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Diffstat (limited to 'crypto/secp256k1/libsecp256k1/sage/secp256k1.sage')
| -rw-r--r-- | crypto/secp256k1/libsecp256k1/sage/secp256k1.sage | 306 |
1 files changed, 306 insertions, 0 deletions
diff --git a/crypto/secp256k1/libsecp256k1/sage/secp256k1.sage b/crypto/secp256k1/libsecp256k1/sage/secp256k1.sage new file mode 100644 index 000000000..a97e732f7 --- /dev/null +++ b/crypto/secp256k1/libsecp256k1/sage/secp256k1.sage @@ -0,0 +1,306 @@ +# Test libsecp256k1' group operation implementations using prover.sage + +import sys + +load("group_prover.sage") +load("weierstrass_prover.sage") + +def formula_secp256k1_gej_double_var(a): + """libsecp256k1's secp256k1_gej_double_var, used by various addition functions""" + rz = a.Z * a.Y + rz = rz * 2 + t1 = a.X^2 + t1 = t1 * 3 + t2 = t1^2 + t3 = a.Y^2 + t3 = t3 * 2 + t4 = t3^2 + t4 = t4 * 2 + t3 = t3 * a.X + rx = t3 + rx = rx * 4 + rx = -rx + rx = rx + t2 + t2 = -t2 + t3 = t3 * 6 + t3 = t3 + t2 + ry = t1 * t3 + t2 = -t4 + ry = ry + t2 + return jacobianpoint(rx, ry, rz) + +def formula_secp256k1_gej_add_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_var""" + if branch == 0: + return (constraints(), constraints(nonzero={a.Infinity : 'a_infinite'}), b) + if branch == 1: + return (constraints(), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a) + z22 = b.Z^2 + z12 = a.Z^2 + u1 = a.X * z22 + u2 = b.X * z12 + s1 = a.Y * z22 + s1 = s1 * b.Z + s2 = b.Y * z12 + s2 = s2 * a.Z + h = -u1 + h = h + u2 + i = -s1 + i = i + s2 + if branch == 2: + r = formula_secp256k1_gej_double_var(a) + return (constraints(), constraints(zero={h : 'h=0', i : 'i=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}), r) + if branch == 3: + return (constraints(), constraints(zero={h : 'h=0', a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={i : 'i!=0'}), point_at_infinity()) + i2 = i^2 + h2 = h^2 + h3 = h2 * h + h = h * b.Z + rz = a.Z * h + t = u1 * h2 + rx = t + rx = rx * 2 + rx = rx + h3 + rx = -rx + rx = rx + i2 + ry = -rx + ry = ry + t + ry = ry * i + h3 = h3 * s1 + h3 = -h3 + ry = ry + h3 + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_ge_var, which assume bz==1""" + if branch == 0: + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(nonzero={a.Infinity : 'a_infinite'}), b) + if branch == 1: + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite'}, nonzero={b.Infinity : 'b_infinite'}), a) + z12 = a.Z^2 + u1 = a.X + u2 = b.X * z12 + s1 = a.Y + s2 = b.Y * z12 + s2 = s2 * a.Z + h = -u1 + h = h + u2 + i = -s1 + i = i + s2 + if (branch == 2): + r = formula_secp256k1_gej_double_var(a) + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r) + if (branch == 3): + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity()) + i2 = i^2 + h2 = h^2 + h3 = h * h2 + rz = a.Z * h + t = u1 * h2 + rx = t + rx = rx * 2 + rx = rx + h3 + rx = -rx + rx = rx + i2 + ry = -rx + ry = ry + t + ry = ry * i + h3 = h3 * s1 + h3 = -h3 + ry = ry + h3 + return (constraints(zero={b.Z - 1 : 'b.z=1'}), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_zinv_var(branch, a, b): + """libsecp256k1's secp256k1_gej_add_zinv_var""" + bzinv = b.Z^(-1) + if branch == 0: + return (constraints(), constraints(nonzero={b.Infinity : 'b_infinite'}), a) + if branch == 1: + bzinv2 = bzinv^2 + bzinv3 = bzinv2 * bzinv + rx = b.X * bzinv2 + ry = b.Y * bzinv3 + rz = 1 + return (constraints(), constraints(zero={b.Infinity : 'b_finite'}, nonzero={a.Infinity : 'a_infinite'}), jacobianpoint(rx, ry, rz)) + azz = a.Z * bzinv + z12 = azz^2 + u1 = a.X + u2 = b.X * z12 + s1 = a.Y + s2 = b.Y * z12 + s2 = s2 * azz + h = -u1 + h = h + u2 + i = -s1 + i = i + s2 + if branch == 2: + r = formula_secp256k1_gej_double_var(a) + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0', i : 'i=0'}), r) + if branch == 3: + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite', h : 'h=0'}, nonzero={i : 'i!