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Merge pull request #191

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4732d26 Convert the field/group/ecdsa constant initialization to static consts (Pieter Wuille)
19f3e76 Remove unused secp256k1_fe_inner_{start, stop} functions (Pieter Wuille)
f1ebfe3 Convert the scalar constant initialization to static consts (Pieter Wuille)
This commit is contained in:
Pieter Wuille 2015-01-22 23:10:39 -05:00
commit a9f350d309
No known key found for this signature in database
GPG key ID: 57896D2FF8F0B657
18 changed files with 150 additions and 309 deletions
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4
src/bench_inv.c
View file

@ -42,11 +42,7 @@ void bench_inv(void* arg) {
}
int main(void) {
secp256k1_ge_start();
bench_inv_t data;
run_benchmark(bench_inv, bench_inv_setup, NULL, &data, 10, 20000);
secp256k1_ge_stop();
return 0;
}

51
src/ecdsa_impl.h
View file

@ -15,43 +15,14 @@
#include "ecmult_gen.h"
#include "ecdsa.h"
typedef struct {
secp256k1_fe_t order_as_fe;
secp256k1_fe_t p_minus_order;
} secp256k1_ecdsa_consts_t;
static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
);
static const secp256k1_ecdsa_consts_t *secp256k1_ecdsa_consts = NULL;
static void secp256k1_ecdsa_start(void) {
if (secp256k1_ecdsa_consts != NULL)
return;
/* Allocate. */
secp256k1_ecdsa_consts_t *ret = (secp256k1_ecdsa_consts_t*)checked_malloc(sizeof(secp256k1_ecdsa_consts_t));
static const unsigned char order[] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
};
secp256k1_fe_set_b32(&ret->order_as_fe, order);
secp256k1_fe_negate(&ret->p_minus_order, &ret->order_as_fe, 1);
secp256k1_fe_normalize_var(&ret->p_minus_order);
/* Set the global pointer. */
secp256k1_ecdsa_consts = ret;
}
static void secp256k1_ecdsa_stop(void) {
if (secp256k1_ecdsa_consts == NULL)
return;
secp256k1_ecdsa_consts_t *c = (secp256k1_ecdsa_consts_t*)secp256k1_ecdsa_consts;
secp256k1_ecdsa_consts = NULL;
free(c);
}
static const secp256k1_fe_t secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
);
static int secp256k1_ecdsa_sig_parse(secp256k1_ecdsa_sig_t *r, const unsigned char *sig, int size) {
if (sig[0] != 0x30) return 0;
@ -146,11 +117,11 @@ static int secp256k1_ecdsa_sig_verify(const secp256k1_ecdsa_sig_t *sig, const se
// xr.x == xr * xr.z^2 mod p, so the signature is valid.
return 1;
}
if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_consts->p_minus_order) >= 0) {
if (secp256k1_fe_cmp_var(&xr, &secp256k1_ecdsa_const_p_minus_order) >= 0) {
// xr + p >= n, so we can skip testing the second case.
return 0;
}
secp256k1_fe_add(&xr, &secp256k1_ecdsa_consts->order_as_fe);
secp256k1_fe_add(&xr, &secp256k1_ecdsa_const_order_as_fe);
if (secp256k1_gej_eq_x_var(&xr, &pr)) {
// (xr + n) * pr.z^2 mod p == pr.x, so the signature is valid.
return 1;
@ -167,9 +138,9 @@ static int secp256k1_ecdsa_sig_recover(const secp256k1_ecdsa_sig_t *sig, secp256
secp256k1_fe_t fx;
VERIFY_CHECK(secp256k1_fe_set_b32(&fx, brx)); /* brx comes from a scalar, so is less than the order; certainly less than p */
if (recid & 2) {
if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_consts->p_minus_order) >= 0)
if (secp256k1_fe_cmp_var(&fx, &secp256k1_ecdsa_const_p_minus_order) >= 0)
return 0;
secp256k1_fe_add(&fx, &secp256k1_ecdsa_consts->order_as_fe);
secp256k1_fe_add(&fx, &secp256k1_ecdsa_const_order_as_fe);
}
secp256k1_ge_t x;
if (!secp256k1_ge_set_xo_var(&x, &fx, recid & 1))

