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Split up ecmult and ecmult_gen entirely

This commit is contained in:
Pieter Wuille 2014-10-26 03:42:24 -07:00
parent bd696ebd3f
commit 949c1ebb5e
7 changed files with 148 additions and 115 deletions
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2
Makefile.am
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@ -14,6 +14,8 @@ noinst_HEADERS += src/ecdsa.h
noinst_HEADERS += src/ecdsa_impl.h
noinst_HEADERS += src/ecmult.h
noinst_HEADERS += src/ecmult_impl.h
noinst_HEADERS += src/ecmult_gen.h
noinst_HEADERS += src/ecmult_gen_impl.h
noinst_HEADERS += src/num.h
noinst_HEADERS += src/num_impl.h
noinst_HEADERS += src/field_10x26.h

1
src/ecdsa_impl.h
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@ -9,6 +9,7 @@
#include "field.h"
#include "group.h"
#include "ecmult.h"
#include "ecmult_gen.h"
#include "ecdsa.h"
void static secp256k1_ecdsa_sig_init(secp256k1_ecdsa_sig_t *r) {

6
src/ecmult.h
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@ -1,5 +1,5 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// 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_
@ -11,8 +11,6 @@
static void secp256k1_ecmult_start(void);
static void secp256k1_ecmult_stop(void);
/** Multiply with the generator: R = a*G */
static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_num_t *a);
/** Double multiply: R = na*A + ng*G */
static void secp256k1_ecmult(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_num_t *na, const secp256k1_num_t *ng);

17
src/ecmult_gen.h Normal file
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@ -0,0 +1,17 @@
// 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_
#define _SECP256K1_ECMULT_GEN_
#include "num.h"
#include "group.h"
static void secp256k1_ecmult_gen_start(void);
static void secp256k1_ecmult_gen_stop(void);
/** Multiply with the generator: R = a*G */
static void secp256k1_ecmult_gen(secp256k1_gej_t *r, const secp256k1_num_t *a);
#endif

123
src/ecmult_gen_impl.h Normal file
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@ -0,0 +1,123 @@
// 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 <assert.h>
#include "num.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.
// 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_gen_consts_t *secp256k1_ecmult_gen_consts = NULL;
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_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);
}
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);
}
#endif

113
src/ecmult_impl.h
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@ -1,5 +1,5 @@
// Copyright (c) 2013 Pieter Wuille
// Distributed under the MIT/X11 software license, see the accompanying
// 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_
@ -71,24 +71,7 @@ typedef struct {
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)
@ -114,69 +97,6 @@ static void secp256k1_ecmult_start(void) {
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;
@ -186,15 +106,6 @@ static void secp256k1_ecmult_stop(void) {
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)
@ -235,26 +146,6 @@ static int secp256k1_ecmult_wnaf(int *wnaf, const secp256k1_num_t *a, int w) {
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;

1
src/secp256k1.c
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@ -10,6 +10,7 @@
#include "field_impl.h"
#include "group_impl.h"
#include "ecmult_impl.h"
#include "ecmult_gen_impl.h"
#include "ecdsa_impl.h"
void secp256k1_start(unsigned int flags) {