-// 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.
+/**********************************************************************
+ * 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_GROUP_IMPL_H_
#define _SECP256K1_GROUP_IMPL_H_
#include "field.h"
#include "group.h"
-void static secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
+static void secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
r->infinity = 1;
}
-void static secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
+static void secp256k1_ge_set_xy(secp256k1_ge_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
}
-int static secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
+static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
return a->infinity;
}
-void static secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
+static void secp256k1_ge_neg(secp256k1_ge_t *r, const secp256k1_ge_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_negate(&r->y, &r->y, 1);
}
-void static secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a) {
+static void secp256k1_ge_get_hex(char *r, int *rlen, const secp256k1_ge_t *a) {
char cx[65]; int lx=65;
char cy[65]; int ly=65;
secp256k1_fe_get_hex(cx, &lx, &a->x);
r[3+lx+ly] = 0;
}
-void static secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
+static void secp256k1_ge_set_gej(secp256k1_ge_t *r, secp256k1_gej_t *a) {
r->infinity = a->infinity;
secp256k1_fe_inv(&a->z, &a->z);
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &a->z);
r->y = a->y;
}
-void static secp256k1_ge_set_gej_var(secp256k1_ge_t *r, secp256k1_gej_t *a) {
+static void secp256k1_ge_set_gej_var(secp256k1_ge_t *r, secp256k1_gej_t *a) {
r->infinity = a->infinity;
if (a->infinity) {
return;
r->y = a->y;
}
-void static secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t r[len], const secp256k1_gej_t a[len]) {
- int count = 0;
+static void secp256k1_ge_set_all_gej_var(size_t len, secp256k1_ge_t r[len], const secp256k1_gej_t a[len]) {
+ size_t count = 0;
secp256k1_fe_t az[len];
- for (int i=0; i<len; i++) {
+ for (size_t i=0; i<len; i++) {
if (!a[i].infinity) {
az[count++] = a[i].z;
}
secp256k1_fe_inv_all_var(count, azi, az);
count = 0;
- for (int i=0; i<len; i++) {
+ for (size_t i=0; i<len; i++) {
r[i].infinity = a[i].infinity;
if (!a[i].infinity) {
secp256k1_fe_t *zi = &azi[count++];
}
}
-void static secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
+static void secp256k1_gej_set_infinity(secp256k1_gej_t *r) {
r->infinity = 1;
secp256k1_fe_set_int(&r->x, 0);
secp256k1_fe_set_int(&r->y, 0);
secp256k1_fe_set_int(&r->z, 0);
}
-void static secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
+static void secp256k1_gej_set_xy(secp256k1_gej_t *r, const secp256k1_fe_t *x, const secp256k1_fe_t *y) {
r->infinity = 0;
r->x = *x;
r->y = *y;
secp256k1_fe_set_int(&r->z, 1);
}
-void static secp256k1_gej_clear(secp256k1_gej_t *r) {
+static void secp256k1_gej_clear(secp256k1_gej_t *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
secp256k1_fe_clear(&r->z);
}
-void static secp256k1_ge_clear(secp256k1_ge_t *r) {
+static void secp256k1_ge_clear(secp256k1_ge_t *r) {
r->infinity = 0;
secp256k1_fe_clear(&r->x);
secp256k1_fe_clear(&r->y);
}
-int static secp256k1_ge_set_xo(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd) {
+static int secp256k1_ge_set_xo(secp256k1_ge_t *r, const secp256k1_fe_t *x, int odd) {
r->x = *x;
secp256k1_fe_t x2; secp256k1_fe_sqr(&x2, x);
secp256k1_fe_t x3; secp256k1_fe_mul(&x3, x, &x2);
return 1;
}
-void static secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
