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389 lines
13 KiB
389 lines
13 KiB
/**********************************************************************
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* Copyright (c) 2013, 2014 Pieter Wuille *
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* Distributed under the MIT software license, see the accompanying *
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* file COPYING or http://www.opensource.org/licenses/mit-license.php.*
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**********************************************************************/
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#ifndef _SECP256K1_ECMULT_IMPL_H_
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#define _SECP256K1_ECMULT_IMPL_H_
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#include "group.h"
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#include "scalar.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. */
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#ifdef USE_ENDOMORPHISM
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/** Two tables for window size 15: 1.375 MiB. */
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#define WINDOW_G 15
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#else
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/** One table for window size 16: 1.375 MiB. */
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#define WINDOW_G 16
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#endif
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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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/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
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* the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
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* contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
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* Prej's Z values are undefined, except for the last value.
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*/
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static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej_t *prej, secp256k1_fe_t *zr, const secp256k1_gej_t *a) {
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secp256k1_gej_t d;
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secp256k1_ge_t a_ge, d_ge;
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int i;
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VERIFY_CHECK(!a->infinity);
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secp256k1_gej_double_var(&d, a, NULL);
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/*
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* Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
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* of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
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*/
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d_ge.x = d.x;
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d_ge.y = d.y;
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d_ge.infinity = 0;
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secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
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prej[0].x = a_ge.x;
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prej[0].y = a_ge.y;
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prej[0].z = a->z;
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prej[0].infinity = 0;
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zr[0] = d.z;
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for (i = 1; i < n; i++) {
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secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
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}
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/*
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* Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
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* the final point's z coordinate is actually used though, so just update that.
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*/
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secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
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}
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/** Fill a table 'pre' with precomputed odd multiples of a.
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*
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* There are two versions of this function:
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* - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
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* resulting point set to a single constant Z denominator, stores the X and Y
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* coordinates as ge_storage points in pre, and stores the global Z in rz.
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* It only operates on tables sized for WINDOW_A wnaf multiples.
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* - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
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* resulting point set to actually affine points, and stores those in pre.
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* It operates on tables of any size, but uses heap-allocated temporaries.
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*
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* To compute a*P + b*G, we compute a table for P using the first function,
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* and for G using the second (which requires an inverse, but it only needs to
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* happen once).
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*/
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static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge_t *pre, secp256k1_fe_t *globalz, const secp256k1_gej_t *a) {
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secp256k1_gej_t prej[ECMULT_TABLE_SIZE(WINDOW_A)];
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secp256k1_fe_t zr[ECMULT_TABLE_SIZE(WINDOW_A)];
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/* Compute the odd multiples in Jacobian form. */
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secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
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/* Bring them to the same Z denominator. */
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secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
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}
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static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage_t *pre, const secp256k1_gej_t *a, const callback_t *cb) {
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secp256k1_gej_t *prej = (secp256k1_gej_t*)checked_malloc(cb, sizeof(secp256k1_gej_t) * n);
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secp256k1_ge_t *prea = (secp256k1_ge_t*)checked_malloc(cb, sizeof(secp256k1_ge_t) * n);
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secp256k1_fe_t *zr = (secp256k1_fe_t*)checked_malloc(cb, sizeof(secp256k1_fe_t) * n);
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int i;
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/* Compute the odd multiples in Jacobian form. */
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secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
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/* Convert them in batch to affine coordinates. */
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secp256k1_ge_set_table_gej_var(n, prea, prej, zr);
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/* Convert them to compact storage form. */
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for (i = 0; i < n; i++) {
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secp256k1_ge_to_storage(&pre[i], &prea[i]);
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}
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free(prea);
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free(prej);
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free(zr);
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}
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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_GE(r,pre,n,w) do { \
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VERIFY_CHECK(((n) & 1) == 1); \
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VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
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VERIFY_CHECK((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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secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \
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} \
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} while(0)
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#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
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VERIFY_CHECK(((n) & 1) == 1); \
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VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
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VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
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if ((n) > 0) { \
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secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
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} else { \
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secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
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secp256k1_ge_neg((r), (r)); \
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} \
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} while(0)
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static void secp256k1_ecmult_context_init(secp256k1_ecmult_context_t *ctx) {
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ctx->pre_g = NULL;
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#ifdef USE_ENDOMORPHISM
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ctx->pre_g_128 = NULL;
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#endif
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}
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static void secp256k1_ecmult_context_build(secp256k1_ecmult_context_t *ctx, const callback_t *cb) {
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secp256k1_gej_t gj;
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if (ctx->pre_g != NULL) {
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return;
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}
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/* get the generator */
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secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
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ctx->pre_g = (secp256k1_ge_storage_t (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
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/* precompute the tables with odd multiples */
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secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
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#ifdef USE_ENDOMORPHISM
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{
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secp256k1_gej_t g_128j;
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int i;
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ctx->pre_g_128 = (secp256k1_ge_storage_t (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
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/* calculate 2^128*generator */
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g_128j = gj;
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for (i = 0; i < 128; i++) {
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secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
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}
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secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
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}
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#endif
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}
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static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context_t *dst,
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const secp256k1_ecmult_context_t *src, const callback_t *cb) {
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if (src->pre_g == NULL) {
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dst->pre_g = NULL;
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} else {
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size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
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dst->pre_g = (secp256k1_ge_storage_t (*)[])checked_malloc(cb, size);
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memcpy(dst->pre_g, src->pre_g, size);
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}
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#ifdef USE_ENDOMORPHISM
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if (src->pre_g_128 == NULL) {
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dst->pre_g_128 = NULL;
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} else {
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size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
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dst->pre_g_128 = (secp256k1_ge_storage_t (*)[])checked_malloc(cb, size);
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memcpy(dst->pre_g_128, src->pre_g_128, size);
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}
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#endif
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}
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static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context_t *ctx) {
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return ctx->pre_g != NULL;
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}
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static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context_t *ctx) {
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free(ctx->pre_g);
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#ifdef USE_ENDOMORPHISM
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free(ctx->pre_g_128);
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#endif
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secp256k1_ecmult_context_init(ctx);
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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 number of set values in wnaf is returned. This number is at most 256, and at most one more
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* than the number of bits in the (absolute value) of the input.