5
src/ecmult_gen_impl.h
View file

@ -37,8 +37,7 @@ static void secp256k1_ecmult_gen_start(void) {
secp256k1_ecmult_gen_consts_t *ret = (secp256k1_ecmult_gen_consts_t*)checked_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);
secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
/* Construct a group element with no known corresponding scalar (nothing up my sleeve). */
secp256k1_gej_t nums_gej;
@ -50,7 +49,7 @@ static void secp256k1_ecmult_gen_start(void) {
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, g);
secp256k1_gej_add_ge_var(&nums_gej, &nums_gej, &secp256k1_ge_const_g);
}
/* compute prec. */

3
src/ecmult_impl.h
View file

@ -91,8 +91,7 @@ static void secp256k1_ecmult_start(void) {
secp256k1_ecmult_consts_t *ret = (secp256k1_ecmult_consts_t*)checked_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);
secp256k1_gej_t gj; secp256k1_gej_set_ge(&gj, &secp256k1_ge_const_g);
#ifdef USE_ENDOMORPHISM
/* calculate 2^128*generator */

15
src/field.h
View file

@ -30,21 +30,6 @@
#error "Please select field implementation"
#endif
typedef struct {
#ifndef USE_NUM_NONE
secp256k1_num_t p;
#endif
secp256k1_fe_t order;
} secp256k1_fe_consts_t;
static const secp256k1_fe_consts_t *secp256k1_fe_consts = NULL;
/** Initialize field element precomputation data. */
static void secp256k1_fe_start(void);
/** Unload field element precomputation data. */
static void secp256k1_fe_stop(void);
/** Normalize a field element. */
static void secp256k1_fe_normalize(secp256k1_fe_t *r);

19
src/field_10x26.h
View file

@ -18,4 +18,23 @@ typedef struct {
#endif
} secp256k1_fe_t;
#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
(d0) & 0x3FFFFFFUL, \
((d0) >> 26) | ((d1) & 0xFFFFFUL) << 6, \
((d1) >> 20) | ((d2) & 0x3FFFUL) << 12, \
((d2) >> 14) | ((d3) & 0xFFUL) << 18, \
((d3) >> 8) | ((d4) & 0x3) << 24, \
((d4) >> 2) & 0x3FFFFFFUL, \
((d4) >> 28) | ((d5) & 0x3FFFFFUL) << 4, \
((d5) >> 22) | ((d6) & 0xFFFF) << 10, \
((d6) >> 16) | ((d7) & 0x3FF) << 16, \
((d7) >> 10) \
}
#ifdef VERIFY
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
#else
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
#endif
#endif

3
src/field_10x26_impl.h
View file

@ -13,9 +13,6 @@
#include "num.h"
#include "field.h"
static void secp256k1_fe_inner_start(void) {}
static void secp256k1_fe_inner_stop(void) {}
#ifdef VERIFY
static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
const uint32_t *d = a->n;

14
src/field_5x52.h
View file

@ -18,4 +18,18 @@ typedef struct {
#endif
} secp256k1_fe_t;
#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
(d0) | ((uint64_t)(d1) & 0xFFFFFUL) << 32, \
((d1) >> 20) | ((uint64_t)(d2)) << 12 | ((uint64_t)(d3) & 0xFFUL) << 44, \
((d3) >> 8) | ((uint64_t)(d4) & 0xFFFFFFFUL) << 24, \
((d4) >> 28) | ((uint64_t)(d5)) << 4 | ((uint64_t)(d6) & 0xFFFFUL) << 36, \
((d6) >> 16) | ((uint64_t)(d7)) << 16 \
}
#ifdef VERIFY
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0)), 1, 1}
#else
#define SECP256K1_FE_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {SECP256K1_FE_CONST_INNER((d7), (d6), (d5), (d4), (d3), (d2), (d1), (d0))}
#endif
#endif