+static void secp256k1_gej_set_ge(secp256k1_gej_t *r, const secp256k1_ge_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_set_int(&r->z, 1);
}
-void static secp256k1_gej_get_x_var(secp256k1_fe_t *r, const secp256k1_gej_t *a) {
+static void secp256k1_gej_get_x_var(secp256k1_fe_t *r, const secp256k1_gej_t *a) {
secp256k1_fe_t zi2; secp256k1_fe_inv_var(&zi2, &a->z); secp256k1_fe_sqr(&zi2, &zi2);
secp256k1_fe_mul(r, &a->x, &zi2);
}
-void static secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
+static void secp256k1_gej_neg(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
r->infinity = a->infinity;
r->x = a->x;
r->y = a->y;
secp256k1_fe_negate(&r->y, &r->y, 1);
}
-int static secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
+static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
return a->infinity;
}
-int static secp256k1_gej_is_valid(const secp256k1_gej_t *a) {
+static int secp256k1_gej_is_valid(const secp256k1_gej_t *a) {
if (a->infinity)
return 0;
- // y^2 = x^3 + 7
- // (Y/Z^3)^2 = (X/Z^2)^3 + 7
- // Y^2 / Z^6 = X^3 / Z^6 + 7
- // Y^2 = X^3 + 7*Z^6
+ /** y^2 = x^3 + 7
+ * (Y/Z^3)^2 = (X/Z^2)^3 + 7
+ * Y^2 / Z^6 = X^3 / Z^6 + 7
+ * Y^2 = X^3 + 7*Z^6
+ */
secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_t x3; secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &a->z);
return secp256k1_fe_equal(&y2, &x3);
}
-int static secp256k1_ge_is_valid(const secp256k1_ge_t *a) {
+static int secp256k1_ge_is_valid(const secp256k1_ge_t *a) {
if (a->infinity)
return 0;
- // y^2 = x^3 + 7
+ /* y^2 = x^3 + 7 */
secp256k1_fe_t y2; secp256k1_fe_sqr(&y2, &a->y);
secp256k1_fe_t x3; secp256k1_fe_sqr(&x3, &a->x); secp256k1_fe_mul(&x3, &x3, &a->x);
secp256k1_fe_t c; secp256k1_fe_set_int(&c, 7);
return secp256k1_fe_equal(&y2, &x3);
}
-void static secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
- if (a->infinity) {
- r->infinity = 1;
- return;
- }
-
- secp256k1_fe_t t5 = a->y;
- secp256k1_fe_normalize(&t5);
- if (secp256k1_fe_is_zero(&t5)) {
- r->infinity = 1;
+static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
+ // For secp256k1, 2Q is infinity if and only if Q is infinity. This is because if 2Q = infinity,
+ // Q must equal -Q, or that Q.y == -(Q.y), or Q.y is 0. For a point on y^2 = x^3 + 7 to have
+ // y=0, x^3 must be -7 mod p. However, -7 has no cube root mod p.
+ r->infinity = a->infinity;
+ if (r->infinity) {
return;
}
secp256k1_fe_t t1,t2,t3,t4;
- secp256k1_fe_mul(&r->z, &t5, &a->z);
- secp256k1_fe_mul_int(&r->z, 2); // Z' = 2*Y*Z (2)
+ secp256k1_fe_mul(&r->z, &a->y, &a->z);
+ secp256k1_fe_mul_int(&r->z, 2); /* Z' = 2*Y*Z (2) */
secp256k1_fe_sqr(&t1, &a->x);
- secp256k1_fe_mul_int(&t1, 3); // T1 = 3*X^2 (3)
- secp256k1_fe_sqr(&t2, &t1); // T2 = 9*X^4 (1)
- secp256k1_fe_sqr(&t3, &t5);
- secp256k1_fe_mul_int(&t3, 2); // T3 = 2*Y^2 (2)
+ secp256k1_fe_mul_int(&t1, 3); /* T1 = 3*X^2 (3) */
+ secp256k1_fe_sqr(&t2, &t1); /* T2 = 9*X^4 (1) */
+ secp256k1_fe_sqr(&t3, &a->y);
+ secp256k1_fe_mul_int(&t3, 2); /* T3 = 2*Y^2 (2) */
secp256k1_fe_sqr(&t4, &t3);
- secp256k1_fe_mul_int(&t4, 2); // T4 = 8*Y^4 (2)
- secp256k1_fe_mul(&t3, &a->x, &t3); // T3 = 2*X*Y^2 (1)
+ secp256k1_fe_mul_int(&t4, 2); /* T4 = 8*Y^4 (2) */
+ secp256k1_fe_mul(&t3, &a->x, &t3); /* T3 = 2*X*Y^2 (1) */
r->x = t3;
- secp256k1_fe_mul_int(&r->x, 4); // X' = 8*X*Y^2 (4)
- secp256k1_fe_negate(&r->x, &r->x, 4); // X' = -8*X*Y^2 (5)
- secp256k1_fe_add(&r->x, &t2); // X' = 9*X^4 - 8*X*Y^2 (6)
- secp256k1_fe_negate(&t2, &t2, 1); // T2 = -9*X^4 (2)
