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Further improve doubling formula using fe_half

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This commit is contained in:
Peter Dettman 2021-12-23 14:18:46 +07:00
parent 557b31fac3
commit 4eb8b932ff
1 changed files with 20 additions and 20 deletions
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40
src/group_impl.h
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@ -271,36 +271,35 @@ static int secp256k1_ge_is_valid_var(const secp256k1_ge *a) {
}
static SECP256K1_INLINE void secp256k1_gej_double(secp256k1_gej *r, const secp256k1_gej *a) {
secp256k1_fe l, s, t, q;
/* Operations: 3 mul, 4 sqr, 8 add/half/mul_int/negate */
secp256k1_fe l, s, t;
r->infinity = a->infinity;
/* Formula used:
* L = (3/2) * X1^2
* S = Y1^2
* T = X1*S
* X3 = L^2 - 2*T
* Y3 = L*(T - X3) - S^2
* T = -X1*S
* X3 = L^2 + 2*T
* Y3 = -(L*(X3 + T) + S^2)
* Z3 = Y1*Z1
*/
secp256k1_fe_mul(&r->z, &a->z, &a->y); /* Z3 = Y1*Z1 (1) */
secp256k1_fe_sqr(&l, &a->x); /* L = X1^2 (1) */
secp256k1_fe_mul_int(&l, 3); /* L = 3*X1^2 (3) */
secp256k1_fe_half(&l); /* L = 3/2*X1^2 (2) */
secp256k1_fe_sqr(&s, &a->y); /* S = Y1^2 (1) */
secp256k1_fe_mul(&t, &a->x, &s); /* T = X1*S (1) */
q = t;
secp256k1_fe_add(&q, &t); /* Q = 2*T (2) */
secp256k1_fe_negate(&r->x, &q, 2); /* X3 = -2*T (3) */
secp256k1_fe_sqr(&q, &l); /* Q = L^2 (1) */
secp256k1_fe_add(&r->x, &q); /* X3 = L^2 - 2*T (4) */
secp256k1_fe_negate(&q, &r->x, 4); /* Q = -X3 (5) */
secp256k1_fe_add(&q, &t); /* Q = T-X3 (6) */
secp256k1_fe_mul(&q, &q, &l); /* Q = L*(T-X3) (1) */
secp256k1_fe_sqr(&s, &s);
secp256k1_fe_negate(&r->y, &s, 1); /* Y3 = -S^2 (2) */
secp256k1_fe_add(&r->y, &q); /* Y3 = L*(T-X3) - S^2 (3) */
secp256k1_fe_sqr(&s, &a->y); /* S = Y1^2 (1) */
secp256k1_fe_sqr(&l, &a->x); /* L = X1^2 (1) */
secp256k1_fe_mul_int(&l, 3); /* L = 3*X1^2 (3) */
secp256k1_fe_half(&l); /* L = 3/2*X1^2 (2) */
secp256k1_fe_negate(&t, &s, 1); /* T = -S (2) */
secp256k1_fe_mul(&t, &t, &a->x); /* T = -X1*S (1) */
secp256k1_fe_sqr(&r->x, &l); /* X3 = L^2 (1) */
secp256k1_fe_add(&r->x, &t); /* X3 = L^2 + T (2) */
secp256k1_fe_add(&r->x, &t); /* X3 = L^2 + 2*T (3) */
secp256k1_fe_sqr(&s, &s); /* S' = S^2 (1) */
secp256k1_fe_add(&t, &r->x); /* T' = X3 + T (4) */
secp256k1_fe_mul(&r->y, &t, &l); /* Y3 = L*(X3 + T) (1) */
secp256k1_fe_add(&r->y, &s); /* Y3 = L*(X3 + T) + S^2 (2) */
secp256k1_fe_negate(&r->y, &r->y, 2); /* Y3 = -(L*(X3 + T) + S^2) (3) */
}
static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, secp256k1_fe *rzr) {
@ -324,6 +323,7 @@ static void secp256k1_gej_double_var(secp256k1_gej *r, const secp256k1_gej *a, s
if (rzr != NULL) {
*rzr = a->y;
secp256k1_fe_normalize_weak(rzr);
}
secp256k1_gej_double(r, a);