github.com/klaytn/klaytn@v1.12.1/crypto/secp256k1/libsecp256k1/src/ecmult_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_ECMULT_IMPL_H_ 8 #define _SECP256K1_ECMULT_IMPL_H_ 9 10 #include <string.h> 11 12 #include "group.h" 13 #include "scalar.h" 14 #include "ecmult.h" 15 16 #if defined(EXHAUSTIVE_TEST_ORDER) 17 /* We need to lower these values for exhaustive tests because 18 * the tables cannot have infinities in them (this breaks the 19 * affine-isomorphism stuff which tracks z-ratios) */ 20 # if EXHAUSTIVE_TEST_ORDER > 128 21 # define WINDOW_A 5 22 # define WINDOW_G 8 23 # elif EXHAUSTIVE_TEST_ORDER > 8 24 # define WINDOW_A 4 25 # define WINDOW_G 4 26 # else 27 # define WINDOW_A 2 28 # define WINDOW_G 2 29 # endif 30 #else 31 /* optimal for 128-bit and 256-bit exponents. */ 32 #define WINDOW_A 5 33 /** larger numbers may result in slightly better performance, at the cost of 34 exponentially larger precomputed tables. */ 35 #ifdef USE_ENDOMORPHISM 36 /** Two tables for window size 15: 1.375 MiB. */ 37 #define WINDOW_G 15 38 #else 39 /** One table for window size 16: 1.375 MiB. */ 40 #define WINDOW_G 16 41 #endif 42 #endif 43 44 /** The number of entries a table with precomputed multiples needs to have. */ 45 #define ECMULT_TABLE_SIZE(w) (1 << ((w)-2)) 46 47 /** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain 48 * the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will 49 * contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z. 50 * Prej's Z values are undefined, except for the last value. 51 */ 52 static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) { 53 secp256k1_gej d; 54 secp256k1_ge a_ge, d_ge; 55 int i; 56 57 VERIFY_CHECK(!a->infinity); 58 59 secp256k1_gej_double_var(&d, a, NULL); 60 61 /* 62 * Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate 63 * of 'd', and scale the 1P starting value's x/y coordinates without changing its z. 64 */ 65 d_ge.x = d.x; 66 d_ge.y = d.y; 67 d_ge.infinity = 0; 68 69 secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z); 70 prej[0].x = a_ge.x; 71 prej[0].y = a_ge.y; 72 prej[0].z = a->z; 73 prej[0].infinity = 0; 74 75 zr[0] = d.z; 76 for (i = 1; i < n; i++) { 77 secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]); 78 } 79 80 /* 81 * Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only 82 * the final point's z coordinate is actually used though, so just update that. 83 */ 84 secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z); 85 } 86 87 /** Fill a table 'pre' with precomputed odd multiples of a. 88 * 89 * There are two versions of this function: 90 * - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its 91 * resulting point set to a single constant Z denominator, stores the X and Y 92 * coordinates as ge_storage points in pre, and stores the global Z in rz. 93 * It only operates on tables sized for WINDOW_A wnaf multiples. 94 * - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its 95 * resulting point set to actually affine points, and stores those in pre. 96 * It operates on tables of any size, but uses heap-allocated temporaries. 97 * 98 * To compute a*P + b*G, we compute a table for P using the first function, 99 * and for G using the second (which requires an inverse, but it only needs to 100 * happen once). 101 */ 102 static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) { 103 secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)]; 104 secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)]; 105 106 /* Compute the odd multiples in Jacobian form. */ 107 secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a); 108 /* Bring them to the same Z denominator. */ 109 secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr); 110 } 111 112 static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) { 113 secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n); 114 secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n); 115 secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n); 116 int i; 117 118 /* Compute the odd multiples in Jacobian form. */ 119 secp256k1_ecmult_odd_multiples_table(n, prej, zr, a); 120 /* Convert them in batch to affine coordinates. */ 121 secp256k1_ge_set_table_gej_var(prea, prej, zr, n); 122 /* Convert them to compact storage form. */ 123 for (i = 0; i < n; i++) { 124 