398 lines
11 KiB
Python
398 lines
11 KiB
Python
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import pickle
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try:
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import unittest2 as unittest
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except ImportError:
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import unittest
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import hypothesis.strategies as st
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from hypothesis import given, assume, settings, example
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from .ellipticcurve import CurveFp, Point, PointJacobi, INFINITY
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from .ecdsa import generator_256, curve_256, generator_224
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from .numbertheory import inverse_mod
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class TestJacobi(unittest.TestCase):
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def test___init__(self):
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curve = object()
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x = 2
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y = 3
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z = 1
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order = 4
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pj = PointJacobi(curve, x, y, z, order)
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self.assertEqual(pj.order(), order)
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self.assertIs(pj.curve(), curve)
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self.assertEqual(pj.x(), x)
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self.assertEqual(pj.y(), y)
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def test_add_with_different_curves(self):
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p_a = PointJacobi.from_affine(generator_256)
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p_b = PointJacobi.from_affine(generator_224)
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with self.assertRaises(ValueError):
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p_a + p_b
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def test_compare_different_curves(self):
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self.assertNotEqual(generator_256, generator_224)
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def test_equality_with_non_point(self):
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pj = PointJacobi.from_affine(generator_256)
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self.assertNotEqual(pj, "value")
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def test_conversion(self):
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pj = PointJacobi.from_affine(generator_256)
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pw = pj.to_affine()
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self.assertEqual(generator_256, pw)
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def test_single_double(self):
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pj = PointJacobi.from_affine(generator_256)
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pw = generator_256.double()
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pj = pj.double()
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self.assertEqual(pj.x(), pw.x())
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self.assertEqual(pj.y(), pw.y())
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def test_double_with_zero_point(self):
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pj = PointJacobi(curve_256, 0, 0, 1)
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pj = pj.double()
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self.assertIs(pj, INFINITY)
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def test_double_with_zero_equivalent_point(self):
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pj = PointJacobi(curve_256, 0, curve_256.p(), 1)
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pj = pj.double()
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self.assertIs(pj, INFINITY)
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def test_double_with_zero_equivalent_point_non_1_z(self):
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pj = PointJacobi(curve_256, 0, curve_256.p(), 2)
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pj = pj.double()
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self.assertIs(pj, INFINITY)
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def test_compare_with_affine_point(self):
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pj = PointJacobi.from_affine(generator_256)
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pa = pj.to_affine()
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self.assertEqual(pj, pa)
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self.assertEqual(pa, pj)
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def test_to_affine_with_zero_point(self):
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pj = PointJacobi(curve_256, 0, 0, 1)
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pa = pj.to_affine()
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self.assertIs(pa, INFINITY)
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def test_add_with_affine_point(self):
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pj = PointJacobi.from_affine(generator_256)
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pa = pj.to_affine()
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s = pj + pa
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self.assertEqual(s, pj.double())
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def test_radd_with_affine_point(self):
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pj = PointJacobi.from_affine(generator_256)
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pa = pj.to_affine()
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s = pa + pj
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self.assertEqual(s, pj.double())
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def test_add_with_infinity(self):
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pj = PointJacobi.from_affine(generator_256)
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s = pj + INFINITY
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self.assertEqual(s, pj)
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def test_add_zero_point_to_affine(self):
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pa = PointJacobi.from_affine(generator_256).to_affine()
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pj = PointJacobi(curve_256, 0, 0, 1)
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s = pj + pa
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self.assertIs(s, pa)
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def test_multiply_by_zero(self):
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pj = PointJacobi.from_affine(generator_256)
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pj = pj * 0
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self.assertIs(pj, INFINITY)
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def test_zero_point_multiply_by_one(self):
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pj = PointJacobi(curve_256, 0, 0, 1)
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pj = pj * 1
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self.assertIs(pj, INFINITY)
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def test_multiply_by_one(self):
