390 lines
13 KiB
C
390 lines
13 KiB
C
|
/**********************************************************************
|
||
|
|
* 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_
|
||
|
|
#define _SECP256K1_ECMULT_IMPL_H_
|
||
|
|
|
||
|
|
#include "group.h"
|
||
|
|
#include "scalar.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. */
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
/** Two tables for window size 15: 1.375 MiB. */
|
||
|
|
#define WINDOW_G 15
|
||
|
|
#else
|
||
|
|
/** One table for window size 16: 1.375 MiB. */
|
||
|
|
#define WINDOW_G 16
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/** The number of entries a table with precomputed multiples needs to have. */
|
||
|
|
#define ECMULT_TABLE_SIZE(w) (1 << ((w)-2))
|
||
|
|
|
||
|
|
/** Fill a table 'prej' with precomputed odd multiples of a. Prej will contain
|
||
|
|
* the values [1*a,3*a,...,(2*n-1)*a], so it space for n values. zr[0] will
|
||
|
|
* contain prej[0].z / a.z. The other zr[i] values = prej[i].z / prej[i-1].z.
|
||
|
|
* Prej's Z values are undefined, except for the last value.
|
||
|
|
*/
|
||
|
|
static void secp256k1_ecmult_odd_multiples_table(int n, secp256k1_gej *prej, secp256k1_fe *zr, const secp256k1_gej *a) {
|
||
|
|
secp256k1_gej d;
|
||
|
|
secp256k1_ge a_ge, d_ge;
|
||
|
|
int i;
|
||
|
|
|
||
|
|
VERIFY_CHECK(!a->infinity);
|
||
|
|
|
||
|
|
secp256k1_gej_double_var(&d, a, NULL);
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Perform the additions on an isomorphism where 'd' is affine: drop the z coordinate
|
||
|
|
* of 'd', and scale the 1P starting value's x/y coordinates without changing its z.
|
||
|
|
*/
|
||
|
|
d_ge.x = d.x;
|
||
|
|
d_ge.y = d.y;
|
||
|
|
d_ge.infinity = 0;
|
||
|
|
|
||
|
|
secp256k1_ge_set_gej_zinv(&a_ge, a, &d.z);
|
||
|
|
prej[0].x = a_ge.x;
|
||
|
|
prej[0].y = a_ge.y;
|
||
|
|
prej[0].z = a->z;
|
||
|
|
prej[0].infinity = 0;
|
||
|
|
|
||
|
|
zr[0] = d.z;
|
||
|
|
for (i = 1; i < n; i++) {
|
||
|
|
secp256k1_gej_add_ge_var(&prej[i], &prej[i-1], &d_ge, &zr[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/*
|
||
|
|
* Each point in 'prej' has a z coordinate too small by a factor of 'd.z'. Only
|
||
|
|
* the final point's z coordinate is actually used though, so just update that.
|
||
|
|
*/
|
||
|
|
secp256k1_fe_mul(&prej[n-1].z, &prej[n-1].z, &d.z);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** Fill a table 'pre' with precomputed odd multiples of a.
|
||
|
|
*
|
||
|
|
* There are two versions of this function:
|
||
|
|
* - secp256k1_ecmult_odd_multiples_table_globalz_windowa which brings its
|
||
|
|
* resulting point set to a single constant Z denominator, stores the X and Y
|
||
|
|
* coordinates as ge_storage points in pre, and stores the global Z in rz.
|
||
|
|
* It only operates on tables sized for WINDOW_A wnaf multiples.
|
||
|
|
* - secp256k1_ecmult_odd_multiples_table_storage_var, which converts its
|
||
|
|
* resulting point set to actually affine points, and stores those in pre.
|
||
|
|
* It operates on tables of any size, but uses heap-allocated temporaries.
|
||
|
|
*
|
||
|
|
* To compute a*P + b*G, we compute a table for P using the first function,
|
||
|
|
* and for G using the second (which requires an inverse, but it only needs to
|
||
|
|
* happen once).