3
src/field_5x52_impl.h
View file

@ -30,9 +30,6 @@
* output.
*/
static void secp256k1_fe_inner_start(void) {}
static void secp256k1_fe_inner_stop(void) {}
#ifdef VERIFY
static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
const uint64_t *d = a->n;

39
src/field_impl.h
View file

@ -206,13 +206,20 @@ static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
#if defined(USE_FIELD_INV_BUILTIN)
secp256k1_fe_inv(r, a);
#elif defined(USE_FIELD_INV_NUM)
static const unsigned char prime[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
};
unsigned char b[32];
secp256k1_fe_t c = *a;
secp256k1_fe_normalize_var(&c);
secp256k1_fe_get_b32(b, &c);
secp256k1_num_t n;
secp256k1_num_t n, m;
secp256k1_num_set_bin(&n, b, 32);
secp256k1_num_mod_inverse(&n, &n, &secp256k1_fe_consts->p);
secp256k1_num_set_bin(&m, prime, 32);
secp256k1_num_mod_inverse(&n, &n, &m);
secp256k1_num_get_bin(b, 32, &n);
VERIFY_CHECK(secp256k1_fe_set_b32(r, b));
#else
@ -244,32 +251,4 @@ static void secp256k1_fe_inv_all_var(size_t len, secp256k1_fe_t r[len], const se
r[0] = u;
}
static void secp256k1_fe_start(void) {
#ifndef USE_NUM_NONE
static const unsigned char secp256k1_fe_consts_p[] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFE,0xFF,0xFF,0xFC,0x2F
};
#endif
if (secp256k1_fe_consts == NULL) {
secp256k1_fe_inner_start();
secp256k1_fe_consts_t *ret = (secp256k1_fe_consts_t*)checked_malloc(sizeof(secp256k1_fe_consts_t));
#ifndef USE_NUM_NONE
secp256k1_num_set_bin(&ret->p, secp256k1_fe_consts_p, sizeof(secp256k1_fe_consts_p));
#endif
secp256k1_fe_consts = ret;
}
}
static void secp256k1_fe_stop(void) {
if (secp256k1_fe_consts != NULL) {
secp256k1_fe_consts_t *c = (secp256k1_fe_consts_t*)secp256k1_fe_consts;
free((void*)c);
secp256k1_fe_consts = NULL;
secp256k1_fe_inner_stop();
}
}
#endif

18
src/group.h
View file

@ -25,24 +25,6 @@ typedef struct {
int infinity; /* whether this represents the point at infinity */
} secp256k1_gej_t;
/** Global constants related to the group */
typedef struct {
secp256k1_ge_t g; /* the generator point */
#ifdef USE_ENDOMORPHISM
/* constants related to secp256k1's efficiently computable endomorphism */
secp256k1_fe_t beta;
#endif
} secp256k1_ge_consts_t;
static const secp256k1_ge_consts_t *secp256k1_ge_consts = NULL;
/** Initialize the group module. */
static void secp256k1_ge_start(void);
/** De-initialize the group module. */
static void secp256k1_ge_stop(void);
/** Set a group element equal to the point at infinity */
static void secp256k1_ge_set_infinity(secp256k1_ge_t *r);

