from binascii import unhexlify from unittest import TestCase from pyecsca.ec.coordinates import AffineCoordinateModel from pyecsca.ec.curve import EllipticCurve from pyecsca.ec.params import get_params from pyecsca.ec.mod import Mod from pyecsca.ec.model import MontgomeryModel from pyecsca.ec.point import Point, InfinityPoint class CurveTests(TestCase): def setUp(self): self.secp128r1 = get_params("secg", "secp128r1", "projective") self.base = self.secp128r1.generator self.affine_base = self.base.to_affine() self.curve25519 = get_params("other", "Curve25519", "xz") self.ed25519 = get_params("other", "Ed25519", "projective") def test_init(self): with self.assertRaises(ValueError): EllipticCurve(MontgomeryModel(), self.secp128r1.curve.coordinate_model, 1, InfinityPoint(self.secp128r1.curve.coordinate_model), parameters={}) with self.assertRaises(ValueError): EllipticCurve(self.secp128r1.curve.model, self.secp128r1.curve.coordinate_model, 15, InfinityPoint(self.secp128r1.curve.coordinate_model), parameters={"c": 0}) with self.assertRaises(ValueError): EllipticCurve(self.secp128r1.curve.model, self.secp128r1.curve.coordinate_model, 15, InfinityPoint(self.secp128r1.curve.coordinate_model), parameters={"a": Mod(1, 5), "b": Mod(2, 5)}) def test_is_neutral(self): self.assertTrue(self.secp128r1.curve.is_neutral(InfinityPoint(self.secp128r1.curve.coordinate_model))) def test_is_on_curve(self): self.assertTrue(self.secp128r1.curve.is_on_curve(self.secp128r1.curve.neutral)) pt = Point(self.secp128r1.curve.coordinate_model, X=Mod(0x161ff7528b899b2d0c28607ca52c5b86, self.secp128r1.curve.prime), Y=Mod(0xcf5ac8395bafeb13c02da292dded7a83, self.secp128r1.curve.prime), Z=Mod(1, self.secp128r1.curve.prime)) self.assertTrue(self.secp128r1.curve.is_on_curve(pt)) self.assertTrue(self.secp128r1.curve.is_on_curve(pt.to_affine())) other = Point(self.secp128r1.curve.coordinate_model, X=Mod(0x161ff7528b899b2d0c28607ca52c5b86, self.secp128r1.curve.prime), Y=Mod(0xaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa, self.secp128r1.curve.prime), Z=Mod(1, self.secp128r1.curve.prime)) self.assertFalse(self.secp128r1.curve.is_on_curve(other)) self.assertFalse(self.secp128r1.curve.is_on_curve(self.curve25519.generator)) def test_affine_add(self): pt = Point(AffineCoordinateModel(self.secp128r1.curve.model), x=Mod(0xeb916224eda4fb356421773573297c15, self.secp128r1.curve.prime), y=Mod(0xbcdaf32a2c08fd4271228fef35070848, self.secp128r1.curve.prime)) self.assertIsNotNone(self.secp128r1.curve.affine_add(self.affine_base, pt)) added = self.secp128r1.curve.affine_add(self.affine_base, self.affine_base) doubled = self.secp128r1.curve.affine_double(self.affine_base) self.assertEqual(added, doubled) self.assertEqual(self.secp128r1.curve.affine_add(self.secp128r1.curve.neutral, pt), pt) self.assertEqual(self.secp128r1.curve.affine_add(pt, self.secp128r1.curve.neutral), pt) def test_affine_double(self): self.assertIsNotNone(self.secp128r1.curve.affine_double(self.affine_base)) self.assertEqual(self.secp128r1.curve.affine_double(self.secp128r1.curve.neutral), self.secp128r1.curve.neutral) def test_affine_negate(self): self.assertIsNotNone(self.secp128r1.curve.affine_negate(self.affine_base)) self.assertEqual(self.secp128r1.curve.affine_negate(self.secp128r1.curve.neutral), self.secp128r1.curve.neutral) with self.assertRaises(ValueError): self.secp128r1.curve.affine_negate(self.base) with self.assertRaises(ValueError): self.secp128r1.curve.affine_negate(self.curve25519.generator) def test_affine_multiply(self): expected = self.affine_base expected = self.secp128r1.curve.affine_double(expected) expected = self.secp128r1.curve.affine_double(expected) expected = self.secp128r1.curve.affine_add(expected, self.affine_base) expected = self.secp128r1.curve.affine_double(expected) self.assertEqual(self.secp128r1.curve.affine_multiply(self.affine_base, 10), expected) self.assertEqual(self.secp128r1.curve.affine_multiply(self.secp128r1.curve.neutral, 10), self.secp128r1.curve.neutral) with self.assertRaises(ValueError): self.secp128r1.curve.affine_multiply(self.base, 10) with self.assertRaises(ValueError): self.secp128r1.curve.affine_multiply(self.curve25519.generator, 10) def test_affine_neutral(self): self.assertIsNone(self.secp128r1.curve.affine_neutral) self.assertIsNone(self.curve25519.curve.affine_neutral) self.assertIsNotNone(self.ed25519.curve.affine_neutral) def test_affine_random(self): for params in [self.secp128r1, self.curve25519, self.ed25519]: for _ in range(20): pt = params.curve.affine_random() self.assertIsNotNone(pt) self.assertTrue(params.curve.is_on_curve(pt)) def test_neutral_is_affine(self): self.assertFalse(self.secp128r1.curve.neutral_is_affine) self.assertFalse(self.curve25519.curve.neutral_is_affine) self.assertTrue(self.ed25519.curve.neutral_is_affine) def test_eq(self): self.assertEqual(self.secp128r1.curve, self.secp128r1.curve) self.assertNotEqual(self.secp128r1.curve, self.curve25519.curve) self.assertNotEqual(self.secp128r1.curve, None) def test_decode(self): affine_curve = self.secp128r1.curve.to_affine() affine_point = self.secp128r1.generator.to_affine() decoded = affine_curve.decode_point(bytes(affine_point)) self.assertEqual(decoded, affine_point) affine_compressed_bytes = unhexlify("03161ff7528b899b2d0c28607ca52c5b86") decoded_compressed = affine_curve.decode_point(affine_compressed_bytes) self.assertEqual(decoded_compressed, affine_point) affine_compressed_bytes = unhexlify("02161ff7528b899b2d0c28607ca52c5b86") decoded_compressed = affine_curve.decode_point(affine_compressed_bytes) decoded_compressed = self.secp128r1.curve.affine_negate(decoded_compressed) self.assertEqual(decoded_compressed, affine_point) infinity_bytes = unhexlify("00") decoded_infinity = affine_curve.decode_point(infinity_bytes) self.assertEqual(affine_curve.neutral, decoded_infinity) with self.assertRaises(ValueError): affine_curve.decode_point(unhexlify("03161ff7528b899b2d0c28607ca52c5b")) with self.assertRaises(ValueError): affine_curve.decode_point(unhexlify("04161ff7528b899b2d0c28607ca52c5b2c5b2c5b2c5b")) with self.assertRaises(ValueError): affine_curve.decode_point(unhexlify("7a161ff7528b899b2d0c28607ca52c5b86")) with self.assertRaises(ValueError): affine_curve.decode_point(unhexlify("03161ff7528b899b2d0c28607ca52c5b88"))