|
||
|
|
*/
|
||
|
|
static void secp256k1_ecmult_odd_multiples_table_globalz_windowa(secp256k1_ge *pre, secp256k1_fe *globalz, const secp256k1_gej *a) {
|
||
|
|
secp256k1_gej prej[ECMULT_TABLE_SIZE(WINDOW_A)];
|
||
|
|
secp256k1_fe zr[ECMULT_TABLE_SIZE(WINDOW_A)];
|
||
|
|
|
||
|
|
/* Compute the odd multiples in Jacobian form. */
|
||
|
|
secp256k1_ecmult_odd_multiples_table(ECMULT_TABLE_SIZE(WINDOW_A), prej, zr, a);
|
||
|
|
/* Bring them to the same Z denominator. */
|
||
|
|
secp256k1_ge_globalz_set_table_gej(ECMULT_TABLE_SIZE(WINDOW_A), pre, globalz, prej, zr);
|
||
|
|
}
|
||
|
|
|
||
|
|
static void secp256k1_ecmult_odd_multiples_table_storage_var(int n, secp256k1_ge_storage *pre, const secp256k1_gej *a, const secp256k1_callback *cb) {
|
||
|
|
secp256k1_gej *prej = (secp256k1_gej*)checked_malloc(cb, sizeof(secp256k1_gej) * n);
|
||
|
|
secp256k1_ge *prea = (secp256k1_ge*)checked_malloc(cb, sizeof(secp256k1_ge) * n);
|
||
|
|
secp256k1_fe *zr = (secp256k1_fe*)checked_malloc(cb, sizeof(secp256k1_fe) * n);
|
||
|
|
int i;
|
||
|
|
|
||
|
|
/* Compute the odd multiples in Jacobian form. */
|
||
|
|
secp256k1_ecmult_odd_multiples_table(n, prej, zr, a);
|
||
|
|
/* Convert them in batch to affine coordinates. */
|
||
|
|
secp256k1_ge_set_table_gej_var(n, prea, prej, zr);
|
||
|
|
/* Convert them to compact storage form. */
|
||
|
|
for (i = 0; i < n; i++) {
|
||
|
|
secp256k1_ge_to_storage(&pre[i], &prea[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
free(prea);
|
||
|
|
free(prej);
|
||
|
|
free(zr);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** The following two macro retrieves a particular odd multiple from a table
|
||
|
|
* of precomputed multiples. */
|
||
|
|
#define ECMULT_TABLE_GET_GE(r,pre,n,w) 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 { \
|
||
|
|
secp256k1_ge_neg((r), &(pre)[(-(n)-1)/2]); \
|
||
|
|
} \
|
||
|
|
} while(0)
|
||
|
|
|
||
|
|
#define ECMULT_TABLE_GET_GE_STORAGE(r,pre,n,w) do { \
|
||
|
|
VERIFY_CHECK(((n) & 1) == 1); \
|
||
|
|
VERIFY_CHECK((n) >= -((1 << ((w)-1)) - 1)); \
|
||
|
|
VERIFY_CHECK((n) <= ((1 << ((w)-1)) - 1)); \
|
||
|
|
if ((n) > 0) { \
|
||
|
|
secp256k1_ge_from_storage((r), &(pre)[((n)-1)/2]); \
|
||
|
|
} else { \
|
||
|
|
secp256k1_ge_from_storage((r), &(pre)[(-(n)-1)/2]); \
|
||
|
|
secp256k1_ge_neg((r), (r)); \
|
||
|
|
} \
|
||
|
|
} while(0)
|
||
|
|
|
||
|
|
static void secp256k1_ecmult_context_init(secp256k1_ecmult_context *ctx) {
|
||
|
|
ctx->pre_g = NULL;
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
ctx->pre_g_128 = NULL;
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