- secp256k1_fe_mul_int(&t3, 6); // T3 = 12*X*Y^2 (6)
- secp256k1_fe_add(&t3, &t2); // T3 = 12*X*Y^2 - 9*X^4 (8)
- secp256k1_fe_mul(&r->y, &t1, &t3); // Y' = 36*X^3*Y^2 - 27*X^6 (1)
- secp256k1_fe_negate(&t2, &t4, 2); // T2 = -8*Y^4 (3)
- secp256k1_fe_add(&r->y, &t2); // Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4)
- r->infinity = 0;
+ secp256k1_fe_mul_int(&r->x, 4); /* X' = 8*X*Y^2 (4) */
+ secp256k1_fe_negate(&r->x, &r->x, 4); /* X' = -8*X*Y^2 (5) */
+ secp256k1_fe_add(&r->x, &t2); /* X' = 9*X^4 - 8*X*Y^2 (6) */
+ secp256k1_fe_negate(&t2, &t2, 1); /* T2 = -9*X^4 (2) */
+ secp256k1_fe_mul_int(&t3, 6); /* T3 = 12*X*Y^2 (6) */
+ secp256k1_fe_add(&t3, &t2); /* T3 = 12*X*Y^2 - 9*X^4 (8) */
+ secp256k1_fe_mul(&r->y, &t1, &t3); /* Y' = 36*X^3*Y^2 - 27*X^6 (1) */
+ secp256k1_fe_negate(&t2, &t4, 2); /* T2 = -8*Y^4 (3) */
+ secp256k1_fe_add(&r->y, &t2); /* Y' = 36*X^3*Y^2 - 27*X^6 - 8*Y^4 (4) */
}
-void static secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
+static void secp256k1_gej_add_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_gej_t *b) {
if (a->infinity) {
*r = *b;
return;
secp256k1_fe_add(&r->y, &h3);
}
-void static secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
+static void secp256k1_gej_add_ge_var(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
if (a->infinity) {
r->infinity = b->infinity;
r->x = b->x;
secp256k1_fe_add(&r->y, &h3);
}
-void static secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
+static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, const secp256k1_ge_t *b) {
VERIFY_CHECK(!b->infinity);
VERIFY_CHECK(a->infinity == 0 || a->infinity == 1);
- // In:
- // Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
- // In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
- // we find as solution for a unified addition/doubling formula:
- // lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
- // x3 = lambda^2 - (x1 + x2)
- // 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
- //
- // Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
- // U1 = X1*Z2^2, U2 = X2*Z1^2
- // S1 = X1*Z2^3, S2 = X2*Z2^3
- // Z = Z1*Z2
- // T = U1+U2
- // M = S1+S2
- // Q = T*M^2
- // R = T^2-U1*U2
- // X3 = 4*(R^2-Q)
- // Y3 = 4*(R*(3*Q-2*R^2)-M^4)
- // Z3 = 2*M*Z
- // (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
-
- secp256k1_fe_t zz; secp256k1_fe_sqr(&zz, &a->z); // z = Z1^2
- secp256k1_fe_t u1 = a->x; secp256k1_fe_normalize(&u1); // u1 = U1 = X1*Z2^2 (1)
- secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &zz); // u2 = U2 = X2*Z1^2 (1)
- secp256k1_fe_t s1 = a->y; secp256k1_fe_normalize(&s1); // s1 = S1 = Y1*Z2^3 (1)
- secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &zz); // s2 = Y2*Z2^2 (1)
- secp256k1_fe_mul(&s2, &s2, &a->z); // s2 = S2 = Y2*Z1^3 (1)
- secp256k1_fe_t z = a->z; // z = Z = Z1*Z2 (8)
- secp256k1_fe_t t = u1; secp256k1_fe_add(&t, &u2); // t = T = U1+U2 (2)
- secp256k1_fe_t m = s1; secp256k1_fe_add(&m, &s2); // m = M = S1+S2 (2)
- secp256k1_fe_t n; secp256k1_fe_sqr(&n, &m); // n = M^2 (1)
- secp256k1_fe_t q; secp256k1_fe_mul(&q, &n, &t); // q = Q = T*M^2 (1)
- secp256k1_fe_sqr(&n, &n); // n = M^4 (1)
- secp256k1_fe_t rr; secp256k1_fe_sqr(&rr, &t); // rr = T^2 (1)
- secp256k1_fe_mul(&t, &u1, &u2); secp256k1_fe_negate(&t, &t, 1); // t = -U1*U2 (2)
- secp256k1_fe_add(&rr, &t); // rr = R = T^2-U1*U2 (3)
- secp256k1_fe_sqr(&t, &rr); // t = R^2 (1)
- secp256k1_fe_mul(&r->z, &m, &z); // r->z = M*Z (1)
+ /** In:
+ * Eric Brier and Marc Joye, Weierstrass Elliptic Curves and Side-Channel Attacks.
