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+/**********************************************************************
+ * 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 "group.h"
+#include "scalar.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. */
+#ifdef USE_ENDOMORPHISM
+/** Two tables for window size 15: 1.375 MiB. */
+#define WINDOW_G 15
+#else
+/** One table for window size 16: 1.375 MiB. */
+#define WINDOW_G 16
+#endif
+
+/** 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 = checked_malloc(sizeof(secp256k1_gej_t) * 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);
+ free(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_var)
+#define ECMULT_TABLE_GET_GE(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_ge_neg_var)
+
+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 */
+#ifdef USE_ENDOMORPHISM
+ secp256k1_ge_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; /* odd multiples of 2^128*generator */
+#endif
+} 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*)checked_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);
+
+#ifdef USE_ENDOMORPHISM
+ /* 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);
+#endif
+
+ /* precompute the tables with odd multiples */
+ secp256k1_ecmult_table_precomp_ge_var(ret->pre_g, &gj, WINDOW_G);
+#ifdef USE_ENDOMORPHISM
+ secp256k1_ecmult_table_precomp_ge_var(ret->pre_g_128, &g_128j, WINDOW_G);
+#endif
+
+ /* 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 number of set values in wnaf is returned. This number is at most 256, and at most one more
+ * - than the number of bits in the (absolute value) of the input.
+ */
+static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_scalar_t *a, int w) {
+ secp256k1_scalar_t s = *a;
+
+ int sign = 1;
+ if (secp256k1_scalar_get_bits(&s, 255, 1)) {
+ secp256k1_scalar_negate(&s, &s);
+ sign = -1;
+ }
+
+ int set_bits = 0;
+ int bit = 0;
+ while (bit < 256) {
+ if (secp256k1_scalar_get_bits(&s, bit, 1) == 0) {
+ bit++;
+ continue;
+ }
+ while (set_bits < bit) {
+ wnaf[set_bits++] = 0;
+ }
+ int now = w;
+ if (bit + now > 256) {
+ now = 256 - bit;
+ }
+ int word = secp256k1_scalar_get_bits_var(&s, bit, now);
+ if (word & (1 << (w-1))) {
+ secp256k1_scalar_add_bit(&s, bit + w);
+ wnaf[set_bits++] = sign * (word - (1 << w));
+ } else {
+ wnaf[set_bits++] = sign * word;
+ }
+ bit += now;
+ }
+ return set_bits;
+}
+
+static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng) {
+ const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
+
+#ifdef USE_ENDOMORPHISM
+ secp256k1_scalar_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_scalar_split_lambda_var(&na_1, &na_lam, na);
+
+ /* build wnaf representation for na_1 and na_lam. */
+ int wnaf_na_1[130]; int bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A);
+ int wnaf_na_lam[130]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
+ VERIFY_CHECK(bits_na_1 <= 130);
+ VERIFY_CHECK(bits_na_lam <= 130);
+ int bits = bits_na_1;
+ if (bits_na_lam > bits) bits = bits_na_lam;
+#else
+ /* build wnaf representation for na. */
+ int wnaf_na[256]; 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]);
+
+ /* Splitted G factors. */
+ secp256k1_scalar_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_scalar_split_128(&ng_1, &ng_128, ng);
+
+ /* 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;
+#else
+ int wnaf_ng[257]; int bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, ng, WINDOW_G);
+ if (bits_ng > bits) bits = bits_ng;
+#endif
+
+ 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);
+ }
+ 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);
+ }
+#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);
+ }
+ if (i < bits_ng && (n = wnaf_ng[i])) {
+ ECMULT_TABLE_GET_GE(&tmpa, c->pre_g, n, WINDOW_G);
+ secp256k1_gej_add_ge_var(r, r, &tmpa);
+ }
+#endif
+ }
+}
+
+#endif