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259 lines
9.5 KiB
259 lines
9.5 KiB
// Copyright (c) 2013 Pieter Wuille
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// Distributed under the MIT/X11 software license, see the accompanying
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// file COPYING or http://www.opensource.org/licenses/mit-license.php.
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#ifndef _SECP256K1_ECMULT_IMPL_H_
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#define _SECP256K1_ECMULT_IMPL_H_
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#include "../num.h"
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#include "../group.h"
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#include "../ecmult.h"
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// optimal for 128-bit and 256-bit exponents.
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#define WINDOW_A 5
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// larger numbers may result in slightly better performance, at the cost of
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// exponentially larger precomputed tables. WINDOW_G == 14 results in 640 KiB.
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#define WINDOW_G 14
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/** Fill a table 'pre' with precomputed odd multiples of a. W determines the size of the table.
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* pre will contains the values [1*a,3*a,5*a,...,(2^(w-1)-1)*a], so it needs place for
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* 2^(w-2) entries.
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*
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* There are two versions of this function:
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* - secp256k1_ecmult_precomp_wnaf_gej, which operates on group elements in jacobian notation,
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* fast to precompute, but slower to use in later additions.
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* - secp256k1_ecmult_precomp_wnaf_ge, which operates on group elements in affine notations,
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* (much) slower to precompute, but a bit faster to use in later additions.
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* To compute a*P + b*G, we use the jacobian version for P, and the affine version for G, as
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* G is constant, so it only needs to be done once in advance.
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*/
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void static secp256k1_ecmult_table_precomp_gej(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
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pre[0] = *a;
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secp256k1_gej_t d; secp256k1_gej_double(&d, &pre[0]);
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for (int i=1; i<(1 << (w-2)); i++)
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secp256k1_gej_add(&pre[i], &d, &pre[i-1]);
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}
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void static secp256k1_ecmult_table_precomp_ge(secp256k1_ge_t *pre, const secp256k1_ge_t *a, int w) {
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pre[0] = *a;
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secp256k1_gej_t x; secp256k1_gej_set_ge(&x, a);
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secp256k1_gej_t d; secp256k1_gej_double(&d, &x);
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for (int i=1; i<(1 << (w-2)); i++) {
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secp256k1_gej_add_ge(&x, &d, &pre[i-1]);
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secp256k1_ge_set_gej(&pre[i], &x);
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}
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}
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/** The number of entries a table with precomputed multiples needs to have. */
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#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
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/** The following two macro retrieves a particular odd multiple from a table
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* of precomputed multiples. */
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#define ECMULT_TABLE_GET(r,pre,n,w,neg) do { \
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assert(((n) & 1) == 1); \
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assert((n) >= -((1 << ((w)-1)) - 1)); \
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assert((n) <= ((1 << ((w)-1)) - 1)); \
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if ((n) > 0) \
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*(r) = (pre)[((n)-1)/2]; \
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else \
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(neg)((r), &(pre)[(-(n)-1)/2]); \
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} while(0)
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#define ECMULT_TABLE_GET_GEJ(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_gej_neg)
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#define ECMULT_TABLE_GET_GE(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_ge_neg)
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typedef struct {
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secp256k1_ge_t pre_g[ECMULT_TABLE_SIZE(WINDOW_G)]; // odd multiples of the generator
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secp256k1_ge_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; // odd multiples of 2^128*generator
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secp256k1_ge_t prec[64][16]; // prec[j][i] = 16^j * (i+1) * G
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secp256k1_ge_t fin; // -(sum(prec[j][0], j=0..63))
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} secp256k1_ecmult_consts_t;
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static const secp256k1_ecmult_consts_t *secp256k1_ecmult_consts = NULL;
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static void secp256k1_ecmult_start(void) {
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if (secp256k1_ecmult_consts != NULL)
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return;
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secp256k1_ecmult_consts_t *ret = (secp256k1_ecmult_consts_t*)malloc(sizeof(secp256k1_ecmult_consts_t));
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secp256k1_ecmult_consts = ret;
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// get the generator
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const secp256k1_ge_t *g = &secp256k1_ge_consts->g;
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// calculate 2^128*generator
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secp256k1_gej_t g_128j; secp256k1_gej_set_ge(&g_128j, g);
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for (int i=0; i<128; i++)
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secp256k1_gej_double(&g_128j, &g_128j);
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secp256k1_ge_t g_128; secp256k1_ge_set_gej(&g_128, &g_128j);
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// precompute the tables with odd multiples
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secp256k1_ecmult_table_precomp_ge(ret->pre_g, g, WINDOW_G);
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secp256k1_ecmult_table_precomp_ge(ret->pre_g_128, &g_128, WINDOW_G);
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// compute prec and fin
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secp256k1_gej_t gg; secp256k1_gej_set_ge(&gg, g);
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secp256k1_ge_t ad = *g;
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secp256k1_gej_t fn; secp256k1_gej_set_infinity(&fn);
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for (int j=0; j<64; j++) {
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secp256k1_ge_set_gej(&ret->prec[j][0], &gg);
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secp256k1_gej_add(&fn, &fn, &gg);
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for (int i=1; i<16; i++) {
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secp256k1_gej_add_ge(&gg, &gg, &ad);
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secp256k1_ge_set_gej(&ret->prec[j][i], &gg);
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}
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ad = ret->prec[j][15];
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}
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secp256k1_ge_set_gej(&ret->fin, &fn);
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secp256k1_ge_neg(&ret->fin, &ret->fin);
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}
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static void secp256k1_ecmult_stop(void) {
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if (secp256k1_ecmult_consts == NULL)
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return;
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secp256k1_ecmult_consts_t *c = (secp256k1_ecmult_consts_t*)secp256k1_ecmult_consts;
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free(c);
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secp256k1_ecmult_consts = NULL;
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}
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/** Convert a number to WNAF notation. The number becomes represented by sum(2^i * wnaf[i], i=0..bits),
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* with the following guarantees:
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* - each wnaf[i] is either 0, or an odd integer between -(1<<(w-1) - 1) and (1<<(w-1) - 1)
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* - two non-zero entries in wnaf are separated by at least w-1 zeroes.