+ * In D. Naccache and P. Paillier, Eds., Public Key Cryptography, vol. 2274 of Lecture Notes in Computer Science, pages 335-345. Springer-Verlag, 2002.
+ * we find as solution for a unified addition/doubling formula:
+ * lambda = ((x1 + x2)^2 - x1 * x2 + a) / (y1 + y2), with a = 0 for secp256k1's curve equation.
+ * x3 = lambda^2 - (x1 + x2)
+ * 2*y3 = lambda * (x1 + x2 - 2 * x3) - (y1 + y2).
+ *
+ * Substituting x_i = Xi / Zi^2 and yi = Yi / Zi^3, for i=1,2,3, gives:
+ * U1 = X1*Z2^2, U2 = X2*Z1^2
+ * S1 = Y1*Z2^3, S2 = Y2*Z1^3
+ * Z = Z1*Z2
+ * T = U1+U2
+ * M = S1+S2
+ * Q = T*M^2
+ * R = T^2-U1*U2
+ * X3 = 4*(R^2-Q)
+ * Y3 = 4*(R*(3*Q-2*R^2)-M^4)
+ * Z3 = 2*M*Z
+ * (Note that the paper uses xi = Xi / Zi and yi = Yi / Zi instead.)
+ */
+
+ secp256k1_fe_t zz; secp256k1_fe_sqr(&zz, &a->z); /* z = Z1^2 */
+ secp256k1_fe_t u1 = a->x; secp256k1_fe_normalize(&u1); /* u1 = U1 = X1*Z2^2 (1) */
+ secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &zz); /* u2 = U2 = X2*Z1^2 (1) */
+ secp256k1_fe_t s1 = a->y; secp256k1_fe_normalize(&s1); /* s1 = S1 = Y1*Z2^3 (1) */
+ secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &zz); /* s2 = Y2*Z2^2 (1) */
+ secp256k1_fe_mul(&s2, &s2, &a->z); /* s2 = S2 = Y2*Z1^3 (1) */
+ secp256k1_fe_t z = a->z; /* z = Z = Z1*Z2 (8) */
+ secp256k1_fe_t t = u1; secp256k1_fe_add(&t, &u2); /* t = T = U1+U2 (2) */
+ secp256k1_fe_t m = s1; secp256k1_fe_add(&m, &s2); /* m = M = S1+S2 (2) */
+ secp256k1_fe_t n; secp256k1_fe_sqr(&n, &m); /* n = M^2 (1) */
+ secp256k1_fe_t q; secp256k1_fe_mul(&q, &n, &t); /* q = Q = T*M^2 (1) */
+ secp256k1_fe_sqr(&n, &n); /* n = M^4 (1) */
+ secp256k1_fe_t rr; secp256k1_fe_sqr(&rr, &t); /* rr = T^2 (1) */
+ secp256k1_fe_mul(&t, &u1, &u2); secp256k1_fe_negate(&t, &t, 1); /* t = -U1*U2 (2) */
+ secp256k1_fe_add(&rr, &t); /* rr = R = T^2-U1*U2 (3) */
+ secp256k1_fe_sqr(&t, &rr); /* t = R^2 (1) */
+ secp256k1_fe_mul(&r->z, &m, &z); /* r->z = M*Z (1) */
