from sympy import FF, symbols from unittest import TestCase from pyecsca.ec.mod import Mod, gcd, extgcd, Undefined, miller_rabin, has_gmp, RawMod, SymbolicMod, jacobi from pyecsca.ec.error import NonInvertibleError, NonResidueError, NonInvertibleWarning, NonResidueWarning from pyecsca.misc.cfg import getconfig, TemporaryConfig class ModTests(TestCase): def test_gcd(self): self.assertEqual(gcd(15, 20), 5) self.assertEqual(extgcd(15, 0), (1, 0, 15)) self.assertEqual(extgcd(15, 20), (-1, 1, 5)) def test_jacobi(self): self.assertEqual(jacobi(5, 1153486465415345646578465454655646543248656451), 1) self.assertEqual(jacobi(564786456646845, 46874698564153465453246546545456849797895547657), -1) self.assertEqual(jacobi(564786456646845, 46874698564153465453246546545456849797895), 0) def test_miller_rabin(self): self.assertTrue(miller_rabin(2)) self.assertTrue(miller_rabin(3)) self.assertTrue(miller_rabin(5)) self.assertFalse(miller_rabin(8)) self.assertTrue(miller_rabin(0xe807561107ccf8fa82af74fd492543a918ca2e9c13750233a9)) self.assertFalse(miller_rabin(0x6f6889deb08da211927370810f026eb4c17b17755f72ea005)) def test_inverse(self): p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff self.assertEqual(Mod(0x702bdafd3c1c837b23a1cb196ed7f9fadb333c5cfe4a462be32adcd67bfb6ac1, p).inverse(), Mod(0x1cb2e5274bba085c4ca88eede75ae77949e7a410c80368376e97ab22eb590f9d, p)) with self.assertRaises(NonInvertibleError): Mod(0, p).inverse() with self.assertRaises(NonInvertibleError): Mod(5, 10).inverse() getconfig().ec.no_inverse_action = "warning" with self.assertRaises(NonInvertibleWarning): Mod(0, p).inverse() with self.assertRaises(NonInvertibleWarning): Mod(5, 10).inverse() getconfig().ec.no_inverse_action = "ignore" Mod(0, p).inverse() Mod(5, 10).inverse() getconfig().ec.no_inverse_action = "error" def test_is_residue(self): self.assertTrue(Mod(4, 11).is_residue()) self.assertFalse(Mod(11, 31).is_residue()) self.assertTrue(Mod(0, 7).is_residue()) self.assertTrue(Mod(1, 2).is_residue()) def test_sqrt(self): p = 0xffffffff00000001000000000000000000000000ffffffffffffffffffffffff self.assertIn(Mod(0xffffffff00000001000000000000000000000000fffffffffffffffffffffffc, p).sqrt(), (0x9add512515b70d9ec471151c1dec46625cd18b37bde7ca7fb2c8b31d7033599d, 0x6522aed9ea48f2623b8eeae3e213b99da32e74c9421835804d374ce28fcca662)) with self.assertRaises(NonResidueError): Mod(0x702bdafd3c1c837b23a1cb196ed7f9fadb333c5cfe4a462be32adcd67bfb6ac1, p).sqrt() getconfig().ec.non_residue_action = "warning" with self.assertRaises(NonResidueWarning): Mod(0x702bdafd3c1c837b23a1cb196ed7f9fadb333c5cfe4a462be32adcd67bfb6ac1, p).sqrt() getconfig().ec.non_residue_action = "ignore" Mod(0x702bdafd3c1c837b23a1cb196ed7f9fadb333c5cfe4a462be32adcd67bfb6ac1, p).sqrt() with TemporaryConfig() as cfg: cfg.ec.non_residue_action = "warning" with