mirror of
https://github.com/bitcoin/bitcoin.git
synced 2025-02-22 12:23:34 -05:00
c259a7cbc0
Set the global pointer to the precomputation table only after initializing it completely, and unset it before doing any uninitialization. This causes fail-fast behavior in case of race conditions between initialization and operations using it.
343 lines
13 KiB
C
343 lines
13 KiB
C
// Copyright (c) 2013 Pieter Wuille
|
|
// Distributed under the MIT/X11 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 <assert.h>
|
|
#include "num.h"
|
|
#include "group.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. WINDOW_G == 14 results in 640 KiB.
|
|
#define WINDOW_G 14
|
|
|
|
/** 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.
|
|
*/
|
|
void static secp256k1_ecmult_table_precomp_gej(secp256k1_gej_t *pre, const secp256k1_gej_t *a, int w) {
|
|
pre[0] = *a;
|
|
secp256k1_gej_t d; secp256k1_gej_double(&d, &pre[0]);
|
|
for (int i=1; i<(1 << (w-2)); i++)
|
|
secp256k1_gej_add(&pre[i], &d, &pre[i-1]);
|
|
}
|
|
|
|
void static secp256k1_ecmult_table_precomp_ge(secp256k1_ge_t *pre, const secp256k1_gej_t *a, int w) {
|
|
const int table_size = 1 << (w-2);
|
|
secp256k1_gej_t prej[table_size];
|
|
prej[0] = *a;
|
|
secp256k1_gej_t d; secp256k1_gej_double(&d, a);
|
|
for (int i=1; i<table_size; i++) {
|
|
secp256k1_gej_add(&prej[i], &d, &prej[i-1]);
|
|
}
|
|
secp256k1_ge_set_all_gej(table_size, pre, 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)
|
|
#define ECMULT_TABLE_GET_GE(r,pre,n,w) ECMULT_TABLE_GET((r),(pre),(n),(w),secp256k1_ge_neg)
|
|
|
|
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
|
|
secp256k1_ge_t pre_g_128[ECMULT_TABLE_SIZE(WINDOW_G)]; // odd multiples of 2^128*generator
|
|
} secp256k1_ecmult_consts_t;
|
|
|
|
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.
|
|
// To make memory access uniform, the bytes of prec(i, n_i) are sliced per value of n_i.
|
|
unsigned char prec[64][sizeof(secp256k1_ge_t)][16]; // prec[j][k][i] = k'th byte of (16^j * i * G + U_i)
|
|
} secp256k1_ecmult_gen_consts_t;
|
|
|
|
static const secp256k1_ecmult_consts_t *secp256k1_ecmult_consts = NULL;
|
|
static const secp256k1_ecmult_gen_consts_t *secp256k1_ecmult_gen_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*)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);
|
|
|
|
// calculate 2^128*generator
|
|
secp256k1_gej_t g_128j = gj;
|
|
for (int i=0; i<128; i++)
|
|
secp256k1_gej_double(&g_128j, &g_128j);
|
|
|
|
// precompute the tables with odd multiples
|
|
secp256k1_ecmult_table_precomp_ge(ret->pre_g, &gj, WINDOW_G);
|
|
secp256k1_ecmult_table_precomp_ge(ret->pre_g_128, &g_128j, WINDOW_G);
|
|
|
|
// Set the global pointer to the precomputation table.
|
|
secp256k1_ecmult_consts = ret;
|
|
}
|
|
|
|
static void secp256k1_ecmult_gen_start(void) {
|
|
if (secp256k1_ecmult_gen_consts != NULL)
|
|
return;
|
|
|
|
// Allocate the precomputation table.
|
|
secp256k1_ecmult_gen_consts_t *ret = (secp256k1_ecmult_gen_consts_t*)malloc(sizeof(secp256k1_ecmult_gen_consts_t));
|
|
|
|
// get the generator
|
|
const secp256k1_ge_t *g = &secp256k1_ge_consts->g;
|
|
secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, g);
|
|
|
|
// Construct a group element with no known corresponding scalar (nothing up my sleeve).
|
|
secp256k1_gej_t nums_gej;
|
|
{
|
|
static const unsigned char nums_b32[32] = "The scalar for this x is unknown";
|
|
secp256k1_fe_t nums_x;
|
|
secp256k1_fe_set_b32(&nums_x, nums_b32);
|
|
secp256k1_ge_t nums_ge;
|
|
VERIFY_CHECK(secp256k1_ge_set_xo(&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(&nums_gej, &nums_gej, g);
|
|
}
|
|
|
|
// compute prec.
|
|
secp256k1_ge_t prec[1024];
|
|
{
|
|
secp256k1_gej_t precj[1024]; // Jacobian versions of prec.
|
|
int j = 0;
|
|
secp256k1_gej_t gbase; gbase = gj; // 16^j * G
|
|
secp256k1_gej_t numsbase; numsbase = nums_gej; // 2^j * nums.
|
|
for (int j=0; j<64; j++) {
|
|
// Set precj[j*16 .. j*16+15] to (numsbase, numsbase + gbase, ..., numsbase + 15*gbase).
|
|
precj[j*16] = numsbase;
|
|
for (int i=1; i<16; i++) {
|
|
secp256k1_gej_add(&precj[j*16 + i], &precj[j*16 + i - 1], &gbase);
|
|
}
|
|
// Multiply gbase by 16.
|
|
for (int i=0; i<4; i++) {
|
|
secp256k1_gej_double(&gbase, &gbase);
|
|
}
|
|
// Multiply numbase by 2.
|
|
secp256k1_gej_double(&numsbase, &numsbase);
|
|
if (j == 62) {
|
|
// In the last iteration, numsbase is (1 - 2^j) * nums instead.