62
src/group_impl.h
View file

@ -13,6 +13,18 @@
#include "field.h"
#include "group.h"
static const secp256k1_ge_t secp256k1_ge_const_g = {
SECP256K1_FE_CONST(
0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,
0x029BFCDBUL, 0x2DCE28D9UL, 0x59F2815BUL, 0x16F81798UL
),
SECP256K1_FE_CONST(
0x483ADA77UL, 0x26A3C465UL, 0x5DA4FBFCUL, 0x0E1108A8UL,
0xFD17B448UL, 0xA6855419UL, 0x9C47D08FUL, 0xFB10D4B8UL
),
0
};
static void secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
r->infinity = 1;
}
@ -396,53 +408,13 @@ static void secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a)
#ifdef USE_ENDOMORPHISM
static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
const secp256k1_fe_t *beta = &secp256k1_ge_consts->beta;
static const secp256k1_fe_t beta = SECP256K1_FE_CONST(
0x7ae96a2bul, 0x657c0710ul, 0x6e64479eul, 0xac3434e9ul,
0x9cf04975ul, 0x12f58995ul, 0xc1396c28ul, 0x719501eeul
);
*r = *a;
secp256k1_fe_mul(&r->x, &r->x, beta);
secp256k1_fe_mul(&r->x, &r->x, &beta);
}
#endif
static void secp256k1_ge_start(void) {
static const unsigned char secp256k1_ge_consts_g_x[] = {
0x79,0xBE,0x66,0x7E,0xF9,0xDC,0xBB,0xAC,
0x55,0xA0,0x62,0x95,0xCE,0x87,0x0B,0x07,
0x02,0x9B,0xFC,0xDB,0x2D,0xCE,0x28,0xD9,
0x59,0xF2,0x81,0x5B,0x16,0xF8,0x17,0x98
};
static const unsigned char secp256k1_ge_consts_g_y[] = {
0x48,0x3A,0xDA,0x77,0x26,0xA3,0xC4,0x65,
0x5D,0xA4,0xFB,0xFC,0x0E,0x11,0x08,0xA8,
0xFD,0x17,0xB4,0x48,0xA6,0x85,0x54,0x19,
0x9C,0x47,0xD0,0x8F,0xFB,0x10,0xD4,0xB8
};
#ifdef USE_ENDOMORPHISM
/* properties of secp256k1's efficiently computable endomorphism */
static const unsigned char secp256k1_ge_consts_beta[] = {
0x7a,0xe9,0x6a,0x2b,0x65,0x7c,0x07,0x10,
0x6e,0x64,0x47,0x9e,0xac,0x34,0x34,0xe9,
0x9c,0xf0,0x49,0x75,0x12,0xf5,0x89,0x95,
0xc1,0x39,0x6c,0x28,0x71,0x95,0x01,0xee
};
#endif
if (secp256k1_ge_consts == NULL) {
secp256k1_ge_consts_t *ret = (secp256k1_ge_consts_t*)checked_malloc(sizeof(secp256k1_ge_consts_t));
#ifdef USE_ENDOMORPHISM
VERIFY_CHECK(secp256k1_fe_set_b32(&ret->beta, secp256k1_ge_consts_beta));
#endif
secp256k1_fe_t g_x, g_y;
VERIFY_CHECK(secp256k1_fe_set_b32(&g_x, secp256k1_ge_consts_g_x));
VERIFY_CHECK(secp256k1_fe_set_b32(&g_y, secp256k1_ge_consts_g_y));
secp256k1_ge_set_xy(&ret->g, &g_x, &g_y);
secp256k1_ge_consts = ret;
}
}
static void secp256k1_ge_stop(void) {
if (secp256k1_ge_consts != NULL) {
secp256k1_ge_consts_t *c = (secp256k1_ge_consts_t*)secp256k1_ge_consts;
free((void*)c);
secp256k1_ge_consts = NULL;
}
}
#endif

3
src/scalar.h
View file

@ -21,9 +21,6 @@
#error "Please select scalar implementation"
#endif
static void secp256k1_scalar_start(void);
static void secp256k1_scalar_stop(void);
/** Clear a scalar to prevent the leak of sensitive data. */
static void secp256k1_scalar_clear(secp256k1_scalar_t *r);

2
src/scalar_4x64.h
View file

@ -14,4 +14,6 @@ typedef struct {
uint64_t d[4];
} secp256k1_scalar_t;
#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{((uint64_t)(d1)) << 32 | (d0), ((uint64_t)(d3)) << 32 | (d2), ((uint64_t)(d5)) << 32 | (d4), ((uint64_t)(d7)) << 32 | (d6)}}
#endif