self.assertRaises(NonResidueWarning): Mod(0x702bdafd3c1c837b23a1cb196ed7f9fadb333c5cfe4a462be32adcd67bfb6ac1, p).sqrt() self.assertEqual(Mod(0, p).sqrt(), Mod(0, p)) q = 0x75d44fee9a71841ae8403c0c251fbad self.assertIn(Mod(0x591e0db18cf1bd81a11b2985a821eb3, q).sqrt(), (0x113b41a1a2b73f636e73be3f9a3716e, 0x64990e4cf7ba44b779cc7dcc8ae8a3f)) getconfig().ec.non_residue_action = "error" def test_eq(self): self.assertEqual(Mod(1, 7), 1) self.assertNotEqual(Mod(1, 7), "1") self.assertEqual(Mod(1, 7), Mod(1, 7)) self.assertNotEqual(Mod(1, 7), Mod(5, 7)) self.assertNotEqual(Mod(1, 7), Mod(1, 5)) def test_pow(self): a = Mod(5, 7) self.assertEqual(a**(-1), a.inverse()) self.assertEqual(a**0, Mod(1, 7)) self.assertEqual(a**(-2), a.inverse()**2) def test_wrong_mod(self): a = Mod(5, 7) b = Mod(4, 11) with self.assertRaises(ValueError): a + b def test_wrong_pow(self): a = Mod(5, 7) c = Mod(4, 11) with self.assertRaises(TypeError): a**c def test_other(self): a = Mod(5, 7) b = Mod(3, 7) self.assertEqual(int(-a), 2) self.assertEqual(str(a), "5") self.assertEqual(6 - a, Mod(1, 7)) self.assertNotEqual(a, b) self.assertEqual(a / b, Mod(4, 7)) self.assertEqual(a // b, Mod(4, 7)) self.assertEqual(5 / b, Mod(4, 7)) self.assertEqual(5 // b, Mod(4, 7)) self.assertEqual(a / 3, Mod(4, 7)) self.assertEqual(a // 3, Mod(4, 7)) self.assertEqual(divmod(a, b), (Mod(1, 7), Mod(2, 7))) self.assertEqual(a + b, Mod(1, 7)) self.assertEqual(5 + b, Mod(1, 7)) self.assertEqual(a + 3, Mod(1, 7)) self.assertNotEqual(a, 6) self.assertIsNotNone(hash(a)) def test_undefined(self): u = Undefined() for k, meth in u.__class__.__dict__.items(): if k in ("__module__", "__new__", "__init__", "__doc__", "__hash__", "__abstractmethods__", "_abc_impl"): continue args = [5 for _ in range(meth.__code__.co_argcount - 1)] if k == "__repr__": self.assertEqual(meth(u), "Undefined") elif k in ("__eq__", "__ne__"): assert not meth(u, *args) else: with self.assertRaises(NotImplementedError): meth(u, *args) def test_implementation(self): if not has_gmp: self.skipTest("Only makes sense if more Mod implementations are available.") with TemporaryConfig() as cfg: cfg.ec.mod_implementation = "python" self.assertIsInstance(Mod(5, 7), RawMod) def test_symbolic(self): x, y = symbols("x y") p = 13 k = FF(p) sx = SymbolicMod(x, p) a = k(3) b = k(5) r = sx * a + b self.assertIsInstance(r, SymbolicMod) self.assertEqual(r.n, p) sa = SymbolicMod(a, p) sb = SymbolicMod(b, p) self.assertEqual(sa, 3) self.assertEqual(sa.inverse(), SymbolicMod(k(9), p)) self.assertEqual(1 / sa, SymbolicMod(k(9), p)) self.assertEqual(sa + sb, 8) self.assertEqual(1 + sa, 4) self.assertEqual(sa - 1, 2) self.assertEqual(1 - sa, 11) self.assertEqual(sa + 1, 4) self.assertEqual(-sa, 10) self.assertEqual(sa / 2, 8) self.assertEqual(2 / sa, 5) self.assertEqual(sa // 2, 8) self.assertEqual(2 // sa, 5) self.assertEqual(int(sa), 3) self.assertNotEqual(sa, sb) self.assertIsNotNone(hash(sa))