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pj = PointJacobi.from_affine(generator_256)
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pw = generator_256 * 1
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pj = pj * 1
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self.assertEqual(pj.x(), pw.x())
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self.assertEqual(pj.y(), pw.y())
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def test_multiply_by_two(self):
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pj = PointJacobi.from_affine(generator_256)
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pw = generator_256 * 2
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pj = pj * 2
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self.assertEqual(pj.x(), pw.x())
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self.assertEqual(pj.y(), pw.y())
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def test_rmul_by_two(self):
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pj = PointJacobi.from_affine(generator_256)
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pw = generator_256 * 2
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pj = 2 * pj
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self.assertEqual(pj, pw)
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def test_compare_non_zero_with_infinity(self):
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pj = PointJacobi.from_affine(generator_256)
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self.assertNotEqual(pj, INFINITY)
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def test_compare_zero_point_with_infinity(self):
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pj = PointJacobi(curve_256, 0, 0, 1)
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self.assertEqual(pj, INFINITY)
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def test_compare_double_with_multiply(self):
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pj = PointJacobi.from_affine(generator_256)
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dbl = pj.double()
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mlpl = pj * 2
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self.assertEqual(dbl, mlpl)
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@settings(max_examples=10)
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@given(st.integers(min_value=0, max_value=int(generator_256.order())))
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def test_multiplications(self, mul):
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pj = PointJacobi.from_affine(generator_256)
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pw = pj.to_affine() * mul
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pj = pj * mul
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self.assertEqual((pj.x(), pj.y()), (pw.x(), pw.y()))
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self.assertEqual(pj, pw)
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@settings(max_examples=10)
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@given(st.integers(min_value=0, max_value=int(generator_256.order())))
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@example(0)
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@example(int(generator_256.order()))
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def test_precompute(self, mul):
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precomp = PointJacobi.from_affine(generator_256, True)
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pj = PointJacobi.from_affine(generator_256)
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a = precomp * mul
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b = pj * mul
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self.assertEqual(a, b)
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@settings(max_examples=10)
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@given(
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st.integers(min_value=1, max_value=int(generator_256.order())),
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st.integers(min_value=1, max_value=int(generator_256.order())),
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)
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@example(3, 3)
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def test_add_scaled_points(self, a_mul, b_mul):
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j_g = PointJacobi.from_affine(generator_256)
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a = PointJacobi.from_affine(j_g * a_mul)
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b = PointJacobi.from_affine(j_g * b_mul)
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c = a + b
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self.assertEqual(c, j_g * (a_mul + b_mul))
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@settings(max_examples=10)
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@given(
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st.integers(min_value=1, max_value=int(generator_256.order())),
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st.integers(min_value=1, max_value=int(generator_256.order())),
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st.integers(min_value=1, max_value=int(curve_256.p() - 1)),
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)
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def test_add_one_scaled_point(self, a_mul, b_mul, new_z):
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j_g = PointJacobi.from_affine(generator_256)
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a = PointJacobi.from_affine(j_g * a_mul)
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b = PointJacobi.from_affine(j_g * b_mul)
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p = curve_256.p()
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assume(inverse_mod(new_z, p))
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new_zz = new_z * new_z % p
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b = PointJacobi(
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curve_256, b.x() * new_zz % p, b.y() * new_zz * new_z % p, new_z
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)
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c = a + b
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self.assertEqual(c, j_g * (a_mul + b_mul))
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@settings(max_examples=10)
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@given(
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st.integers(min_value=1, max_value=int(generator_256.order())),
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st.integers(min_value=1, max_value=int(generator_256.order())),
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st.integers(min_value=1, max_value=int(curve_256.p() - 1)),
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)
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@example(1, 1, 1)
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@example(3, 3, 3)
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@example(2, int(generator_256.order() - 2), 1)
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@example(2, int(generator_256.order() - 2), 3)
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def test_add_same_scale_points(self, a_mul, b_mul, new_z):
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j_g = PointJacobi.from_affine(generator_256)
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a = PointJacobi.from_affine(j_g * a_mul)
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b = PointJacobi.from_affine(j_g * b_mul)
