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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_GEN_IMPL_H_
#define _SECP256K1_ECMULT_GEN_IMPL_H_
#include "scalar.h"
#include "group.h"
#include "ecmult_gen.h"
typedef struct {
/* For accelerating the computation of a*G:
* To harden against timing attacks, use the following mechanism:
* * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
* * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
* * U_i = U * 2^i (for i=0..62)
* * U_i = U * (1-2^63) (for i=63)
* where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
* For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
* precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
* None of the resulting prec group elements have a known scalar, and neither do any of
* the intermediate sums while computing a*G.
*/
secp256k1_ge_storage_t prec[64][16]; /* prec[j][i] = 16^j * i * G + U_i */
} secp256k1_ecmult_gen_consts_t;
static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_consts = NULL;
static void secp256k1_ecmult_gen_start(void) {
secp256k1_ge_t prec[1024];
secp256k1_gej_t gj;
secp256k1_gej_t nums_gej;
secp256k1_ecmult_gen_consts_t *ret;
int i, j;
if (secp256k1_ecmult_gen_consts != NULL)
return;
/* Allocate the precomputation table. */
ret = (secp256k1_ecmult_gen_consts_t*)checked_malloc(sizeof(secp256k1_ecmult_gen_consts_t));
/* get the generator */
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
/* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
{
static const unsigned char nums_b32[33] = "The scalar for this x is unknown";
secp256k1_fe_t nums_x;
secp256k1_ge_t nums_ge;
VERIFY_CHECK(secp256k1_fe_set_b32(&nums_x, nums_b32));
VERIFY_CHECK(secp256k1_ge_set_xo_var(&nums_ge, &nums_x, 0));
secp256k1_gej_set_ge(&nums_gej, &nums_ge);
/* Add G to make the bits in x uniformly distributed. */
secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g);
}
/* compute prec. */
{
secp256k1_gej_t precj[1024]; /* Jacobian versions of prec. */
secp256k1_gej_t gbase;
secp256k1_gej_t numsbase;
gbase = gj; /* 16^j * G */
numsbase = nums_gej; /* 2^j * nums. */
for (j = 0; j < 64; j++) {
/* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
precj[j*16] = numsbase;
for (i = 1; i < 16; i++) {
secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
}
/* Multiply gbase by 16. */
for (i = 0; i < 4; i++) {
secp256k1_gej_double_var(&gbase, &gbase);
}
/* Multiply numbase by 2. */
secp256k1_gej_double_var(&numsbase, &numsbase);
if (j == 62) {
/* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
secp256k1_gej_neg(&numsbase, &numsbase);
secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej);
}
}
secp256k1_ge_set_all_gej_var(1024, prec, precj);
}
for (j = 0; j < 64; j++) {
for (i = 0; i < 16; i++) {
secp256k1_ge_to_storage(&ret->prec[j][i], &prec[j*16 + i]);
}
}
/* Set the global pointer to the precomputation table. */
secp256k1_ecmult_gen_consts = ret;
}
static void secp256k1_ecmult_gen_stop(void) {
secp256k1_ecmult_gen_consts_t *c;
if (secp256k1_ecmult_gen_consts == NULL)
return;
c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts;
secp256k1_ecmult_gen_consts = NULL;
free(c);
}
static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *gn) {
const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts;
secp256k1_ge_t add;
secp256k1_ge_storage_t adds;
int bits;
int i, j;
secp256k1_gej_set_infinity(r);
add.infinity = 0;
for (j = 0; j < 64; j++) {
bits = secp256k1_scalar_get_bits(gn, j * 4, 4);
for (i = 0; i < 16; i++) {
secp256k1_ge_storage_cmov(&adds, &c->prec[j][i], i == bits);
}
secp256k1_ge_from_storage(&add, &adds);
secp256k1_gej_add_ge(r, r, &add);
}
bits = 0;
secp256k1_ge_clear(&add);
}
#endif
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