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* - the index of the highest non-zero entry in wnaf (=return value-1) is at most bits, where
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* bits is the number of bits necessary to represent the absolute value of the input.
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*/
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static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_num_t *a, int w) {
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int ret = 0;
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int zeroes = 0;
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secp256k1_num_t x;
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secp256k1_num_init(&x);
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secp256k1_num_copy(&x, a);
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int sign = 1;
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if (secp256k1_num_is_neg(&x)) {
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sign = -1;
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secp256k1_num_negate(&x);
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}
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while (!secp256k1_num_is_zero(&x)) {
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while (!secp256k1_num_is_odd(&x)) {
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zeroes++;
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secp256k1_num_shift(&x, 1);
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}
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int word = secp256k1_num_shift(&x, w);
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while (zeroes) {
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wnaf[ret++] = 0;
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zeroes--;
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}
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if (word & (1 << (w-1))) {
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secp256k1_num_inc(&x);
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wnaf[ret++] = sign * (word - (1 << w));
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} else {
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wnaf[ret++] = sign * word;
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}
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zeroes = w-1;
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}
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secp256k1_num_free(&x);
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return ret;
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}
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void static secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_num_t *gn) {
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secp256k1_num_t n;
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secp256k1_num_init(&n);
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secp256k1_num_copy(&n, gn);
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const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
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secp256k1_gej_set_ge(r, &c->prec[0][secp256k1_num_shift(&n, 4)]);
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for (int j=1; j<64; j++)
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secp256k1_gej_add_ge(r, r, &c->prec[j][secp256k1_num_shift(&n, 4)]);
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secp256k1_num_free(&n);
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secp256k1_gej_add_ge(r, r, &c->fin);
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}
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void static secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_num_t *na, const secp256k1_num_t *ng) {
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const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
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#ifdef USE_ENDOMORPHISM
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secp256k1_num_t na_1, na_lam;
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secp256k1_num_init(&na_1);
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secp256k1_num_init(&na_lam);
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// split na into na_1 and na_lam (where na = na_1 + na_lam*lambda, and na_1 and na_lam are ~128 bit)
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secp256k1_gej_split_exp(&na_1, &na_lam, na);
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// build wnaf representation for na_1 and na_lam.
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int wnaf_na_1[129]; int bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A);
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int wnaf_na_lam[129]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
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int bits = bits_na_1;
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if (bits_na_lam > bits) bits = bits_na_lam;
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// calculate a_lam = a*lambda
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secp256k1_gej_t a_lam; secp256k1_gej_mul_lambda(&a_lam, a);
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// calculate odd multiples of a_lam
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secp256k1_gej_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
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secp256k1_ecmult_table_precomp_gej(pre_a_lam, &a_lam, WINDOW_A);
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#else
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// build wnaf representation for na.
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int wnaf_na[257]; int bits_na = secp256k1_ecmult_wnaf(wnaf_na, na, WINDOW_A);
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int bits = bits_na;
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#endif
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// calculate odd multiples of a
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secp256k1_gej_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
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secp256k1_ecmult_table_precomp_gej(pre_a, a, WINDOW_A);
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// Splitted G factors.
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secp256k1_num_t ng_1, ng_128;
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secp256k1_num_init(&ng_1);
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secp256k1_num_init(&ng_128);
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// 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)
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secp256k1_num_split(&ng_1, &ng_128, ng, 128);
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// Build wnaf representation for ng_1 and ng_128
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int wnaf_ng_1[129]; int bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, &ng_1, WINDOW_G);
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int wnaf_ng_128[129]; int bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, &ng_128, WINDOW_G);
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if (bits_ng_1 > bits) bits = bits_ng_1;
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if (bits_ng_128 > bits) bits = bits_ng_128;
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secp256k1_gej_set_infinity(r);
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secp256k1_gej_t tmpj;
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secp256k1_ge_t tmpa;
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for (int i=bits-1; i>=0; i--) {
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secp256k1_gej_double(r, r);
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int n;
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#ifdef USE_ENDOMORPHISM
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if (i < bits_na_1 && (n = wnaf_na_1[i])) {
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ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
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secp256k1_gej_add(r, r, &tmpj);
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}
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if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
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ECMULT_TABLE_GET_GEJ(&tmpj, pre_a_lam, n, WINDOW_A);
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secp256k1_gej_add(r, r, &tmpj);
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}
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#else
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if (i < bits_na && (n = wnaf_na[i])) {
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ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
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secp256k1_gej_add(r, r, &tmpj);
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}
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#endif
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if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
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ECMULT_TABLE_GET_GE(&tmpa, c->pre_g, n, WINDOW_G);
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secp256k1_gej_add_ge(r, r, &tmpa);
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}
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if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
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ECMULT_TABLE_GET_GE(&tmpa, c->pre_g_128, n, WINDOW_G);
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secp256k1_gej_add_ge(r, r, &tmpa);
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}
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}
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#ifdef USE_ENDOMORPHISM
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secp256k1_num_free(&na_1);
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secp256k1_num_free(&na_lam);
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#endif
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secp256k1_num_free(&ng_1);
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secp256k1_num_free(&ng_128);
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}
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#endif
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