2
src/scalar_8x32.h
View file

@ -14,4 +14,6 @@ typedef struct {
uint32_t d[8];
} secp256k1_scalar_t;
#define SECP256K1_SCALAR_CONST(d7, d6, d5, d4, d3, d2, d1, d0) {{(d0), (d1), (d2), (d3), (d4), (d5), (d6), (d7)}}
#endif

196
src/scalar_impl.h
View file

@ -24,121 +24,6 @@
#error "Please select scalar implementation"
#endif
typedef struct {
#ifndef USE_NUM_NONE
secp256k1_num_t order;
#endif
#ifdef USE_ENDOMORPHISM
secp256k1_scalar_t minus_lambda, minus_b1, minus_b2, g1, g2;
#endif
} secp256k1_scalar_consts_t;
static const secp256k1_scalar_consts_t *secp256k1_scalar_consts = NULL;
static void secp256k1_scalar_start(void) {
if (secp256k1_scalar_consts != NULL)
return;
/* Allocate. */
secp256k1_scalar_consts_t *ret = (secp256k1_scalar_consts_t*)checked_malloc(sizeof(secp256k1_scalar_consts_t));
#ifndef USE_NUM_NONE
static const unsigned char secp256k1_scalar_consts_order[] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
};
secp256k1_num_set_bin(&ret->order, secp256k1_scalar_consts_order, sizeof(secp256k1_scalar_consts_order));
#endif
#ifdef USE_ENDOMORPHISM
/**
* Lambda is a scalar which has the property for secp256k1 that point multiplication by
* it is efficiently computable (see secp256k1_gej_mul_lambda). */
static const unsigned char secp256k1_scalar_consts_lambda[32] = {
0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,
0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,
0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72
};
/**
* "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
* (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
* and k2 have a small size.
* It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
*
* - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
* - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
* - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
* - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
*
* The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
* k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
* compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
*
* g1, g2 are precomputed constants used to replace division with a rounded multiplication
* when decomposing the scalar for an endomorphism-based point multiplication.
*
* The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
* Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
*
* The derivation is described in the paper "Efficient Software Implementation of Public-Key
* Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
* Section 4.3 (here we use a somewhat higher-precision estimate):
* d = a1*b2 - b1*a2
* g1 = round((2^272)*b2/d)
* g2 = round((2^272)*b1/d)
*
* (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
* as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
*/
static const unsigned char secp256k1_scalar_consts_minus_b1[32] = {
0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,
0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3
};
static const unsigned char secp256k1_scalar_consts_b2[32] = {
0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,
0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15
};
static const unsigned char secp256k1_scalar_consts_g1[32] = {
0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
0x00,0x00,0x00,0x00,0x00,0x00,0x30,0x86,
0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,
0x90,0xe4,0x92,0x84,0xeb,0x15,0x3d,0xab
};
static const unsigned char secp256k1_scalar_consts_g2[32] = {
0x00,0x00,0x00,0x00,0x00,0x00,0x00,0x00,
0x00,0x00,0x00,0x00,0x00,0x00,0xe4,0x43,
0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,
0x7f,0xa9,0x0a,0xbf,0xe4,0xc4,0x22,0x12
};
secp256k1_scalar_set_b32(&ret->minus_lambda, secp256k1_scalar_consts_lambda, NULL);
secp256k1_scalar_negate(&ret->minus_lambda, &ret->minus_lambda);
secp256k1_scalar_set_b32(&ret->minus_b1, secp256k1_scalar_consts_minus_b1, NULL);
secp256k1_scalar_set_b32(&ret->minus_b2, secp256k1_scalar_consts_b2, NULL);
secp256k1_scalar_negate(&ret->minus_b2, &ret->minus_b2);
secp256k1_scalar_set_b32(&ret->g1, secp256k1_scalar_consts_g1, NULL);
secp256k1_scalar_set_b32(&ret->g2, secp256k1_scalar_consts_g2, NULL);
#endif
/* Set the global pointer. */
secp256k1_scalar_consts = ret;
}
static void secp256k1_scalar_stop(void) {
if (secp256k1_scalar_consts == NULL)
return;
secp256k1_scalar_consts_t *c = (secp256k1_scalar_consts_t*)secp256k1_scalar_consts;
secp256k1_scalar_consts = NULL;
free(c);
}
#ifndef USE_NUM_NONE
static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_t *a) {
unsigned char c[32];
@ -147,7 +32,13 @@ static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_