secp256k1_fe_normalize(&r->z);
int infinity = secp256k1_fe_is_zero(&r->z) * (1 - a->infinity);
- secp256k1_fe_mul_int(&r->z, 2 * (1 - a->infinity)); // r->z = Z3 = 2*M*Z (2)
- r->x = t; // r->x = R^2 (1)
- secp256k1_fe_negate(&q, &q, 1); // q = -Q (2)
- secp256k1_fe_add(&r->x, &q); // r->x = R^2-Q (3)
+ secp256k1_fe_mul_int(&r->z, 2 * (1 - a->infinity)); /* r->z = Z3 = 2*M*Z (2) */
+ r->x = t; /* r->x = R^2 (1) */
+ secp256k1_fe_negate(&q, &q, 1); /* q = -Q (2) */
+ secp256k1_fe_add(&r->x, &q); /* r->x = R^2-Q (3) */
secp256k1_fe_normalize(&r->x);
- secp256k1_fe_mul_int(&q, 3); // q = -3*Q (6)
- secp256k1_fe_mul_int(&t, 2); // t = 2*R^2 (2)
- secp256k1_fe_add(&t, &q); // t = 2*R^2-3*Q (8)
- secp256k1_fe_mul(&t, &t, &rr); // t = R*(2*R^2-3*Q) (1)
- secp256k1_fe_add(&t, &n); // t = R*(2*R^2-3*Q)+M^4 (2)
- secp256k1_fe_negate(&r->y, &t, 2); // r->y = R*(3*Q-2*R^2)-M^4 (3)
+ secp256k1_fe_mul_int(&q, 3); /* q = -3*Q (6) */
+ secp256k1_fe_mul_int(&t, 2); /* t = 2*R^2 (2) */
+ secp256k1_fe_add(&t, &q); /* t = 2*R^2-3*Q (8) */
+ secp256k1_fe_mul(&t, &t, &rr); /* t = R*(2*R^2-3*Q) (1) */
+ secp256k1_fe_add(&t, &n); /* t = R*(2*R^2-3*Q)+M^4 (2) */
+ secp256k1_fe_negate(&r->y, &t, 2); /* r->y = R*(3*Q-2*R^2)-M^4 (3) */
secp256k1_fe_normalize(&r->y);
- secp256k1_fe_mul_int(&r->x, 4 * (1 - a->infinity)); // r->x = X3 = 4*(R^2-Q)
- secp256k1_fe_mul_int(&r->y, 4 * (1 - a->infinity)); // r->y = Y3 = 4*R*(3*Q-2*R^2)-4*M^4 (4)
+ secp256k1_fe_mul_int(&r->x, 4 * (1 - a->infinity)); /* r->x = X3 = 4*(R^2-Q) */
+ secp256k1_fe_mul_int(&r->y, 4 * (1 - a->infinity)); /* r->y = Y3 = 4*R*(3*Q-2*R^2)-4*M^4 (4) */
- // In case a->infinity == 1, the above code results in r->x, r->y, and r->z all equal to 0.
- // Add b->x to x, b->y to y, and 1 to z in that case.
+ /** In case a->infinity == 1, the above code results in r->x, r->y, and r->z all equal to 0.
+ * Add b->x to x, b->y to y, and 1 to z in that case.