static void secp256k1_ecmult_context_build(secp256k1_ecmult_context *ctx, const secp256k1_callback *cb) {
|
||
|
|
secp256k1_gej gj;
|
||
|
|
|
||
|
|
if (ctx->pre_g != NULL) {
|
||
|
|
return;
|
||
|
|
}
|
||
|
|
|
||
|
|
/* get the generator */
|
||
|
|
secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
|
||
|
|
|
||
|
|
ctx->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
|
||
|
|
|
||
|
|
/* precompute the tables with odd multiples */
|
||
|
|
secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g, &gj, cb);
|
||
|
|
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
{
|
||
|
|
secp256k1_gej g_128j;
|
||
|
|
int i;
|
||
|
|
|
||
|
|
ctx->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, sizeof((*ctx->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G));
|
||
|
|
|
||
|
|
/* calculate 2^128*generator */
|
||
|
|
g_128j = gj;
|
||
|
|
for (i = 0; i < 128; i++) {
|
||
|
|
secp256k1_gej_double_var(&g_128j, &g_128j, NULL);
|
||
|
|
}
|
||
|
|
secp256k1_ecmult_odd_multiples_table_storage_var(ECMULT_TABLE_SIZE(WINDOW_G), *ctx->pre_g_128, &g_128j, cb);
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
static void secp256k1_ecmult_context_clone(secp256k1_ecmult_context *dst,
|
||
|
|
const secp256k1_ecmult_context *src, const secp256k1_callback *cb) {
|
||
|
|
if (src->pre_g == NULL) {
|
||
|
|
dst->pre_g = NULL;
|
||
|
|
} else {
|
||
|
|
size_t size = sizeof((*dst->pre_g)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
|
||
|
|
dst->pre_g = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
|
||
|
|
memcpy(dst->pre_g, src->pre_g, size);
|
||
|
|
}
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
if (src->pre_g_128 == NULL) {
|
||
|
|
dst->pre_g_128 = NULL;
|
||
|
|
} else {
|
||
|
|
size_t size = sizeof((*dst->pre_g_128)[0]) * ECMULT_TABLE_SIZE(WINDOW_G);
|
||
|
|
dst->pre_g_128 = (secp256k1_ge_storage (*)[])checked_malloc(cb, size);
|
||
|
|
memcpy(dst->pre_g_128, src->pre_g_128, size);
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
static int secp256k1_ecmult_context_is_built(const secp256k1_ecmult_context *ctx) {
|
||
|
|
return ctx->pre_g != NULL;
|
||
|
|
}
|
||
|
|
|
||
|
|
static void secp256k1_ecmult_context_clear(secp256k1_ecmult_context *ctx) {
|
||
|
|
free(ctx->pre_g);
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
free(ctx->pre_g_128);
|
||
|
|
#endif
|
||
|
|
secp256k1_ecmult_context_init(ctx);
|
||
|
|
}
|
||
|
|
|
||
|
|
/** 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 number of set values in wnaf is returned. This number is at most 256, and at most one more
|
||
|
|
* than the number of bits in the (absolute value) of the input.