secp256k1_ge_to_storage(&pre[i], &prea[i]); 125 } 126 127 free(prea); 128 free(prej); 129 free(zr); 130 } 131 132 /** The following two macro retrieves a particular odd multiple from a table 133 * of precomputed multiples. */ 134 #define ECMULT_TABLE_GET_GE(r,pre,n,w) do { \ 135 VERIFY_CHECK(((n) & 1) == 1); \ 136 VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ 137 VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ 138 if ((n) > 0) { \ 139 *(r) = (pre)[((n)-1)/2]; \ 140 } else { \ 141 secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \ 142 } \ 143 } while(0) 144 145 #define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \ 146 VERIFY_CHECK(((n) & 1) == 1); \ 147 VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ 148 VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ 149 if ((n) > 0) { \ 150 secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \ 151 } else { \ 152 secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \ 153 secp256k1_ge_neg((r), (r)); \ 154 } \ 155 } while(0) 156 157 static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) { 158 ctx->pre_g = NULL; 159 #ifdef USE_ENDOMORPHISM 160 ctx->pre_g_128 = NULL; 161 #endif 162 } 163 164 static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) { 165 secp256k1_gej gj; 166 167 if (ctx->pre_g != NULL) { 168 return; 169 } 170 171 /* get the generator */ 172 secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g); 173 174 ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G)); 175 176 /* precompute the tables with odd multiples */ 177 secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb); 178 179 #ifdef USE_ENDOMORPHISM 180 { 181 secp256k1_gej g_128j; 182 int i; 183 184 ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G)); 185 186 /* calculate 2^128*generator */ 187 g_128j = gj; 188 for (i = 0; i < 128; i++) { 189 secp256k1_gej_double_var(&g_128j, &g_128j, NULL); 190 } 191 secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb); 192 } 193 #endif 194 } 195 196 static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst, 197 const secp256k1_ecmult_context *src, const secp256k1_callback *cb) { 198 if (src->pre_g == NULL) { 199 dst->pre_g = NULL; 200 } else { 201 size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G); 202 dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size); 203 memcpy(dst->pre_g, src->pre_g, size); 204 } 205 #ifdef USE_ENDOMORPHISM 206 if (src->pre_g_128 == NULL) { 207 dst->pre_g_128 = NULL; 208 } else { 209 size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G); 210 dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size); 211 memcpy(dst->pre_g_128, src->pre_g_128, size); 212 } 213 #endif 214 } 215 216 static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) { 217 return ctx->pre_g != NULL; 218 } 219 220 static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) { 221 free(ctx->pre_g); 222 #ifdef USE_ENDOMORPHISM 223 free(ctx->pre_g_128); 224 #endif 225 secp256k1_ecmult_context_init(ctx); 226 } 227 228 /** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits), 229 * with the following guarantees: 230 * - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1) 231 * - two non-zero entries in wnaf are separated by at least w-1 zeroes. 232 * - the number of set values in wnaf is returned. This number is at most 256, and at most one more 233 * than the number of bits in the (absolute value) of the input. 234 */ 235 static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) { 236 secp256k1_scalar s = *a; 237 int last_set_bit = -1; 238 int bit = 0; 239 int sign = 1; 240 int carry = 0; 241 242 VERIFY_CHECK(wnaf != NULL); 243 VERIFY_CHECK(0 <= len && len <= 256); 244 VERIFY_CHECK(a != NULL); 245 VERIFY_CHECK(2 <= w && w <= 31); 246 247 memset(wnaf, 0, len * sizeof(wnaf[0])); 248 249 if (secp256k1_scalar_get_bits(&s, 255, 1)) { 250 secp256k1_scalar_negate(&s, &s); 251 sign = -1; 252 } 253 254 while (bit < len) { 255 int now; 256 int word; 257 if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) { 258 bit++; 259 continue; 260 } 261 262 now = w; 263 if (now > len - bit) { 264 now = len - bit; 265 } 266 267 word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry; 268 269 carry = (word >> (w-1)) & 1; 270 word -= carry << w; 271 272 wnaf[bit] = sign * word; 273 last_set_bit = bit; 274 275 