+ */
t = b->x; secp256k1_fe_mul_int(&t, a->infinity);
secp256k1_fe_add(&r->x, &t);
t = b->y; secp256k1_fe_mul_int(&t, a->infinity);
-void static secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a) {
+static void secp256k1_gej_get_hex(char *r, int *rlen, const secp256k1_gej_t *a) {
secp256k1_gej_t c = *a;
secp256k1_ge_t t; secp256k1_ge_set_gej(&t, &c);
secp256k1_ge_get_hex(r, rlen, &t);
}
#ifdef USE_ENDOMORPHISM
-void static secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
+static void secp256k1_gej_mul_lambda(secp256k1_gej_t *r, const secp256k1_gej_t *a) {
const secp256k1_fe_t *beta = &secp256k1_ge_consts->beta;
*r = *a;
secp256k1_fe_mul(&r->x, &r->x, beta);
}
-
-void static secp256k1_gej_split_exp_var(secp256k1_num_t *r1, secp256k1_num_t *r2, const secp256k1_num_t *a) {
- const secp256k1_ge_consts_t *c = secp256k1_ge_consts;
- secp256k1_num_t bnc1, bnc2, bnt1, bnt2, bnn2;
-
- secp256k1_num_copy(&bnn2, &c->order);
- secp256k1_num_shift(&bnn2, 1);
-
- secp256k1_num_mul(&bnc1, a, &c->a1b2);
- secp256k1_num_add(&bnc1, &bnc1, &bnn2);
- secp256k1_num_div(&bnc1, &bnc1, &c->order);
-
- secp256k1_num_mul(&bnc2, a, &c->b1);
- secp256k1_num_add(&bnc2, &bnc2, &bnn2);
- secp256k1_num_div(&bnc2, &bnc2, &c->order);
-
- secp256k1_num_mul(&bnt1, &bnc1, &c->a1b2);
- secp256k1_num_mul(&bnt2, &bnc2, &c->a2);
- secp256k1_num_add(&bnt1, &bnt1, &bnt2);
- secp256k1_num_sub(r1, a, &bnt1);
- secp256k1_num_mul(&bnt1, &bnc1, &c->b1);
- secp256k1_num_mul(&bnt2, &bnc2, &c->a1b2);
- secp256k1_num_sub(r2, &bnt1, &bnt2);
-}
#endif
-void static secp256k1_ge_start(void) {
+static void secp256k1_ge_start(void) {
static const unsigned char secp256k1_ge_consts_order[] = {
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,
0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFF,0xFE,
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_lambda[] = {
- 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
- };
+ /* 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
};
- static const unsigned char secp256k1_ge_consts_a1b2[] = {
- 0x30,0x86,0xd2,0x21,0xa7,0xd4,0x6b,0xcd,
- 0xe8,0x6c,0x90,0xe4,0x92,0x84,0xeb,0x15
- };
- static const unsigned char secp256k1_ge_consts_b1[] = {
- 0xe4,0x43,0x7e,0xd6,0x01,0x0e,0x88,0x28,
- 0x6f,0x54,0x7f,0xa9,0x0a,0xbf,0xe4,0xc3
- };
- static const unsigned char secp256k1_ge_consts_a2[] = {
- 0x01,
- 0x14,0xca,0x50,0xf7,0xa8,0xe2,0xf3,0xf6,
- 0x57,0xc1,0x10,0x8d,0x9d,0x44,0xcf,0xd8
- };
#endif
if (secp256k1_ge_consts == NULL) {
secp256k1_ge_consts_t *ret = (secp256k1_ge_consts_t*)malloc(sizeof(secp256k1_ge_consts_t));
secp256k1_num_copy(&ret->half_order, &ret->order);
secp256k1_num_shift(&ret->half_order, 1);
#ifdef USE_ENDOMORPHISM
- secp256k1_num_set_bin(&ret->lambda, secp256k1_ge_consts_lambda, sizeof(secp256k1_ge_consts_lambda));
- secp256k1_num_set_bin(&ret->a1b2, secp256k1_ge_consts_a1b2, sizeof(secp256k1_ge_consts_a1b2));
- secp256k1_num_set_bin(&ret->a2, secp256k1_ge_consts_a2, sizeof(secp256k1_ge_consts_a2));
- secp256k1_num_set_bin(&ret->b1, secp256k1_ge_consts_b1, sizeof(secp256k1_ge_consts_b1));
- secp256k1_fe_set_b32(&ret->beta, secp256k1_ge_consts_beta);
+ VERIFY_CHECK(secp256k1_fe_set_b32(&ret->beta, secp256k1_ge_consts_beta));
#endif
secp256k1_fe_t g_x, g_y;
- secp256k1_fe_set_b32(&g_x, secp256k1_ge_consts_g_x);
- secp256k1_fe_set_b32(&g_y, secp256k1_ge_consts_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;
}
}
-void static secp256k1_ge_stop(void) {
+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);
projects / secp256k1.git / blobdiff