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*/
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static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar_t *a, int w) {
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secp256k1_scalar_t s = *a;
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int last_set_bit = -1;
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int bit = 0;
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int sign = 1;
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int carry = 0;
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VERIFY_CHECK(wnaf != NULL);
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VERIFY_CHECK(0 <= len && len <= 256);
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VERIFY_CHECK(a != NULL);
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VERIFY_CHECK(2 <= w && w <= 31);
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memset(wnaf, 0, len * sizeof(wnaf[0]));
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if (secp256k1_scalar_get_bits(&s, 255, 1)) {
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secp256k1_scalar_negate(&s, &s);
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sign = -1;
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}
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while (bit < len) {
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int now;
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int word;
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if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
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bit++;
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continue;
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}
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now = w;
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if (now > len - bit) {
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now = len - bit;
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}
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word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
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carry = (word >> (w-1)) & 1;
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word -= carry << w;
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wnaf[bit] = sign * word;
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last_set_bit = bit;
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bit += now;
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}
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#ifdef VERIFY
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CHECK(carry == 0);
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while (bit < 256) {
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CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
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}
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#endif
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return last_set_bit + 1;
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}
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static void secp256k1_ecmult(const secp256k1_ecmult_context_t *ctx, secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_scalar_t *na, const secp256k1_scalar_t *ng) {
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secp256k1_ge_t pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
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secp256k1_ge_t tmpa;
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secp256k1_fe_t Z;
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#ifdef USE_ENDOMORPHISM
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secp256k1_ge_t pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
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secp256k1_scalar_t na_1, na_lam;
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/* Splitted G factors. */
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secp256k1_scalar_t ng_1, ng_128;
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int wnaf_na_1[130];
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int wnaf_na_lam[130];
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int bits_na_1;
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int bits_na_lam;
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int wnaf_ng_1[129];
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int bits_ng_1;
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int wnaf_ng_128[129];
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int bits_ng_128;
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#else
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int wnaf_na[256];
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int bits_na;
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int wnaf_ng[256];
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int bits_ng;
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#endif
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int i;
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int bits;
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#ifdef USE_ENDOMORPHISM
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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_scalar_split_lambda(&na_1, &na_lam, na);
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/* build wnaf representation for na_1 and na_lam. */
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bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, 130, &na_1, WINDOW_A);
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bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A);
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VERIFY_CHECK(bits_na_1 <= 130);
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VERIFY_CHECK(bits_na_lam <= 130);
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bits = bits_na_1;
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if (bits_na_lam > bits) {
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bits = bits_na_lam;
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}
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#else
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/* build wnaf representation for na. */
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bits_na = secp256k1_ecmult_wnaf(wnaf_na, 256, na, WINDOW_A);
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bits = bits_na;
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#endif
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/* Calculate odd multiples of a.
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* All multiples are brought to the same Z 'denominator', which is stored
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* in Z. Due to secp256k1' isomorphism we can do all operations pretending
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* that the Z coordinate was 1, use affine addition formulae, and correct
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* the Z coordinate of the result once at the end.
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* The exception is the precomputed G table points, which are actually
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* affine. Compared to the base used for other points, they have a Z ratio
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* of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
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* isomorphism to efficiently add with a known Z inverse.
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*/
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secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a);
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#ifdef USE_ENDOMORPHISM
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for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
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secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
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}
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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_scalar_split_128(&ng_1, &ng_128, ng);
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/* Build wnaf representation for ng_1 and ng_128 */
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bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G);
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bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
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if (bits_ng_1 > bits) {
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bits = bits_ng_1;
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}
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if (bits_ng_128 > bits) {
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bits = bits_ng_128;
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}
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#else
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bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G);
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if (bits_ng > bits) {
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bits = bits_ng;
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}
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#endif
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secp256k1_gej_set_infinity(r);
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for (i = bits - 1; i >= 0; i--) {
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int n;
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secp256k1_gej_double_var(r, r, NULL);
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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_GE(&tmpa, pre_a, n, WINDOW_A);
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secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
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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_GE(&tmpa, pre_a_lam, n, WINDOW_A);
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secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
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}
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if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
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ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
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secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
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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_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
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secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
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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_GE(&tmpa, pre_a, n, WINDOW_A);
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secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
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}
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if (i < bits_ng && (n = wnaf_ng[i])) {
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ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
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secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
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}
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#endif
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}
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if (!r->infinity) {
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secp256k1_fe_mul(&r->z, &r->z, &Z);
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}
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}
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#endif
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