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-rw-r--r--src/secp256k1/src/group_impl.h519
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diff --git a/src/secp256k1/src/group_impl.h b/src/secp256k1/src/group_impl.h
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+/**********************************************************************
+ * 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 <string.h>
+
+#include "num.h"
+#include "field.h"
+#include "group.h"
+
+static void secp256k1_ge_set_infinity(secp256k1_ge_t *r) {
+ r->infinity = 1;
+}
+
+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;
+}
+
+static int secp256k1_ge_is_infinity(const secp256k1_ge_t *a) {
+ return a->infinity;
+}
+
+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_normalize(&r->y);
+ secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+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);
+ secp256k1_fe_get_hex(cy, &ly, &a->y);
+ lx = strlen(cx);
+ ly = strlen(cy);
+ int len = lx + ly + 3 + 1;
+ if (*rlen < len) {
+ *rlen = len;
+ return;
+ }
+ *rlen = len;
+ r[0] = '(';
+ memcpy(r+1, cx, lx);
+ r[1+lx] = ',';
+ memcpy(r+2+lx, cy, ly);
+ r[2+lx+ly] = ')';
+ r[3+lx+ly] = 0;
+}
+
+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);
+ secp256k1_fe_t z3; secp256k1_fe_mul(&z3, &a->z, &z2);
+ secp256k1_fe_mul(&a->x, &a->x, &z2);
+ secp256k1_fe_mul(&a->y, &a->y, &z3);
+ secp256k1_fe_set_int(&a->z, 1);
+ r->x = a->x;
+ r->y = a->y;
+}
+
+static void secp256k1_ge_set_gej_var(secp256k1_ge_t *r, secp256k1_gej_t *a) {
+ r->infinity = a->infinity;
+ if (a->infinity) {
+ return;
+ }
+ secp256k1_fe_inv_var(&a->z, &a->z);
+ secp256k1_fe_t z2; secp256k1_fe_sqr(&z2, &a->z);
+ secp256k1_fe_t z3; secp256k1_fe_mul(&z3, &a->z, &z2);
+ secp256k1_fe_mul(&a->x, &a->x, &z2);
+ secp256k1_fe_mul(&a->y, &a->y, &z3);
+ secp256k1_fe_set_int(&a->z, 1);
+ r->x = a->x;
+ r->y = a->y;
+}
+
+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 (size_t i=0; i<len; i++) {
+ if (!a[i].infinity) {
+ az[count++] = a[i].z;
+ }
+ }
+
+ secp256k1_fe_t azi[count];
+ secp256k1_fe_inv_all_var(count, azi, az);
+
+ count = 0;
+ for (size_t i=0; i<len; i++) {
+ r[i].infinity = a[i].infinity;
+ if (!a[i].infinity) {
+ secp256k1_fe_t *zi = &azi[count++];
+ secp256k1_fe_t zi2; secp256k1_fe_sqr(&zi2, zi);
+ secp256k1_fe_t zi3; secp256k1_fe_mul(&zi3, &zi2, zi);
+ secp256k1_fe_mul(&r[i].x, &a[i].x, &zi2);
+ secp256k1_fe_mul(&r[i].y, &a[i].y, &zi3);
+ }
+ }
+}
+
+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);
+}
+
+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);
+}
+
+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);
+}
+
+static void secp256k1_ge_clear(secp256k1_ge_t *r) {
+ r->infinity = 0;
+ secp256k1_fe_clear(&r->x);
+ secp256k1_fe_clear(&r->y);
+}
+
+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);
+ r->infinity = 0;
+ secp256k1_fe_t c; secp256k1_fe_set_int(&c, 7);
+ secp256k1_fe_add(&c, &x3);
+ if (!secp256k1_fe_sqrt(&r->y, &c))
+ return 0;
+ secp256k1_fe_normalize(&r->y);
+ if (secp256k1_fe_is_odd(&r->y) != odd)
+ secp256k1_fe_negate(&r->y, &r->y, 1);
+ return 1;
+}
+
+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);
+}
+
+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);
+}
+
+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;
+ r->z = a->z;
+ secp256k1_fe_normalize(&r->y);
+ secp256k1_fe_negate(&r->y, &r->y, 1);
+}
+
+static int secp256k1_gej_is_infinity(const secp256k1_gej_t *a) {
+ return a->infinity;
+}
+
+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
+ */
+ 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);
+ secp256k1_fe_t z6; secp256k1_fe_sqr(&z6, &z2); secp256k1_fe_mul(&z6, &z6, &z2);
+ secp256k1_fe_mul_int(&z6, 7);
+ secp256k1_fe_add(&x3, &z6);
+ secp256k1_fe_normalize(&y2);
+ secp256k1_fe_normalize(&x3);
+ return secp256k1_fe_equal(&y2, &x3);
+}
+
+static int secp256k1_ge_is_valid(const secp256k1_ge_t *a) {
+ if (a->infinity)
+ return 0;
+ /* 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);
+ secp256k1_fe_add(&x3, &c);
+ secp256k1_fe_normalize(&y2);
+ secp256k1_fe_normalize(&x3);
+ return secp256k1_fe_equal(&y2, &x3);
+}
+
+static void 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;
+ 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_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_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) */
