1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
|
from unittest import TestCase
from pyecsca.ec.coordinates import AffineCoordinateModel
from pyecsca.ec.params import get_params
from pyecsca.ec.mod import Mod
from pyecsca.ec.model import ShortWeierstrassModel, MontgomeryModel
from pyecsca.ec.point import Point, InfinityPoint
class PointTests(TestCase):
def setUp(self):
self.secp128r1 = get_params("secg", "secp128r1", "projective")
self.base = self.secp128r1.generator
self.coords = self.secp128r1.curve.coordinate_model
self.affine = AffineCoordinateModel(ShortWeierstrassModel())
def test_construction(self):
with self.assertRaises(ValueError):
Point(self.coords)
def test_to_affine(self):
pt = Point(
self.coords,
X=Mod(0x161FF7528B899B2D0C28607CA52C5B86, self.secp128r1.curve.prime),
Y=Mod(0xCF5AC8395BAFEB13C02DA292DDED7A83, self.secp128r1.curve.prime),
Z=Mod(1, self.secp128r1.curve.prime),
)
affine = pt.to_affine()
self.assertIsInstance(affine.coordinate_model, AffineCoordinateModel)
self.assertSetEqual(set(affine.coords.keys()), set(self.affine.variables))
self.assertEqual(affine.coords["x"], pt.coords["X"])
self.assertEqual(affine.coords["y"], pt.coords["Y"])
self.assertEqual(affine.to_affine(), affine)
affine = InfinityPoint(self.coords).to_affine()
self.assertIsInstance(affine, InfinityPoint)
def test_to_model(self):
affine = Point(
self.affine,
x=Mod(0xABCD, self.secp128r1.curve.prime),
y=Mod(0xEF, self.secp128r1.curve.prime),
)
projective_model = self.coords
other = affine.to_model(projective_model, self.secp128r1.curve)
self.assertEqual(other.coordinate_model, projective_model)
self.assertSetEqual(set(other.coords.keys()), set(projective_model.variables))
self.assertEqual(other.coords["X"], affine.coords["x"])
self.assertEqual(other.coords["Y"], affine.coords["y"])
self.assertEqual(other.coords["Z"], Mod(1, self.secp128r1.curve.prime))
infty = InfinityPoint(AffineCoordinateModel(self.secp128r1.curve.model))
other_infty = infty.to_model(self.coords, self.secp128r1.curve)
self.assertIsInstance(other_infty, InfinityPoint)
with self.assertRaises(ValueError):
self.base.to_model(self.coords, self.secp128r1.curve)
def test_to_from_affine(self):
pt = Point(
self.coords,
X=Mod(0x161FF7528B899B2D0C28607CA52C5B86, self.secp128r1.curve.prime),
Y=Mod(0xCF5AC8395BAFEB13C02DA292DDED7A83, self.secp128r1.curve.prime),
Z=Mod(1, self.secp128r1.curve.prime),
)
other = pt.to_affine().to_model(self.coords, self.secp128r1.curve)
self.assertEqual(pt, other)
def test_equals(self):
pt = Point(
self.coords,
X=Mod(0x4, self.secp128r1.curve.prime),
Y=Mod(0x6, self.secp128r1.curve.prime),
Z=Mod(2, self.secp128r1.curve.prime),
)
other = Point(
self.coords,
X=Mod(0x2, self.secp128r1.curve.prime),
Y=Mod(0x3, self.secp128r1.curve.prime),
Z=Mod(1, self.secp128r1.curve.prime),
)
third = Point(
self.coords,
X=Mod(0x5, self.secp128r1.curve.prime),
Y=Mod(0x3, self.secp128r1.curve.prime),
Z=Mod(1, self.secp128r1.curve.prime),
)
self.assertTrue(pt.equals(other))
self.assertNotEqual(pt, other)
self.assertFalse(pt.equals(2))
self.assertNotEqual(pt, 2)
self.assertFalse(pt.equals(third))
self.assertNotEqual(pt, third)
self.assertTrue(pt.equals_scaled(other))
self.assertTrue(pt.equals_affine(other))
self.assertFalse(pt.equals_scaled(third))
infty_one = InfinityPoint(self.coords)
infty_other = InfinityPoint(self.coords)
self.assertTrue(infty_one.equals(infty_other))
self.assertTrue(infty_one.equals_affine(infty_other))
self.assertTrue(infty_one.equals_scaled(infty_other))
self.assertEqual(infty_one, infty_other)
self.assertFalse(pt.equals(infty_one))
self.assertFalse(pt.equals_affine(infty_one))
self.assertFalse(pt.equals_scaled(infty_one))
mont = MontgomeryModel()
different = Point(
mont.coordinates["xz"],
X=Mod(
0x64DACCD2656420216545E5F65221EB,
0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA,
),
Z=Mod(1, 0xAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA),
)
self.assertFalse(pt.equals(different))
self.assertNotEqual(pt, different)
def test_bytes(self):
pt = Point(
self.coords,
X=Mod(0x4, self.secp128r1.curve.prime),
Y=Mod(0x6, self.secp128r1.curve.prime),
Z=Mod(2, self.secp128r1.curve.prime),
)
self.assertEqual(
bytes(pt),
b"\x04\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x04\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x06\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x00\x02",
)
self.assertEqual(bytes(InfinityPoint(self.coords)), b"\x00")
|
