From 39bff708309e27d6c3606f911d02282b890fe3f0 Mon Sep 17 00:00:00 2001 From: Tim Ruffing Date: Fri, 4 Feb 2022 15:24:33 +0100 Subject: [PATCH] group: Further simply gej_add_ge --- sage/prove_group_implementations.sage | 11 ++++------- src/group_impl.h | 25 ++++++++++++++++++------- 2 files changed, 22 insertions(+), 14 deletions(-) diff --git a/sage/prove_group_implementations.sage b/sage/prove_group_implementations.sage index b6bdfa3e76..3aa5ad911e 100644 --- a/sage/prove_group_implementations.sage +++ b/sage/prove_group_implementations.sage @@ -195,12 +195,6 @@ def formula_secp256k1_gej_add_ge(branch, a, b): n = m t = rr_alt^2 rz = a.Z * m_alt - infinity = False - if (branch & 4) != 0: - infinity = True - zeroes.update({rz : 'r.z = 0'}) - else: - nonzeroes.update({rz : 'r.z != 0'}) t = t + q rx = t t = t * 2 @@ -213,8 +207,11 @@ def formula_secp256k1_gej_add_ge(branch, a, b): rx = b.X ry = b.Y rz = 1 - if infinity: + if (branch & 4) != 0: + zeroes.update({rz : 'r.z = 0'}) return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity()) + else: + nonzeroes.update({rz : 'r.z != 0'}) return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), jacobianpoint(rx, ry, rz)) def formula_secp256k1_gej_add_ge_old(branch, a, b): diff --git a/src/group_impl.h b/src/group_impl.h index a028cc53c6..118fc749b0 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -492,11 +492,11 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const /* Operations: 7 mul, 5 sqr, 24 add/cmov/half/mul_int/negate/normalize_weak/normalizes_to_zero */ secp256k1_fe zz, u1, u2, s1, s2, t, tt, m, n, q, rr; secp256k1_fe m_alt, rr_alt; - int infinity, degenerate; + int degenerate; VERIFY_CHECK(!b->infinity); VERIFY_CHECK(a->infinity == 0 || a->infinity == 1); - /** In: + /* 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: @@ -558,8 +558,8 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_fe_negate(&m_alt, &u2, 1); /* Malt = -X2*Z1^2 */ secp256k1_fe_mul(&tt, &u1, &m_alt); /* tt = -U1*U2 (2) */ secp256k1_fe_add(&rr, &tt); /* rr = R = T^2-U1*U2 (3) */ - /** If lambda = R/M = R/0 we have a problem (except in the "trivial" - * case that Z = z1z2 = 0, and this is special-cased later on). */ + /* If lambda = R/M = R/0 we have a problem (except in the "trivial" + * case that Z = z1z2 = 0, and this is special-cased later on). */ degenerate = secp256k1_fe_normalizes_to_zero(&m); /* This only occurs when y1 == -y2 and x1^3 == x2^3, but x1 != x2. * This means either x1 == beta*x2 or beta*x1 == x2, where beta is @@ -587,7 +587,6 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_fe_cmov(&n, &m, degenerate); /* n = M^3 * Malt (2) */ secp256k1_fe_sqr(&t, &rr_alt); /* t = Ralt^2 (1) */ secp256k1_fe_mul(&r->z, &a->z, &m_alt); /* r->z = Z3 = Malt*Z (1) */ - infinity = secp256k1_fe_normalizes_to_zero(&r->z) & ~a->infinity; secp256k1_fe_add(&t, &q); /* t = Ralt^2 + Q (2) */ r->x = t; /* r->x = X3 = Ralt^2 + Q (2) */ secp256k1_fe_mul_int(&t, 2); /* t = 2*X3 (4) */ @@ -597,11 +596,23 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_fe_negate(&r->y, &t, 3); /* r->y = -(Ralt*(2*X3 + Q) + M^3*Malt) (4) */ secp256k1_fe_half(&r->y); /* r->y = Y3 = -(Ralt*(2*X3 + Q) + M^3*Malt)/2 (3) */ - /** In case a->infinity == 1, replace r with (b->x, b->y, 1). */ + /* In case a->infinity == 1, replace r with (b->x, b->y, 1). */ secp256k1_fe_cmov(&r->x, &b->x, a->infinity); secp256k1_fe_cmov(&r->y, &b->y, a->infinity); secp256k1_fe_cmov(&r->z, &secp256k1_fe_one, a->infinity); - r->infinity = infinity; + + /* If a->infinity = 1 then r->infinity = (r->z == 0) = (1 == 0) = false. + * + * Now assume a->infinity = 0. This implies Z = Z1 != 0. + * + * Case y1 = -y2: + * We have degenerate = true, r->z = (x1 - x2) * Z. + * Then r->infinity = ((x1 - x2)Z == 0) = (x1 == -x2) = (a == -b). + * + * Case y1 != -y2: + * We have degenerate = false, r->z = (y1 + y2) * Z. + * Then r->infinity = ((y1 + y2)Z == 0) = (y1 == y2) = false. */ + r->infinity = secp256k1_fe_normalizes_to_zero(&r->z); } static void secp256k1_gej_rescale(secp256k1_gej *r, const secp256k1_fe *s) {