}
static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
*r = secp256k1_scalar_consts->order;
static const unsigned char order[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
};
secp256k1_num_set_bin(r, order, 32);
}
#endif
@ -308,9 +199,10 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_
#elif defined(USE_SCALAR_INV_NUM)
unsigned char b[32];
secp256k1_scalar_get_b32(b, x);
secp256k1_num_t n;
secp256k1_num_t n, m;
secp256k1_num_set_bin(&n, b, 32);
secp256k1_num_mod_inverse(&n, &n, &secp256k1_scalar_consts->order);
secp256k1_scalar_order_get_num(&m);
secp256k1_num_mod_inverse(&n, &n, &m);
secp256k1_num_get_bin(b, 32, &n);
secp256k1_scalar_set_b32(r, b, NULL);
#else
@ -319,16 +211,74 @@ static void secp256k1_scalar_inverse_var(secp256k1_scalar_t *r, const secp256k1_
}
#ifdef USE_ENDOMORPHISM
/**
* The Secp256k1 curve has an endomorphism, where lambda * (x, y) = (beta * x, y), where
* lambda is {0x53,0x63,0xad,0x4c,0xc0,0x5c,0x30,0xe0,0xa5,0x26,0x1c,0x02,0x88,0x12,0x64,0x5a,
* 0x12,0x2e,0x22,0xea,0x20,0x81,0x66,0x78,0xdf,0x02,0x96,0x7c,0x1b,0x23,0xbd,0x72}
*
* "Guide to Elliptic Curve Cryptography" (Hankerson, Menezes, Vanstone) gives an algorithm
* (algorithm 3.74) to find k1 and k2 given k, such that k1 + k2 * lambda == k mod n, and k1
* and k2 have a small size.
* It relies on constants a1, b1, a2, b2. These constants for the value of lambda above are:
*
* - a1 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
* - b1 = -{0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3}
* - a2 = {0x01,0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8}
* - b2 = {0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15}
*
* The algorithm then computes c1 = round(b1 * k / n) and c2 = round(b2 * k / n), and gives
* k1 = k - (c1*a1 + c2*a2) and k2 = -(c1*b1 + c2*b2). Instead, we use modular arithmetic, and
* compute k1 as k - k2 * lambda, avoiding the need for constants a1 and a2.
*
* g1, g2 are precomputed constants used to replace division with a rounded multiplication
* when decomposing the scalar for an endomorphism-based point multiplication.
*
* The possibility of using precomputed estimates is mentioned in "Guide to Elliptic Curve
* Cryptography" (Hankerson, Menezes, Vanstone) in section 3.5.
*
* The derivation is described in the paper "Efficient Software Implementation of Public-Key
* Cryptography on Sensor Networks Using the MSP430X Microcontroller" (Gouvea, Oliveira, Lopez),
* Section 4.3 (here we use a somewhat higher-precision estimate):
* d = a1*b2 - b1*a2
* g1 = round((2^272)*b2/d)
* g2 = round((2^272)*b1/d)
*
* (Note that 'd' is also equal to the curve order here because [a1,b1] and [a2,b2] are found
* as outputs of the Extended Euclidean Algorithm on inputs 'order' and 'lambda').
*
* The function below splits a in r1 and r2, such that r1 + lambda * r2 == a (mod order).
*/
static void secp256k1_scalar_split_lambda_var(secp256k1_scalar_t *r1, secp256k1_scalar_t *r2, const secp256k1_scalar_t *a) {
static const secp256k1_scalar_t minus_lambda = SECP256K1_SCALAR_CONST(
0xAC9C52B3UL, 0x3FA3CF1FUL, 0x5AD9E3FDUL, 0x77ED9BA4UL,
0xA880B9FCUL, 0x8EC739C2UL, 0xE0CFC810UL, 0xB51283CFUL
);
static const secp256k1_scalar_t minus_b1 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00000000UL,
0xE4437ED6UL, 0x010E8828UL, 0x6F547FA9UL, 0x0ABFE4C3UL
);
static const secp256k1_scalar_t minus_b2 = SECP256K1_SCALAR_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0x8A280AC5UL, 0x0774346DUL, 0xD765CDA8UL, 0x3DB1562CUL
);
static const secp256k1_scalar_t g1 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x00003086UL,
0xD221A7D4UL, 0x6BCDE86CUL, 0x90E49284UL, 0xEB153DABUL
);
static const secp256k1_scalar_t g2 = SECP256K1_SCALAR_CONST(
0x00000000UL, 0x00000000UL, 0x00000000UL, 0x0000E443UL,
0x7ED6010EUL, 0x88286F54UL, 0x7FA90ABFUL, 0xE4C42212UL
);
VERIFY_CHECK(r1 != a);
VERIFY_CHECK(r2 != a);
secp256k1_scalar_t c1, c2;
secp256k1_scalar_mul_shift_var(&c1, a, &secp256k1_scalar_consts->g1, 272);
secp256k1_scalar_mul_shift_var(&c2, a, &secp256k1_scalar_consts->g2, 272);
secp256k1_scalar_mul(&c1, &c1, &secp256k1_scalar_consts->minus_b1);
secp256k1_scalar_mul(&c2, &c2, &secp256k1_scalar_consts->minus_b2);
secp256k1_scalar_mul_shift_var(&c1, a, &g1, 272);
secp256k1_scalar_mul_shift_var(&c2, a, &g2, 272);
secp256k1_scalar_mul(&c1, &c1, &minus_b1);
secp256k1_scalar_mul(&c2, &c2, &minus_b2);
secp256k1_scalar_add(r2, &c1, &c2);
secp256k1_scalar_mul(r1, r2, &secp256k1_scalar_consts->minus_lambda);
secp256k1_scalar_mul(r1, r2, &minus_lambda);
secp256k1_scalar_add(r1, r1, a);
}
#endif