|
||
|
|
*/
|
||
|
|
static int secp256k1_ecmult_wnaf(int *wnaf, int len, const secp256k1_scalar *a, int w) {
|
||
|
|
secp256k1_scalar s = *a;
|
||
|
|
int last_set_bit = -1;
|
||
|
|
int bit = 0;
|
||
|
|
int sign = 1;
|
||
|
|
int carry = 0;
|
||
|
|
|
||
|
|
VERIFY_CHECK(wnaf != NULL);
|
||
|
|
VERIFY_CHECK(0 <= len && len <= 256);
|
||
|
|
VERIFY_CHECK(a != NULL);
|
||
|
|
VERIFY_CHECK(2 <= w && w <= 31);
|
||
|
|
|
||
|
|
memset(wnaf, 0, len * sizeof(wnaf[0]));
|
||
|
|
|
||
|
|
if (secp256k1_scalar_get_bits(&s, 255, 1)) {
|
||
|
|
secp256k1_scalar_negate(&s, &s);
|
||
|
|
sign = -1;
|
||
|
|
}
|
||
|
|
|
||
|
|
while (bit < len) {
|
||
|
|
int now;
|
||
|
|
int word;
|
||
|
|
if (secp256k1_scalar_get_bits(&s, bit, 1) == (unsigned int)carry) {
|
||
|
|
bit++;
|
||
|
|
continue;
|
||
|
|
}
|
||
|
|
|
||
|
|
now = w;
|
||
|
|
if (now > len - bit) {
|
||
|
|
now = len - bit;
|
||
|
|
}
|
||
|
|
|
||
|
|
word = secp256k1_scalar_get_bits_var(&s, bit, now) + carry;
|
||
|
|
|
||
|
|
carry = (word >> (w-1)) & 1;
|
||
|
|
word -= carry << w;
|
||
|
|
|
||
|
|
wnaf[bit] = sign * word;
|
||
|
|
last_set_bit = bit;
|
||
|
|
|
||
|
|
bit += now;
|
||
|
|
}
|
||
|
|
#ifdef VERIFY
|
||
|
|
CHECK(carry == 0);
|
||
|
|
while (bit < 256) {
|
||
|
|
CHECK(secp256k1_scalar_get_bits(&s, bit++, 1) == 0);
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
return last_set_bit + 1;
|
||
|
|
}
|
||
|
|
|
||
|
|
static void secp256k1_ecmult(const secp256k1_ecmult_context *ctx, secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_scalar *na, const secp256k1_scalar *ng) {
|
||
|
|
secp256k1_ge pre_a[ECMULT_TABLE_SIZE(WINDOW_A)];
|
||
|
|
secp256k1_ge tmpa;
|
||
|
|
secp256k1_fe Z;
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
secp256k1_ge pre_a_lam[ECMULT_TABLE_SIZE(WINDOW_A)];
|
||
|
|
secp256k1_scalar na_1, na_lam;
|
||
|
|
/* Splitted G factors. */
|
||
|
|
secp256k1_scalar ng_1, ng_128;
|
||
|
|
int wnaf_na_1[130];
|
||
|
|
int wnaf_na_lam[130];
|
||
|
|
int bits_na_1;
|
||
|
|
int bits_na_lam;
|
||
|
|
int wnaf_ng_1[129];
|
||
|
|
int bits_ng_1;
|
||
|
|
int wnaf_ng_128[129];
|
||
|
|
int bits_ng_128;
|
||
|
|
#else
|
||
|
|
int wnaf_na[256];
|
||
|
|
int bits_na;
|
||
|
|
int wnaf_ng[256];
|
||
|
|
int bits_ng;
|
||
|
|
#endif
|
||
|
|
int i;
|
||
|
|
int bits;
|
||
|
|
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
/* 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_scalar_split_lambda(&na_1, &na_lam, na);
|
||
|
|
|
||
|
|
/* build wnaf representation for na_1 and na_lam. */
|
||
|
|
bits_na_1 = secp256k1_ecmult_wnaf(wnaf_na_1, 130, &na_1, WINDOW_A);
|
||
|
|
bits_na_lam = secp256k1_ecmult_wnaf(wnaf_na_lam, 130, &na_lam, WINDOW_A);
|
||
|
|
VERIFY_CHECK(bits_na_1 <= 130);
|
||
|
|
VERIFY_CHECK(bits_na_lam <= 130);
|
||
|
|
bits = bits_na_1;
|
||
|
|
if (bits_na_lam > bits) {
|
||
|
|
bits = bits_na_lam;
|
||
|
|
}
|
||
|
|
#else
|
||
|
|
/* build wnaf representation for na. */
|
||
|
|
bits_na = secp256k1_ecmult_wnaf(wnaf_na, 256, na, WINDOW_A);
|
||
|
|
bits = bits_na;
|
||
|
|
#endif
|
||
|
|
|
||
|
|
/* Calculate odd multiples of a.
|
||
|
|
* All multiples are brought to the same Z 'denominator', which is stored
|
||
|
|
* in Z. Due to secp256k1' isomorphism we can do all operations pretending
|
||
|
|
* that the Z coordinate was 1, use affine addition formulae, and correct
|
||
|
|
* the Z coordinate of the result once at the end.