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p = curve_256.p()
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assume(inverse_mod(new_z, p))
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new_zz = new_z * new_z % p
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a = PointJacobi(
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curve_256, a.x() * new_zz % p, a.y() * new_zz * new_z % p, new_z
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)
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b = PointJacobi(
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curve_256, b.x() * new_zz % p, b.y() * new_zz * new_z % p, new_z
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)
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c = a + b
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self.assertEqual(c, j_g * (a_mul + b_mul))
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@settings(max_examples=14)
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@given(
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st.integers(min_value=1, max_value=int(generator_256.order())),
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st.integers(min_value=1, max_value=int(generator_256.order())),
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st.lists(
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st.integers(min_value=1, max_value=int(curve_256.p() - 1)),
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min_size=2,
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max_size=2,
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unique=True,
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),
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)
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@example(2, 2, [2, 1])
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@example(2, 2, [2, 3])
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@example(2, int(generator_256.order() - 2), [2, 3])
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@example(2, int(generator_256.order() - 2), [2, 1])
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def test_add_different_scale_points(self, a_mul, b_mul, new_z):
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j_g = PointJacobi.from_affine(generator_256)
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a = PointJacobi.from_affine(j_g * a_mul)
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b = PointJacobi.from_affine(j_g * b_mul)
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p = curve_256.p()
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assume(inverse_mod(new_z[0], p))
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assume(inverse_mod(new_z[1], p))
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new_zz0 = new_z[0] * new_z[0] % p
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new_zz1 = new_z[1] * new_z[1] % p
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a = PointJacobi(
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curve_256,
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a.x() * new_zz0 % p,
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a.y() * new_zz0 * new_z[0] % p,
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new_z[0],
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)
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b = PointJacobi(
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curve_256,
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b.x() * new_zz1 % p,
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b.y() * new_zz1 * new_z[1] % p,
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new_z[1],
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)
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c = a + b
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self.assertEqual(c, j_g * (a_mul + b_mul))
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def test_add_point_3_times(self):
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j_g = PointJacobi.from_affine(generator_256)
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self.assertEqual(j_g * 3, j_g + j_g + j_g)
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def test_mul_add_inf(self):
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j_g = PointJacobi.from_affine(generator_256)
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self.assertEqual(j_g, j_g.mul_add(1, INFINITY, 1))
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def test_mul_add_same(self):
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j_g = PointJacobi.from_affine(generator_256)
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self.assertEqual(j_g * 2, j_g.mul_add(1, j_g, 1))
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def test_mul_add_precompute(self):
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j_g = PointJacobi.from_affine(generator_256, True)
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b = PointJacobi.from_affine(j_g * 255, True)
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self.assertEqual(j_g * 256, j_g + b)
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self.assertEqual(j_g * (5 + 255 * 7), j_g * 5 + b * 7)
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self.assertEqual(j_g * (5 + 255 * 7), j_g.mul_add(5, b, 7))
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def test_mul_add_precompute_large(self):
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j_g = PointJacobi.from_affine(generator_256, True)
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b = PointJacobi.from_affine(j_g * 255, True)
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self.assertEqual(j_g * 256, j_g + b)
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self.assertEqual(
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j_g * (0xFF00 + 255 * 0xF0F0), j_g * 0xFF00 + b * 0xF0F0
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)
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self.assertEqual(
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j_g * (0xFF00 + 255 * 0xF0F0), j_g.mul_add(0xFF00, b, 0xF0F0)
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)
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def test_mul_add_to_mul(self):
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j_g = PointJacobi.from_affine(generator_256)
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a = j_g * 3
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b = j_g.mul_add(2, j_g, 1)
|
||
|
|
|
||
|
|
self.assertEqual(a, b)
|
||
|
|
|
||
|
|
def test_mul_add(self):
|
||
|
|
j_g = PointJacobi.from_affine(generator_256)
|
||
|
|
|
||
|
|
w_a = generator_256 * 255
|
||
|
|
w_b = generator_256 * (0xA8 * 0xF0)
|
||
|
|
j_b = j_g * 0xA8
|
||
|
|
|
||
|
|
ret = j_g.mul_add(255, j_b, 0xF0)
|
||
|
|
|
||
|
|
self.assertEqual(ret.to_affine(), w_a + w_b)
|
||
|
|
|
||
|
|
def test_mul_add_large(self):
|
||
|
|
j_g = PointJacobi.from_affine(generator_256)
|
||
|
|
b = PointJacobi.from_affine(j_g * 255)
|
||
|
|
|
||
|
|
self.assertEqual(j_g * 256, j_g + b)
|
||
|
|
self.assertEqual(
|
||
|
|
j_g * (0xFF00 + 255 * 0xF0F0), j_g * 0xFF00 + b * 0xF0F0
|
||
|
|
)
|
||
|
|
self.assertEqual(
|
||
|
|
j_g * (0xFF00 + 255 * 0xF0F0), j_g.mul_add(0xFF00, b, 0xF0F0)
|
||
|
|
)
|
||
|
|
|
||
|
|
def test_equality(self):
|
||
|
|
pj1 = PointJacobi(curve=CurveFp(23, 1, 1, 1), x=2, y=3, z=1, order=1)
|
||
|
|
pj2 = PointJacobi(curve=CurveFp(23, 1, 1, 1), x=2, y=3, z=1, order=1)
|
||
|
|
self.assertEqual(pj1, pj2)
|
||
|
|
|
||
|
|
def test_pickle(self):
|
||
|
|
pj = PointJacobi(curve=CurveFp(23, 1, 1, 1), x=2, y=3, z=1, order=1)
|
||
|
|
self.assertEqual(pickle.loads(pickle.dumps(pj)), pj)
|