=0'}), point_at_infinity()) + i2 = i^2 + h2 = h^2 + h3 = h * h2 + rz = a.Z + rz = rz * h + t = u1 * h2 + rx = t + rx = rx * 2 + rx = rx + h3 + rx = -rx + rx = rx + i2 + ry = -rx + ry = ry + t + ry = ry * i + h3 = h3 * s1 + h3 = -h3 + ry = ry + h3 + return (constraints(), constraints(zero={a.Infinity : 'a_finite', b.Infinity : 'b_finite'}, nonzero={h : 'h!=0'}), jacobianpoint(rx, ry, rz)) + +def formula_secp256k1_gej_add_ge(branch, a, b): + """libsecp256k1's secp256k1_gej_add_ge""" + zeroes = {} + nonzeroes = {} + a_infinity = False + if (branch & 4) != 0: + nonzeroes.update({a.Infinity : 'a_infinite'}) + a_infinity = True + else: + zeroes.update({a.Infinity : 'a_finite'}) + zz = a.Z^2 + u1 = a.X + u2 = b.X * zz + s1 = a.Y + s2 = b.Y * zz + s2 = s2 * a.Z + t = u1 + t = t + u2 + m = s1 + m = m + s2 + rr = t^2 + m_alt = -u2 + tt = u1 * m_alt + rr = rr + tt + degenerate = (branch & 3) == 3 + if (branch & 1) != 0: + 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 + if not degenerate: + rr_alt = rr + m_alt = m + n = m_alt^2 + q = n * t + n = n^2 + if degenerate: + 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'}) + rz = rz * 2 + q = -q + t = t + q + rx = t + t = t * 2 + t = t + q + t = t * rr_alt + t = t + n + ry = -t + rx = rx * 4 + ry = ry * 4 + if a_infinity: + rx = b.X + ry = b.Y + rz = 1 + if infinity: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zeroes, nonzero=nonzeroes), point_at_infinity()) + 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): + """libsecp256k1's old secp256k1_gej_add_ge, which fails when ay+by=0 but ax!=bx""" + a_infinity = (branch & 1) != 0 + zero = {} + nonzero = {} + if a_infinity: + nonzero.update({a.Infinity : 'a_infinite'}) + else: + zero.update({a.Infinity : 'a_finite'}) + zz = a.Z^2 + u1 = a.X + u2 = b.X * zz + s1 = a.Y + s2 = b.Y * zz + s2 = s2 * a.Z + z = a.Z + t = u1 + t = t + u2 + m = s1 + m = m + s2 + n = m^2 + q = n * t + n = n^2 + rr = t^2 + t = u1 * u2 + t = -t + rr = rr + t + t = rr^2 + rz = m * z + infinity = False + if (branch & 2) != 0: + if not a_infinity: + infinity = True + else: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(nonzero={z : 'conflict_a'}, zero={z : 'conflict_b'}), point_at_infinity()) + zero.update({rz : 'r.z=0'}) + else: + nonzero.update({rz : 'r.z!=0'}) + rz = rz * (0 if a_infinity else 2) + rx = t + q = -q + rx = rx + q + q = q * 3 + t = t * 2 + t = t + q + t = t * rr + t = t + n + ry = -t + rx = rx * (0 if a_infinity else 4) + ry = ry * (0 if a_infinity else 4) + t = b.X + t = t * (1 if a_infinity else 0) + rx = rx + t + t = b.Y + t = t * (1 if a_infinity else 0) + ry = ry + t + t = (1 if a_infinity else 0) + rz = rz + t + if infinity: + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), point_at_infinity()) + return (constraints(zero={b.Z - 1 : 'b.z=1', b.Infinity : 'b_finite'}), constraints(zero=zero, nonzero=nonzero), jacobianpoint(rx, ry, rz)) + +if __name__ == "__main__": + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var) + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var) + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var) + check_symbolic_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge) + 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": + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_var", 0, 7, 5, formula_secp256k1_gej_add_var, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_var", 0, 7, 5, formula_secp256k1_gej_add_ge_var, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_zinv_var", 0, 7, 5, formula_secp256k1_gej_add_zinv_var, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge", 0, 7, 16, formula_secp256k1_gej_add_ge, 43) + check_exhaustive_jacobian_weierstrass("secp256k1_gej_add_ge_old [should fail]", 0, 7, 4, formula_secp256k1_gej_add_ge_old, 43) |