|
|
secp256k1_gej_neg(&numsbase, &numsbase);
|
|
secp256k1_gej_add(&numsbase, &numsbase, &nums_gej);
|
|
}
|
|
}
|
|
secp256k1_ge_set_all_gej(1024, prec, precj);
|
|
}
|
|
for (int j=0; j<64; j++) {
|
|
for (int i=0; i<16; i++) {
|
|
const unsigned char* raw = (const unsigned char*)(&prec[j*16 + i]);
|
|
for (int k=0; k<sizeof(secp256k1_ge_t); k++)
|
|
ret->prec[j][k][i] = raw[k];
|
|
}
|
|
}
|
|
|
|
// Set the global pointer to the precomputation table.
|
|
secp256k1_ecmult_gen_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);
|
|
}
|
|
|
|
static void secp256k1_ecmult_gen_stop(void) {
|
|
if (secp256k1_ecmult_gen_consts == NULL)
|
|
return;
|
|
|
|
secp256k1_ecmult_gen_consts_t *c = (secp256k1_ecmult_gen_consts_t*)secp256k1_ecmult_gen_consts;
|
|
secp256k1_ecmult_gen_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 index of the highest non-zero entry in wnaf (=return value-1) is at most bits, where
|
|
* bits is the number of bits necessary to represent the absolute value of the input.
|
|
*/
|
|
static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_num_t *a, int w) {
|
|
int ret = 0;
|
|
int zeroes = 0;
|
|
secp256k1_num_t x;
|
|
secp256k1_num_init(&x);
|
|
secp256k1_num_copy(&x, a);
|
|
int sign = 1;
|
|
if (secp256k1_num_is_neg(&x)) {
|
|
sign = -1;
|
|
secp256k1_num_negate(&x);
|
|
}
|
|
while (!secp256k1_num_is_zero(&x)) {
|
|
while (!secp256k1_num_is_odd(&x)) {
|
|
zeroes++;
|
|
secp256k1_num_shift(&x, 1);
|
|
}
|
|
int word = secp256k1_num_shift(&x, w);
|
|
while (zeroes) {
|
|
wnaf[ret++] = 0;
|
|
zeroes--;
|
|
}
|
|
if (word & (1 << (w-1))) {
|
|
secp256k1_num_inc(&x);
|
|
wnaf[ret++] = sign * (word - (1 << w));
|
|
} else {
|
|
wnaf[ret++] = sign * word;
|
|
}
|
|
zeroes = w-1;
|
|
}
|
|
secp256k1_num_free(&x);
|
|
return ret;
|
|
}
|
|
|
|
void static secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_num_t *gn) {
|
|
secp256k1_num_t n;
|
|
secp256k1_num_init(&n);
|
|
secp256k1_num_copy(&n, gn);
|
|
const secp256k1_ecmult_gen_consts_t *c = secp256k1_ecmult_gen_consts;
|
|
secp256k1_gej_set_infinity(r);
|
|
secp256k1_ge_t add;
|
|
int bits;
|
|
for (int j=0; j<64; j++) {
|
|
bits = secp256k1_num_shift(&n, 4);
|
|
for (int k=0; k<sizeof(secp256k1_ge_t); k++)
|
|
((unsigned char*)(&add))[k] = c->prec[j][k][bits];
|
|
secp256k1_gej_add_ge(r, r, &add);
|
|
}
|
|
bits = 0;
|
|
secp256k1_ge_clear(&add);
|
|
secp256k1_num_clear(&n);
|
|
secp256k1_num_free(&n);
|
|
}
|
|
|
|
void static secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_num_t *na, const secp256k1_num_t *ng) {
|
|
const secp256k1_ecmult_consts_t *c = secp256k1_ecmult_consts;
|
|
|
|
#ifdef USE_ENDOMORPHISM
|
|
secp256k1_num_t na_1, na_lam;
|
|
secp256k1_num_init(&na_1);
|
|
secp256k1_num_init(&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_gej_split_exp(&na_1, &na_lam, na);
|
|
|
|
// build wnaf representation for na_1 and na_lam.
|
|
int wnaf_na_1[129]; int bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, &na_1, WINDOW_A);
|
|
int wnaf_na_lam[129]; int bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, &na_lam, WINDOW_A);
|
|
int bits = bits_na_1;
|
|
if (bits_na_lam > bits) bits = bits_na_lam;
|
|
#else
|
|
// build wnaf representation for na.
|
|
int wnaf_na[257]; 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(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]);
|
|
#endif
|
|
|
|
// Splitted G factors.
|
|
secp256k1_num_t ng_1, ng_128;
|
|
secp256k1_num_init(&ng_1);
|
|
secp256k1_num_init(&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_num_split(&ng_1, &ng_128, ng, 128);
|
|
|
|
// 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;
|
|
|
|
secp256k1_gej_set_infinity(r);
|
|
secp256k1_gej_t tmpj;
|
|
secp256k1_ge_t tmpa;
|
|
|
|
for (int i=bits-1; i>=0; i--) {
|
|
secp256k1_gej_double(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(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(r, r, &tmpj);
|
|
}
|
|
#else
|
|
if (i < bits_na && (n = wnaf_na[i])) {
|
|
ECMULT_TABLE_GET_GEJ(&tmpj, pre_a, n, WINDOW_A);
|
|
secp256k1_gej_add(r, r, &tmpj);
|
|
}
|
|
#endif
|
|
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(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(r, r, &tmpa);
|
|
}
|
|
}
|
|
|
|
#ifdef USE_ENDOMORPHISM
|
|
secp256k1_num_free(&na_1);
|
|
secp256k1_num_free(&na_lam);
|
|
#endif
|
|
secp256k1_num_free(&ng_1);
|
|
secp256k1_num_free(&ng_128);
|
|
}
|
|
|
|
#endif
|