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Diffstat (limited to 'src/ecmult_impl.h')
| -rw-r--r-- | src/ecmult_impl.h | 222 |
1 files changed, 222 insertions, 0 deletions
diff --git a/src/ecmult_impl.h b/src/ecmult_impl.h new file mode 100644 index 0000000000..508902564e --- /dev/null +++ b/src/ecmult_impl.h @@ -0,0 +1,222 @@ +/********************************************************************** + * Copyright (c) 2013, 2014 Pieter Wuille * + * Distributed under the MIT software license, see the accompanying * + * file COPYING or http://www.opensource.org/licenses/mit-license.php.* + **********************************************************************/ + +#ifndef _SECP256K1_ECMULT_IMPL_H_ +#define _SECP256K1_ECMULT_IMPL_H_ + +#include "num.h" +#include "group.h" +#include "ecmult.h" + +/* optimal for 128-bit and 256-bit exponents. */ +#define WINDOW_A 5 + +/** larger numbers may result in slightly better performance, at the cost of + exponentially larger precomputed tables. WINDOW_G == 14 results in 640 KiB. */ +#define WINDOW_G 14 + +/** Fill a table 'pre' with precomputed odd multiples of a. W determines the size of the table. + * pre will contains the values [1*a,3*a,5*a,...,(2^(w-1)-1)*a], so it needs place for + * 2^(w-2) entries. + * + * There are two versions of this function: + * - secp256k1_ecmult_precomp_wnaf_gej, which operates on group elements in jacobian notation, + * fast to precompute, but slower to use in later additions. + * - secp256k1_ecmult_precomp_wnaf_ge, which operates on group elements in affine notations, + * (much) slower to precompute, but a bit faster to use in later additions. + * To compute a*P + b*G, we use the jacobian version for P, and the affine version for G, as + * G is constant, so it only needs to be done once in advance. + */ +static void secp256k1_ecmult_table_precomp_gej_var(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) { + pre[0] = *a; + secp256k1_gej_t d; secp256k1_gej_double_var(&d, &pre[0]); + for (int i=1; i<(1 << (w-2)); i++) + secp256k1_gej_add_var(&pre[i], &d, &pre[i-1]); +} + +static void secp256k1_ecmult_table_precomp_ge_var(secp256k1_ge_t *pre, const secp256k1_gej_t *a, int w) { + const int table_size = 1 << (w-2); + secp256k1_gej_t prej[table_size]; + prej[0] = *a; + secp256k1_gej_t d; secp256k1_gej_double_var(&d, a); + for (int i=1; i<table_size; i++) { + secp256k1_gej_add_var(&prej[i], &d, &prej[i-1]); + } + secp256k1_ge_set_all_gej_var(table_size, pre, prej); +} + +/** The number of entries a table with precomputed multiples needs to have. */ +#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2)) + +/** The following two macro retrieves a particular odd multiple from a table + * of precomputed multiples. */ +#define ECMULT_TABLE_GET(r,pre,n,w,neg) do { \ + VERIFY_CHECK(((n) & 1) == 1); \ + VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \ + VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \ + if ((n) > 0) \ + *(r) = (pre)[((n)-1)/2]; \ + else \ + (neg)((r), &(pre)[(-(n)-1)/2]); \ +} while(0) + +#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_gej_neg) +#define ECMULT_TABLE_GET_GE(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_ge_neg) + +typedef struct { + /* For accelerating the computation of a*P + b*G: */ + secp256k1_ge_t pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of the generator */ + secp256k1_ge_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of 2^128*generator */ +} secp256k1_ecmult_consts_t; + +static const secp256k1_ecmult_consts_t *secp256k1_ecmult_consts = NULL; + +static void secp256k1_ecmult_start(void) { + if (secp256k1_ecmult_consts != NULL) + return; + + /* Allocate the precomputation table. */ + secp256k1_ecmult_consts_t *ret = (secp256k1_ecmult_consts_t*)malloc(sizeof(secp256k1_ecmult_consts_t)); + + /* get the generator */ + const secp256k1_ge_t *g = &secp256k1_ge_consts->g; + secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, g); + + /* calculate 2^128*generator */ + secp256k1_gej_t g_128j = gj; + for (int i=0; i<128; i++) + secp256k1_gej_double_var(&g_128j, &g_128j); + + /* precompute the tables with odd multiples */ + secp256k1_ecmult_table_precomp_ge_var(ret->pre_g, &gj, WINDOW_G); + secp256k1_ecmult_table_precomp_ge_var(ret->pre_g_128, &g_128j, WINDOW_G); + + /* Set the global pointer to the precomputation table. */ + secp256k1_ecmult_consts = ret; +} + +static void secp256k1_ecmult_stop(void) { + if (secp256k1_ecmult_consts == NULL) + return; + + secp256k1_ecmult_consts_t *c = (secp256k1_ecmult_consts_t*)secp256k1_ecmult_consts; + secp256k1_ecmult_consts = NULL; + free(c); +} + +/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits), + * with the following guarantees: + * - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1) + * - two non-zero entries in wnaf are separated by at least w-1 zeroes. + * - the index of the highest non-zero entry in wnaf (=return value-1) is at most bits, where + * bits is the number of bits necessary to represent the absolute value of the input. + */ +static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_num_t *a, int w) { + int ret = 0; + int zeroes = 0; + secp256k1_num_t x; + secp256k1_num_copy(&x, a); + int sign = 1; + if (secp256k1_num_is_neg(&x)) { + sign = -1; + secp256k1_num_negate(&x); + } + while (!secp256k1_num_is_zero(&x)) { + while (!secp256k1_num_is_odd(&x)) { + zeroes++; + secp256k1_num_shift(&x, 1); + } + int word = secp256k1_num_shift(&x, w); + while (zeroes) { + wnaf[ret++] = 0; + zeroes--; + } + if (word & (1 << (w-1))) { + secp256k1_num_inc(&x); + wnaf[ret++] = sign * (word - (1 << w)); + } else { + wnaf[ret++] = sign * word; + } + zeroes = w-1; + } + return ret; +} + +static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_num_t *na, const secp256k1_num_t *ng) { + const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts; + +#ifdef USE_ENDOMORPHISM + secp256k1_num_t na_1, na_lam; + /* split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit) */ + secp256k1_gej_split_exp_var(&na_1, &na_lam, na); + + /* build wnaf representation for na_1 and na_lam. */ + int wnaf_na_1[129]; int bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A); + int wnaf_na_lam[129]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A); + int bits = bits_na_1; + if (bits_na_lam > bits) bits = bits_na_lam; +#else + /* build wnaf representation for na. */ + int wnaf_na[257]; int bits_na = secp256k1_ecmult_wnaf(wnaf_na, na, WINDOW_A); + int bits = bits_na; +#endif + + /* calculate odd multiples of a */ + secp256k1_gej_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)]; + secp256k1_ecmult_table_precomp_gej_var(pre_a, a, WINDOW_A); + +#ifdef USE_ENDOMORPHISM + secp256k1_gej_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)]; + for (int i=0; i<ECMULT_TABLE_SIZE(WINDOW_A); i++) + secp256k1_gej_mul_lambda(&pre_a_lam[i], &pre_a[i]); +#endif + + /* Splitted G factors. */ + secp256k1_num_t ng_1, ng_128; + + /* 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) */ + secp256k1_num_split(&ng_1, &ng_128, ng, 128); + + /* Build wnaf representation for ng_1 and ng_128 */ + int wnaf_ng_1[129]; int bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, &ng_1, WINDOW_G); + int wnaf_ng_128[129]; int bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G); + if (bits_ng_1 > bits) bits = bits_ng_1; + if (bits_ng_128 > bits) bits = bits_ng_128; + + secp256k1_gej_set_infinity(r); + secp256k1_gej_t tmpj; + secp256k1_ge_t tmpa; + + for (int i=bits-1; i>=0; i--) { + secp256k1_gej_double_var(r, r); + int n; +#ifdef USE_ENDOMORPHISM + if (i < bits_na_1 && (n = wnaf_na_1[i])) { + ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A); + secp256k1_gej_add_var(r, r, &tmpj); + } + if (i < bits_na_lam && (n = wnaf_na_lam[i])) { + ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_lam, n, WINDOW_A); + secp256k1_gej_add_var(r, r, &tmpj); + } +#else + if (i < bits_na && (n = wnaf_na[i])) { + ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A); + secp256k1_gej_add_var(r, r, &tmpj); + } +#endif + if (i < bits_ng_1 && (n = wnaf_ng_1[i])) { + ECMULT_TABLE_GET_GE(&tmpa, c->pre_g, n, WINDOW_G); + secp256k1_gej_add_ge_var(r, r, &tmpa); + } + if (i < bits_ng_128 && (n = wnaf_ng_128[i])) { + ECMULT_TABLE_GET_GE(&tmpa, c->pre_g_128, n, WINDOW_G); + secp256k1_gej_add_ge_var(r, r, &tmpa); + } + } +} + +#endif |