phantom/bitcoin
1
0
Fork 0
mirror of https://github.com/bitcoin/bitcoin.git synced 2025-01-10 20:03:34 -03:00
Code Issues Projects Releases Packages Wiki Activity Actions 1

Some comments explaining some of the constants in the code.

Browse source
This commit is contained in:
Gregory Maxwell 2015-02-02 01:47:23 +00:00
parent f88343f2eb
commit 6efd6e7777
7 changed files with 32 additions and 0 deletions
Show stats Download patch file Download diff file Expand all files Collapse all files

22
src/ecdsa_impl.h
View file

@ -15,11 +15,33 @@
#include "ecmult_gen.h"
#include "ecdsa.h"
/** Group order for secp256k1 defined as 'n' in "Standards for Efficient Cryptography" (SEC2) 2.7.1
* sage: for t in xrange(1023, -1, -1):
* .. p = 2**256 - 2**32 - t
* .. if p.is_prime():
* .. print '%x'%p
* .. break
* 'fffffffffffffffffffffffffffffffffffffffffffffffffffffffefffffc2f'
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (EllipticCurve ([F (a), F (b)]).order())
* 'fffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141'
*/
static const secp256k1_fe_t secp256k1_ecdsa_const_order_as_fe = SECP256K1_FE_CONST(
0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFFUL, 0xFFFFFFFEUL,
0xBAAEDCE6UL, 0xAF48A03BUL, 0xBFD25E8CUL, 0xD0364141UL
);
/** Difference between field and order, values 'p' and 'n' values defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
* sage: p = 0xFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F
* sage: a = 0
* sage: b = 7
* sage: F = FiniteField (p)
* sage: '%x' % (p - EllipticCurve ([F (a), F (b)]).order())
* '14551231950b75fc4402da1722fc9baee'
*/
static const secp256k1_fe_t secp256k1_ecdsa_const_p_minus_order = SECP256K1_FE_CONST(
0, 0, 0, 1, 0x45512319UL, 0x50B75FC4UL, 0x402DA172UL, 0x2FC9BAEEUL
);

1
src/field_10x26.h
View file

@ -18,6 +18,7 @@ typedef struct {
#endif
} secp256k1_fe_t;
/* Unpacks a constant into a overlapping multi-limbed FE element. */
#define SECP256K1_FE_CONST_INNER(d7, d6, d5, d4, d3, d2, d1, d0) { \
(d0) & 0x3FFFFFFUL, \
((d0) >> 26) | ((d1) & 0xFFFFFUL) << 6, \

1
src/field_5x52.h
View file

@ -18,6 +18,7 @@ typedef struct {
#endif
} secp256k1_fe_t;
/* Unpacks a constant into a overlapping multi-limbed FE element. */
#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, \

1
src/field_5x52_impl.h
View file

@ -34,6 +34,7 @@
static void secp256k1_fe_verify(const secp256k1_fe_t *a) {
const uint64_t *d = a->n;
int m = a->normalized ? 1 : 2 * a->magnitude, r = 1;
/* secp256k1 'p' value defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
r &= (d[0] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[1] <= 0xFFFFFFFFFFFFFULL * m);
r &= (d[2] <= 0xFFFFFFFFFFFFFULL * m);

3
src/field_impl.h
View file

@ -29,6 +29,7 @@ static void secp256k1_fe_get_hex(char *r64, const secp256k1_fe_t *a) {
secp256k1_fe_normalize(&b);
secp256k1_fe_get_b32(tmp, &b);
for (i=0; i<32; i++) {
/* Hex character table. */
static const char *c = "0123456789ABCDEF";
r64[2*i] = c[(tmp[i] >> 4) & 0xF];
r64[2*i+1] = c[(tmp[i]) & 0xF];
@ -38,6 +39,7 @@ static void secp256k1_fe_get_hex(char *r64, const secp256k1_fe_t *a) {
static int secp256k1_fe_set_hex(secp256k1_fe_t *r, const char *a64) {
int i;
unsigned char tmp[32];
/* Byte to hex value table. */
static const int cvt[256] = {0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
0, 0, 0, 0, 0, 0, 0,0,0,0,0,0,0,0,0,0,
@ -203,6 +205,7 @@ static void secp256k1_fe_inv_var(secp256k1_fe_t *r, const secp256k1_fe_t *a) {
secp256k1_fe_inv(r, a);
#elif defined(USE_FIELD_INV_NUM)
secp256k1_num_t n, m;
/* secp256k1 field prime, value p defined in "Standards for Efficient Cryptography" (SEC2) 2.7.1. */
static const unsigned char prime[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,

3
src/group_impl.h
View file

@ -13,6 +13,9 @@
#include "field.h"
#include "group.h"
/** Generator for secp256k1, value 'g' defined in
* "Standards for Efficient Cryptography" (SEC2) 2.7.1.
*/
static const secp256k1_ge_t secp256k1_ge_const_g = {
SECP256K1_FE_CONST(
0x79BE667EUL, 0xF9DCBBACUL, 0x55A06295UL, 0xCE870B07UL,

1
src/scalar_impl.h
View file

@ -31,6 +31,7 @@ static void secp256k1_scalar_get_num(secp256k1_num_t *r, const secp256k1_scalar_
secp256k1_num_set_bin(r, c, 32);
}
/** secp256k1 curve order, see secp256k1_ecdsa_const_order_as_fe in ecdsa_impl.h */
static void secp256k1_scalar_order_get_num(secp256k1_num_t *r) {
static const unsigned char order[32] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,