8
src/secp256k1.c
View file

@ -20,10 +20,6 @@
#include "hash_impl.h"
void secp256k1_start(unsigned int flags) {
secp256k1_fe_start();
secp256k1_ge_start();
secp256k1_scalar_start();
secp256k1_ecdsa_start();
if (flags & SECP256K1_START_SIGN) {
secp256k1_ecmult_gen_start();
}
@ -35,10 +31,6 @@ void secp256k1_start(unsigned int flags) {
void secp256k1_stop(void) {
secp256k1_ecmult_stop();
secp256k1_ecmult_gen_stop();
secp256k1_ecdsa_stop();
secp256k1_scalar_stop();
secp256k1_ge_stop();
secp256k1_fe_stop();
}
int secp256k1_ecdsa_verify(const unsigned char *msg32, const unsigned char *sig, int siglen, const unsigned char *pubkey, int pubkeylen) {

12
src/tests.c
View file

@ -1657,12 +1657,6 @@ int main(int argc, char **argv) {
/* initializing a second time shouldn't cause any harm or memory leaks. */
secp256k1_start(SECP256K1_START_SIGN | SECP256K1_START_VERIFY);
/* Likewise, re-running the internal init functions should be harmless. */
secp256k1_fe_start();
secp256k1_ge_start();
secp256k1_scalar_start();
secp256k1_ecdsa_start();
run_sha256_tests();
run_hmac_sha256_tests();
run_rfc6979_hmac_sha256_tests();
@ -1707,11 +1701,5 @@ int main(int argc, char **argv) {
/* shutting down twice shouldn't cause any double frees. */
secp256k1_stop();
/* Same for the internal shutdown functions. */
secp256k1_fe_stop();
secp256k1_ge_stop();
secp256k1_scalar_stop();
secp256k1_ecdsa_stop();
return 0;
}