bit += now; 276 } 277 #ifdef VERIFY 278 CHECK(carry == 0); 279 while (bit < 256) { 280 CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0); 281 } 282 #endif 283 return last_set_bit + 1; 284 } 285 286 static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) { 287 secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; 288 secp256k1_ge tmpa; 289 secp256k1_fe Z; 290 #ifdef USE_ENDOMORPHISM 291 secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; 292 secp256k1_scalar na_1, na_lam; 293 /* Splitted G factors. */ 294 secp256k1_scalar ng_1, ng_128; 295 int wnaf_na_1[130]; 296 int wnaf_na_lam[130]; 297 int bits_na_1; 298 int bits_na_lam; 299 int wnaf_ng_1[129]; 300 int bits_ng_1; 301 int wnaf_ng_128[129]; 302 int bits_ng_128; 303 #else 304 int wnaf_na[256]; 305 int bits_na; 306 int wnaf_ng[256]; 307 int bits_ng; 308 #endif 309 int i; 310 int bits; 311 312 #ifdef USE_ENDOMORPHISM 313 /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */ 314 secp256k1_scalar_split_lambda(&na_1, &na_lam, na); 315 316 /* build wnaf representation for na_1 and na_lam. */ 317 bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, 130, &na_1, WINDOW_A); 318 bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A); 319 VERIFY_CHECK(bits_na_1 <= 130); 320 VERIFY_CHECK(bits_na_lam <= 130); 321 bits = bits_na_1; 322 if (bits_na_lam > bits) { 323 bits = bits_na_lam; 324 } 325 #else 326 /* build wnaf representation for na. */ 327 bits_na = secp256k1_ecmult_wnaf(wnaf_na, 256, na, WINDOW_A); 328 bits = bits_na; 329 #endif 330 331 /* Calculate odd multiples of a. 332 * All multiples are brought to the same Z 'denominator', which is stored 333 * in Z. Due to secp256k1' isomorphism we can do all operations pretending 334 * that the Z coordinate was 1, use affine addition formulae, and correct 335 * the Z coordinate of the result once at the end. 336 * The exception is the precomputed G table points, which are actually 337 * affine. Compared to the base used for other points, they have a Z ratio 338 * of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same 339 * isomorphism to efficiently add with a known Z inverse. 340 */ 341 secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a); 342 343 #ifdef USE_ENDOMORPHISM 344 for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) { 345 secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]); 346 } 347 348 /* split ng into ng_1 and ng_128 (where gn = gn_1 + gn_128*2^128, and gn_1 and gn_128 are ~128 bit) */ 349 secp256k1_scalar_split_128(&ng_1, &ng_128, ng); 350 351 /* Build wnaf representation for ng_1 and ng_128 */ 352 bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G); 353 bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G); 354 if (bits_ng_1 > bits) { 355 bits = bits_ng_1; 356 } 357 if (bits_ng_128 > bits) { 358 bits = bits_ng_128; 359 } 360 #else 361 bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G); 362 if (bits_ng > bits) { 363 bits = bits_ng; 364 } 365 #endif 366 367 secp256k1_gej_set_infinity(r); 368 369 for (i = bits - 1; i >= 0; i--) { 370 int n; 371 secp256k1_gej_double_var(r, r, NULL); 372 #ifdef USE_ENDOMORPHISM 373 if (i < bits_na_1 && (n = wnaf_na_1[i])) { 374 ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); 375 secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); 376 } 377 if (i < bits_na_lam && (n = wnaf_na_lam[i])) { 378 ECMULT_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A); 379 secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); 380 } 381 if (i < bits_ng_1 && (n = wnaf_ng_1[i])) { 382 ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G); 383 secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); 384 } 385 if (i < bits_ng_128 && (n = wnaf_ng_128[i])) { 386 ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G); 387 secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); 388 } 389 #else 390 if (i < bits_na && (n = wnaf_na[i])) { 391 ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A); 392 secp256k1_gej_add_ge_var(r, r, &tmpa, NULL); 393 } 394 if (i < bits_ng && (n = wnaf_ng[i])) { 395 ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G); 396 secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z); 397 } 398 #endif 399 } 400 401 if (!r->infinity) { 402 secp256k1_fe_mul(&r->z, &r->z, &Z); 403 } 404 } 405 406 #endif