diff --git a/sage/prove_group_implementations.sage b/sage/prove_group_implementations.sage index 652bd87f110b2..23799be52b6b1 100644 --- a/sage/prove_group_implementations.sage +++ b/sage/prove_group_implementations.sage @@ -148,7 +148,7 @@ def formula_secp256k1_gej_add_ge(branch, a, b): zeroes = {} nonzeroes = {} a_infinity = False - if (branch & 4) != 0: + if (branch & 2) != 0: nonzeroes.update({a.Infinity : 'a_infinite'}) a_infinity = True else: @@ -167,15 +167,11 @@ def formula_secp256k1_gej_add_ge(branch, a, b): m_alt = -u2 tt = u1 * m_alt rr = rr + tt - degenerate = (branch & 3) == 3 - if (branch & 1) != 0: + degenerate = (branch & 1) != 0 + if degenerate: zeroes.update({m : 'm_zero'}) else: nonzeroes.update({m : 'm_nonzero'}) - if (branch & 2) != 0: - zeroes.update({rr : 'rr_zero'}) - else: - nonzeroes.update({rr : 'rr_nonzero'}) rr_alt = s1 rr_alt = rr_alt * 2 m_alt = m_alt + u1 @@ -190,13 +186,6 @@ def formula_secp256k1_gej_add_ge(branch, a, b): n = m t = rr_alt^2 rz = a.Z * m_alt - infinity = False - if (branch & 8) != 0: - if not a_infinity: - infinity = True - zeroes.update({rz : 'r.z=0'}) - else: - nonzeroes.update({rz : 'r.z!=0'}) t = t + q rx = t t = t * 2 @@ -209,8 +198,11 @@ 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): @@ -280,14 +272,14 @@ if __name__ == "__main__": success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var) success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var) success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var) - success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge) + success = success & check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 8, formula_secp256k1_gej_add_ge) success = success & (not check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old)) if len(sys.argv) >= 2 and sys.argv[1] == "--exhaustive": success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43) success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43) success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43) - success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43) + success = success & check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 8, formula_secp256k1_gej_add_ge, 43) success = success & (not check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43)) sys.exit(int(not success)) diff --git a/src/group_impl.h b/src/group_impl.h index 3a57ee8ab0805..111ee68bab56a 100644 --- a/src/group_impl.h +++ b/src/group_impl.h @@ -532,11 +532,11 @@ 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: @@ -598,10 +598,9 @@ 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 = 0/0 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) & - secp256k1_fe_normalizes_to_zero(&rr); + /* 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 * a nontrivial cube root of one. In either case, an alternate @@ -613,7 +612,7 @@ static void secp256k1_gej_add_ge(secp256k1_gej *r, const secp256k1_gej *a, const secp256k1_fe_cmov(&rr_alt, &rr, !degenerate); secp256k1_fe_cmov(&m_alt, &m, !degenerate); - /* Now Ralt / Malt = lambda and is guaranteed not to be 0/0. + /* Now Ralt / Malt = lambda and is guaranteed not to be Ralt / 0. * From here on out Ralt and Malt represent the numerator * and denominator of lambda; R and M represent the explicit * expressions x1^2 + x2^2 + x1x2 and y1 + y2. */ @@ -628,7 +627,6 @@ 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) */ @@ -638,11 +636,28 @@ 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; + + /* Set r->infinity if r->z is 0. + * + * If a->infinity is set, then r->infinity = (r->z == 0) = (1 == 0) = false, + * which is correct because the function assumes that b is not infinity. + * + * Now assume !a->infinity. This implies Z = Z1 != 0. + * + * Case y1 = -y2: + * In this case we could have a = -b, namely if x1 = x2. + * We have degenerate = true, r->z = (x1 - x2) * Z. + * Then r->infinity = ((x1 - x2)Z == 0) = (x1 == x2) = (a == -b). + * + * Case y1 != -y2: + * In this case, we can't have a = -b. + * 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) {