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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"))
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