } 187 188 static int secp256k1_fe_normalizes_to_zero_var(secp256k1_fe *r) { 189 uint64_t t0, t1, t2, t3, t4; 190 uint64_t z0, z1; 191 uint64_t x; 192 193 t0 = r->n[0]; 194 t4 = r->n[4]; 195 196 /* Reduce t4 at the start so there will be at most a single carry from the first pass */ 197 x = t4 >> 48; 198 199 /* The first pass ensures the magnitude is 1, ... */ 200 t0 += x * 0x1000003D1ULL; 201 202 /* z0 tracks a possible raw value of 0, z1 tracks a possible raw value of P */ 203 z0 = t0 & 0xFFFFFFFFFFFFFULL; 204 z1 = z0 ^ 0x1000003D0ULL; 205 206 /* Fast return path should catch the majority of cases */ 207 if ((z0 != 0ULL) & (z1 != 0xFFFFFFFFFFFFFULL)) { 208 return 0; 209 } 210 211 t1 = r->n[1]; 212 t2 = r->n[2]; 213 t3 = r->n[3]; 214 215 t4 &= 0x0FFFFFFFFFFFFULL; 216 217 t1 += (t0 >> 52); 218 t2 += (t1 >> 52); t1 &= 0xFFFFFFFFFFFFFULL; z0 |= t1; z1 &= t1; 219 t3 += (t2 >> 52); t2 &= 0xFFFFFFFFFFFFFULL; z0 |= t2; z1 &= t2; 220 t4 += (t3 >> 52); t3 &= 0xFFFFFFFFFFFFFULL; z0 |= t3; z1 &= t3; 221 z0 |= t4; z1 &= t4 ^ 0xF000000000000ULL; 222 223 /* ... except for a possible carry at bit 48 of t4 (i.e. bit 256 of the field element) */ 224 VERIFY_CHECK(t4 >> 49 == 0); 225 226 return (z0 == 0) | (z1 == 0xFFFFFFFFFFFFFULL); 227 } 228 229 SECP256K1_INLINE static void secp256k1_fe_set_int(secp256k1_fe *r, int a) { 230 r->n[0] = a; 231 r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0; 232 #ifdef VERIFY 233 r->magnitude = 1; 234 r->normalized = 1; 235 secp256k1_fe_verify(r); 236 #endif 237 } 238 239 SECP256K1_INLINE static int secp256k1_fe_is_zero(const secp256k1_fe *a) { 240 const uint64_t *t = a->n; 241 #ifdef VERIFY 242 VERIFY_CHECK(a->normalized); 243 secp256k1_fe_verify(a); 244 #endif 245 return (t[0] | t[1] | t[2] | t[3] | t[4]) == 0; 246 } 247 248 SECP256K1_INLINE static int secp256k1_fe_is_odd(const secp256k1_fe *a) { 249 #ifdef VERIFY 250 VERIFY_CHECK(a->normalized); 251 secp256k1_fe_verify(a); 252 #endif 253 return a->n[0] & 1; 254 } 255 256 SECP256K1_INLINE static void secp256k1_fe_clear(secp256k1_fe *a) { 257 int i; 258 #ifdef VERIFY 259 a->magnitude = 0; 260 a->normalized = 1; 261 #endif 262 for (i=0; i<5; i++) { 263 a->n[i] = 0; 264 } 265 } 266 267 static int secp256k1_fe_cmp_var(const secp256k1_fe *a, const secp256k1_fe *b) { 268 int i; 269 #ifdef VERIFY 270 VERIFY_CHECK(a->normalized); 271 VERIFY_CHECK(b->normalized); 272 secp256k1_fe_verify(a); 273 secp256k1_fe_verify(b); 274 #endif 275 for (i = 4; i >= 0; i--) { 276 if (a->n[i] > b->n[i]) { 277 return 1; 278 } 279 if (a->n[i] < b->n[i]) { 280 return -1; 281 } 282 } 283 return 0; 284 } 285 286 static int secp256k1_fe_set_b32(secp256k1_fe *r, const unsigned char *a) { 287 int i; 288 r->n[0] = r->n[1] = r->n[2] = r->n[3] = r->n[4] = 0; 289 for (i=0; i<32; i++) { 290 int j; 291 for (j=0; j<2; j++) { 292 int limb = (8*i+4*j)/52; 293 int shift = (8*i+4*j)%52; 294 r->n[limb] |= (uint64_t)((a[31-i] >> (4*j)) & 0xF) << shift; 295 } 296 } 297 if (r->n[4] == 0x0FFFFFFFFFFFFULL && (r->n[3] & r->n[2] & r->n[1]) == 0xFFFFFFFFFFFFFULL && r->n[0] >= 0xFFFFEFFFFFC2FULL) { 298 return 0; 299 } 300 #ifdef VERIFY 301 r->magnitude = 1; 302 r->normalized = 1; 303 secp256k1_fe_verify(r); 304 #endif 305 return 1; 306 } 307 308 /** Convert a field element to a 32-byte big endian value. Requires the input to be normalized */ 309 static void secp256k1_fe_get_b32(unsigned char *r, const secp256k1_fe *a) { 310 int i; 311 #ifdef VERIFY 312 VERIFY_CHECK(a->normalized); 313 secp256k1_fe_verify(a); 314 #endif 315 for (i=0; i<32; i++) { 316 int j; 317 int c = 0; 318 for (j=0; j<2; j++) { 319 int limb = (8*i+4*j)/52; 320 int shift = (8*i+4*j)%52; 321 c |= ((a->n[limb] >> shift) & 0xF) << (4 * j); 322 } 323 r[31-i] = c; 324 } 325 } 326 327 SECP256K1_INLINE static void secp256k1_fe_negate(secp256k1_fe *r, const secp256k1_fe *a, int m) { 328 #ifdef VERIFY 