+ 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;
+}
+
+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;
+ }
+ if (b->infinity) {
+ *r = *a;
+ return;
+ }
+ r->infinity = 0;
+ secp256k1_fe_t z22; secp256k1_fe_sqr(&z22, &b->z);
+ secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &a->z);
+ secp256k1_fe_t u1; secp256k1_fe_mul(&u1, &a->x, &z22);
+ secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
+ secp256k1_fe_t s1; secp256k1_fe_mul(&s1, &a->y, &z22); secp256k1_fe_mul(&s1, &s1, &b->z);
+ secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+ secp256k1_fe_normalize(&u1);
+ secp256k1_fe_normalize(&u2);
+ if (secp256k1_fe_equal(&u1, &u2)) {
+ secp256k1_fe_normalize(&s1);
+ secp256k1_fe_normalize(&s2);
+ if (secp256k1_fe_equal(&s1, &s2)) {
+ secp256k1_gej_double_var(r, a);
+ } else {
+ r->infinity = 1;
+ }
+ return;
+ }
+ secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+ secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+ secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
+ secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
+ secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
+ secp256k1_fe_mul(&r->z, &a->z, &b->z); secp256k1_fe_mul(&r->z, &r->z, &h);
+ secp256k1_fe_t t; secp256k1_fe_mul(&t, &u1, &h2);
+ r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+ secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+ secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+ secp256k1_fe_add(&r->y, &h3);
+}
+
+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;
+ r->y = b->y;
+ secp256k1_fe_set_int(&r->z, 1);
+ return;
+ }
+ if (b->infinity) {
+ *r = *a;
+ return;
+ }
+ r->infinity = 0;
+ secp256k1_fe_t z12; secp256k1_fe_sqr(&z12, &a->z);
+ secp256k1_fe_t u1 = a->x; secp256k1_fe_normalize(&u1);
+ secp256k1_fe_t u2; secp256k1_fe_mul(&u2, &b->x, &z12);
+ secp256k1_fe_t s1 = a->y; secp256k1_fe_normalize(&s1);
+ secp256k1_fe_t s2; secp256k1_fe_mul(&s2, &b->y, &z12); secp256k1_fe_mul(&s2, &s2, &a->z);
+ secp256k1_fe_normalize(&u1);
+ secp256k1_fe_normalize(&u2);
+ if (secp256k1_fe_equal(&u1, &u2)) {
+ secp256k1_fe_normalize(&s1);
+ secp256k1_fe_normalize(&s2);
+ if (secp256k1_fe_equal(&s1, &s2)) {
+ secp256k1_gej_double_var(r, a);
+ } else {
+ r->infinity = 1;
+ }
+ return;
+ }
+ secp256k1_fe_t h; secp256k1_fe_negate(&h, &u1, 1); secp256k1_fe_add(&h, &u2);
+ secp256k1_fe_t i; secp256k1_fe_negate(&i, &s1, 1); secp256k1_fe_add(&i, &s2);
+ secp256k1_fe_t i2; secp256k1_fe_sqr(&i2, &i);
+ secp256k1_fe_t h2; secp256k1_fe_sqr(&h2, &h);
+ secp256k1_fe_t h3; secp256k1_fe_mul(&h3, &h, &h2);
+ r->z = a->z; secp256k1_fe_mul(&r->z, &r->z, &h);
+ secp256k1_fe_t t; secp256k1_fe_mul(&t, &u1, &h2);
+ r->x = t; secp256k1_fe_mul_int(&r->x, 2); secp256k1_fe_add(&r->x, &h3); secp256k1_fe_negate(&r->x, &r->x, 3); secp256k1_fe_add(&r->x, &i2);
+ secp256k1_fe_negate(&r->y, &r->x, 5); secp256k1_fe_add(&r->y, &t); secp256k1_fe_mul(&r->y, &r->y, &i);
+ secp256k1_fe_mul(&h3, &h3, &s1); secp256k1_fe_negate(&h3, &h3, 1);
+ secp256k1_fe_add(&r->y, &h3);
+}
+
+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) */
+ 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_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_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) */
+
+ /** 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);
+ secp256k1_fe_add(&r->y, &t);
+ secp256k1_fe_set_int(&t, a->infinity);
+ secp256k1_fe_add(&r->z, &t);
+ r->infinity = infinity;
+}
+
+
+
+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
+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);
+}
+
+static void 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
+
+
+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,
+ 0xBA,0xAE,0xDC,0xE6,0xAF,0x48,0xA0,0x3B,
+ 0xBF,0xD2,0x5E,0x8C,0xD0,0x36,0x41,0x41
+ };
+ 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_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
+ };
+ 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_set_bin(&ret->order, secp256k1_ge_consts_order, sizeof(secp256k1_ge_consts_order));
+ 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);
+#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);
+ 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
generated by cgit v1.2.3 (git 2.26.2) at 2024-09-02 04:03:12 +0000