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Switch to C89 comments in prep for making the whole codebase C89 compatible.

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This commit is contained in:
Gregory Maxwell
2014-11-15 15:28:10 +00:00
parent 21288f2d05
commit 71712b27e5
38 changed files with 802 additions and 716 deletions
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155
src/group_impl.h
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@@ -1,6 +1,8 @@
// 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_
@@ -176,10 +178,11 @@ static int secp256k1_gej_is_infinity(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);
@@ -194,7 +197,7 @@ static int secp256k1_gej_is_valid(const secp256k1_gej_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);
@@ -219,25 +222,25 @@ static void secp256k1_gej_double_var(secp256k1_gej_t *r, const secp256k1_gej_t *
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_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_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(&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)
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;
}
@@ -329,63 +332,65 @@ static void secp256k1_gej_add_ge(secp256k1_gej_t *r, const secp256k1_gej_t *a, c
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.)
/** 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_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);
@@ -456,7 +461,7 @@ static void secp256k1_ge_start(void) {
0x9C,0x47,0xD0,0x8F,0xFB,0x10,0xD4,0xB8
};
#ifdef USE_ENDOMORPHISM
// properties of secp256k1's efficiently computable 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,