329 VERIFY_CHECK(a->magnitude <= m); 330 secp256k1_fe_verify(a); 331 #endif 332 r->n[0] = 0xFFFFEFFFFFC2FULL * 2 * (m + 1) - a->n[0]; 333 r->n[1] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[1]; 334 r->n[2] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[2]; 335 r->n[3] = 0xFFFFFFFFFFFFFULL * 2 * (m + 1) - a->n[3]; 336 r->n[4] = 0x0FFFFFFFFFFFFULL * 2 * (m + 1) - a->n[4]; 337 #ifdef VERIFY 338 r->magnitude = m + 1; 339 r->normalized = 0; 340 secp256k1_fe_verify(r); 341 #endif 342 } 343 344 SECP256K1_INLINE static void secp256k1_fe_mul_int(secp256k1_fe *r, int a) { 345 r->n[0] *= a; 346 r->n[1] *= a; 347 r->n[2] *= a; 348 r->n[3] *= a; 349 r->n[4] *= a; 350 #ifdef VERIFY 351 r->magnitude *= a; 352 r->normalized = 0; 353 secp256k1_fe_verify(r); 354 #endif 355 } 356 357 SECP256K1_INLINE static void secp256k1_fe_add(secp256k1_fe *r, const secp256k1_fe *a) { 358 #ifdef VERIFY 359 secp256k1_fe_verify(a); 360 #endif 361 r->n[0] += a->n[0]; 362 r->n[1] += a->n[1]; 363 r->n[2] += a->n[2]; 364 r->n[3] += a->n[3]; 365 r->n[4] += a->n[4]; 366 #ifdef VERIFY 367 r->magnitude += a->magnitude; 368 r->normalized = 0; 369 secp256k1_fe_verify(r); 370 #endif 371 } 372 373 static void secp256k1_fe_mul(secp256k1_fe *r, const secp256k1_fe *a, const secp256k1_fe * SECP256K1_RESTRICT b) { 374 #ifdef VERIFY 375 VERIFY_CHECK(a->magnitude <= 8); 376 VERIFY_CHECK(b->magnitude <= 8); 377 secp256k1_fe_verify(a); 378 secp256k1_fe_verify(b); 379 VERIFY_CHECK(r != b); 380 #endif 381 secp256k1_fe_mul_inner(r->n, a->n, b->n); 382 #ifdef VERIFY 383 r->magnitude = 1; 384 r->normalized = 0; 385 secp256k1_fe_verify(r); 386 #endif 387 } 388 389 static void secp256k1_fe_sqr(secp256k1_fe *r, const secp256k1_fe *a) { 390 #ifdef VERIFY 391 VERIFY_CHECK(a->magnitude <= 8); 392 secp256k1_fe_verify(a); 393 #endif 394 secp256k1_fe_sqr_inner(r->n, a->n); 395 #ifdef VERIFY 396 r->magnitude = 1; 397 r->normalized = 0; 398 secp256k1_fe_verify(r); 399 #endif 400 } 401 402 static SECP256K1_INLINE void secp256k1_fe_cmov(secp256k1_fe *r, const secp256k1_fe *a, int flag) { 403 uint64_t mask0, mask1; 404 mask0 = flag + ~((uint64_t)0); 405 mask1 = ~mask0; 406 r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); 407 r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); 408 r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); 409 r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); 410 r->n[4] = (r->n[4] & mask0) | (a->n[4] & mask1); 411 #ifdef VERIFY 412 if (a->magnitude > r->magnitude) { 413 r->magnitude = a->magnitude; 414 } 415 r->normalized &= a->normalized; 416 #endif 417 } 418 419 static SECP256K1_INLINE void secp256k1_fe_storage_cmov(secp256k1_fe_storage *r, const secp256k1_fe_storage *a, int flag) { 420 uint64_t mask0, mask1; 421 mask0 = flag + ~((uint64_t)0); 422 mask1 = ~mask0; 423 r->n[0] = (r->n[0] & mask0) | (a->n[0] & mask1); 424 r->n[1] = (r->n[1] & mask0) | (a->n[1] & mask1); 425 r->n[2] = (r->n[2] & mask0) | (a->n[2] & mask1); 426 r->n[3] = (r->n[3] & mask0) | (a->n[3] & mask1); 427 } 428 429 static void secp256k1_fe_to_storage(secp256k1_fe_storage *r, const secp256k1_fe *a) { 430 #ifdef VERIFY 431 VERIFY_CHECK(a->normalized); 432 #endif 433 r->n[0] = a->n[0] | a->n[1] << 52; 434 r->n[1] = a->n[1] >> 12 | a->n[2] << 40; 435 r->n[2] = a->n[2] >> 24 | a->n[3] << 28; 436 r->n[3] = a->n[3] >> 36 | a->n[4] << 16; 437 } 438 439 static SECP256K1_INLINE void secp256k1_fe_from_storage(secp256k1_fe *r, const secp256k1_fe_storage *a) { 440 r->n[0] = a->n[0] & 0xFFFFFFFFFFFFFULL; 441 r->n[1] = a->n[0] >> 52 | ((a->n[1] << 12) & 0xFFFFFFFFFFFFFULL); 442 r->n[2] = a->n[1] >> 40 | ((a->n[2] << 24) & 0xFFFFFFFFFFFFFULL); 443 r->n[3] = a->n[2] >> 28 | ((a->n[3] << 36) & 0xFFFFFFFFFFFFFULL); 444 r->n[4] = a->n[3] >> 16; 445 #ifdef VERIFY 446 r->magnitude = 1; 447 r->normalized = 1; 448 #endif 449 } 450 451 #endif