119 lines
4.8 KiB
C
119 lines
4.8 KiB
C
/**********************************************************************
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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_GEN_IMPL_H_
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#define _SECP256K1_ECMULT_GEN_IMPL_H_
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#include "scalar.h"
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#include "group.h"
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#include "ecmult_gen.h"
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typedef struct {
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/* For accelerating the computation of a*G:
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* To harden against timing attacks, use the following mechanism:
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* * Break up the multiplicand into groups of 4 bits, called n_0, n_1, n_2, ..., n_63.
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* * Compute sum(n_i * 16^i * G + U_i, i=0..63), where:
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* * U_i = U * 2^i (for i=0..62)
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* * U_i = U * (1-2^63) (for i=63)
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* where U is a point with no known corresponding scalar. Note that sum(U_i, i=0..63) = 0.
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* For each i, and each of the 16 possible values of n_i, (n_i * 16^i * G + U_i) is
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* precomputed (call it prec(i, n_i)). The formula now becomes sum(prec(i, n_i), i=0..63).
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* None of the resulting prec group elements have a known scalar, and neither do any of
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* the intermediate sums while computing a*G.
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* To make memory access uniform, the bytes of prec(i, n_i) are sliced per value of n_i. */
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unsigned char prec[64][sizeof(secp256k1_ge_t)][16]; /* prec[j][k][i] = k'th byte of (16^j * i * G + U_i) */
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} secp256k1_ecmult_gen_consts_t;
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static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_consts = NULL;
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static void secp256k1_ecmult_gen_start(void) {
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if (secp256k1_ecmult_gen_consts != NULL)
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return;
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/* Allocate the precomputation table. */
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secp256k1_ecmult_gen_consts_t *ret = (secp256k1_ecmult_gen_consts_t*)malloc(sizeof(secp256k1_ecmult_gen_consts_t));
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/* get the generator */
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const secp256k1_ge_t *g = &secp256k1_ge_consts->g;
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secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, g);
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/* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
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secp256k1_gej_t nums_gej;
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{
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static const unsigned char nums_b32[32] = "The scalar for this x is unknown";
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secp256k1_fe_t nums_x;
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secp256k1_fe_set_b32(&nums_x, nums_b32);
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secp256k1_ge_t nums_ge;
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VERIFY_CHECK(secp256k1_ge_set_xo(&nums_ge, &nums_x, 0));
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secp256k1_gej_set_ge(&nums_gej, &nums_ge);
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/* Add G to make the bits in x uniformly distributed. */
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secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, g);
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}
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/* compute prec. */
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secp256k1_ge_t prec[1024];
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{
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secp256k1_gej_t precj[1024]; /* Jacobian versions of prec. */
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secp256k1_gej_t gbase; gbase = gj; /* 16^j * G */
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secp256k1_gej_t numsbase; numsbase = nums_gej; /* 2^j * nums. */
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for (int j=0; j<64; j++) {
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/* Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase). */
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precj[j*16] = numsbase;
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for (int i=1; i<16; i++) {
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secp256k1_gej_add_var(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
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}
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/* Multiply gbase by 16. */
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for (int i=0; i<4; i++) {
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secp256k1_gej_double_var(&gbase, &gbase);
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}
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/* Multiply numbase by 2. */
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secp256k1_gej_double_var(&numsbase, &numsbase);
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if (j == 62) {
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/* In the last iteration, numsbase is (1 - 2^j) * nums instead. */
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secp256k1_gej_neg(&numsbase, &numsbase);
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secp256k1_gej_add_var(&numsbase, &numsbase, &nums_gej);
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}
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}
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secp256k1_ge_set_all_gej_var(1024, prec, precj);
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}
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for (int j=0; j<64; j++) {
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for (int i=0; i<16; i++) {
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const unsigned char* raw = (const unsigned char*)(&prec[j*16 + i]);
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for (size_t k=0; k<sizeof(secp256k1_ge_t); k++)
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ret->prec[j][k][i] = raw[k];
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}
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}
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/* Set the global pointer to the precomputation table. */
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secp256k1_ecmult_gen_consts = ret;
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}
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static void secp256k1_ecmult_gen_stop(void) {
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if (secp256k1_ecmult_gen_consts == NULL)
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return;
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secp256k1_ecmult_gen_consts_t *c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts;
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secp256k1_ecmult_gen_consts = NULL;
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free(c);
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}
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static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_scalar_t *gn) {
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const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts;
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secp256k1_gej_set_infinity(r);
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secp256k1_ge_t add;
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int bits;
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for (int j=0; j<64; j++) {
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bits = secp256k1_scalar_get_bits(gn, j * 4, 4);
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for (size_t k=0; k<sizeof(secp256k1_ge_t); k++)
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((unsigned char*)(&add))[k] = c->prec[j][k][bits];
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secp256k1_gej_add_ge(r, r, &add);
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}
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bits = 0;
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secp256k1_ge_clear(&add);
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}
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#endif
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