|
||
|
|
* The exception is the precomputed G table points, which are actually
|
||
|
|
* affine. Compared to the base used for other points, they have a Z ratio
|
||
|
|
* of 1/Z, so we can use secp256k1_gej_add_zinv_var, which uses the same
|
||
|
|
* isomorphism to efficiently add with a known Z inverse.
|
||
|
|
*/
|
||
|
|
secp256k1_ecmult_odd_multiples_table_globalz_windowa(pre_a, &Z, a);
|
||
|
|
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
for (i = 0; i < ECMULT_TABLE_SIZE(WINDOW_A); i++) {
|
||
|
|
secp256k1_ge_mul_lambda(&pre_a_lam[i], &pre_a[i]);
|
||
|
|
}
|
||
|
|
|
||
|
|
/* 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_scalar_split_128(&ng_1, &ng_128, ng);
|
||
|
|
|
||
|
|
/* Build wnaf representation for ng_1 and ng_128 */
|
||
|
|
bits_ng_1 = secp256k1_ecmult_wnaf(wnaf_ng_1, 129, &ng_1, WINDOW_G);
|
||
|
|
bits_ng_128 = secp256k1_ecmult_wnaf(wnaf_ng_128, 129, &ng_128, WINDOW_G);
|
||
|
|
if (bits_ng_1 > bits) {
|
||
|
|
bits = bits_ng_1;
|
||
|
|
}
|
||
|
|
if (bits_ng_128 > bits) {
|
||
|
|
bits = bits_ng_128;
|
||
|
|
}
|
||
|
|
#else
|
||
|
|
bits_ng = secp256k1_ecmult_wnaf(wnaf_ng, 256, ng, WINDOW_G);
|
||
|
|
if (bits_ng > bits) {
|
||
|
|
bits = bits_ng;
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
|
||
|
|
secp256k1_gej_set_infinity(r);
|
||
|
|
|
||
|
|
for (i = bits - 1; i >= 0; i--) {
|
||
|
|
int n;
|
||
|
|
secp256k1_gej_double_var(r, r, NULL);
|
||
|
|
#ifdef USE_ENDOMORPHISM
|
||
|
|
if (i < bits_na_1 && (n = wnaf_na_1[i])) {
|
||
|
|
ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
|
||
|
|
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
|
||
|
|
}
|
||
|
|
if (i < bits_na_lam && (n = wnaf_na_lam[i])) {
|
||
|
|
ECMULT_TABLE_GET_GE(&tmpa, pre_a_lam, n, WINDOW_A);
|
||
|
|
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
|
||
|
|
}
|
||
|
|
if (i < bits_ng_1 && (n = wnaf_ng_1[i])) {
|
||
|
|
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
|
||
|
|
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
|
||
|
|
}
|
||
|
|
if (i < bits_ng_128 && (n = wnaf_ng_128[i])) {
|
||
|
|
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g_128, n, WINDOW_G);
|
||
|
|
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
|
||
|
|
}
|
||
|
|
#else
|
||
|
|
if (i < bits_na && (n = wnaf_na[i])) {
|
||
|
|
ECMULT_TABLE_GET_GE(&tmpa, pre_a, n, WINDOW_A);
|
||
|
|
secp256k1_gej_add_ge_var(r, r, &tmpa, NULL);
|
||
|
|
}
|
||
|
|
if (i < bits_ng && (n = wnaf_ng[i])) {
|
||
|
|
ECMULT_TABLE_GET_GE_STORAGE(&tmpa, *ctx->pre_g, n, WINDOW_G);
|
||
|
|
secp256k1_gej_add_zinv_var(r, r, &tmpa, &Z);
|
||
|
|
}
|
||
|
|
#endif
|
||
|
|
}
|
||
|
|
|
||
|
|
if (!r->infinity) {
|
||
|
|
secp256k1_fe_mul(&r->z, &r->z, &Z);
|
||
|
|
}
|
||
|
|
}
|
||
|
|
|
||
|
|
#endif
|