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
|
from unittest import TestCase
from sympy import FF, symbols
from pyecsca.ec.mod import SymbolicMod, Mod
from pyecsca.misc.cfg import TemporaryConfig
from pyecsca.ec.error import UnsatisfiedAssumptionError
from pyecsca.ec.params import get_params
from pyecsca.ec.point import Point
class FormulaTests(TestCase):
def setUp(self):
self.secp128r1 = get_params("secg", "secp128r1", "projective")
self.add = self.secp128r1.curve.coordinate_model.formulas["add-2007-bl"]
self.dbl = self.secp128r1.curve.coordinate_model.formulas["dbl-2007-bl"]
self.mdbl = self.secp128r1.curve.coordinate_model.formulas["mdbl-2007-bl"]
self.jac_secp128r1 = get_params("secg", "secp128r1", "jacobian")
self.jac_dbl = self.jac_secp128r1.curve.coordinate_model.formulas[
"dbl-1998-hnm"
]
def test_wrong_call(self):
with self.assertRaises(ValueError):
self.add(self.secp128r1.curve.prime)
with self.assertRaises(ValueError):
self.add(
self.secp128r1.curve.prime,
self.secp128r1.generator.to_affine(),
self.secp128r1.generator.to_affine(),
)
def test_indices(self):
self.assertEqual(self.add.input_index, 1)
self.assertEqual(self.add.output_index, 3)
def test_inputs_outputs(self):
self.assertEqual(self.add.inputs, {"X1", "Y1", "Z1", "X2", "Y2", "Z2"})
self.assertEqual(self.add.outputs, {"X3", "Y3", "Z3"})
def test_eq(self):
self.assertEqual(self.add, self.add)
self.assertNotEqual(self.add, self.dbl)
def test_num_ops(self):
self.assertEqual(self.add.num_operations, 33)
self.assertEqual(self.add.num_multiplications, 17)
self.assertEqual(self.add.num_divisions, 0)
self.assertEqual(self.add.num_inversions, 0)
self.assertEqual(self.add.num_powers, 0)
self.assertEqual(self.add.num_squarings, 6)
self.assertEqual(self.add.num_addsubs, 10)
def test_assumptions(self):
res = self.mdbl(
self.secp128r1.curve.prime,
self.secp128r1.generator,
**self.secp128r1.curve.parameters
)
self.assertIsNotNone(res)
coords = {
name: value * 5 for name, value in self.secp128r1.generator.coords.items()
}
other = Point(self.secp128r1.generator.coordinate_model, **coords)
with self.assertRaises(UnsatisfiedAssumptionError):
self.mdbl(
self.secp128r1.curve.prime, other, **self.secp128r1.curve.parameters
)
with TemporaryConfig() as cfg:
cfg.ec.unsatisfied_formula_assumption_action = "ignore"
pt = self.mdbl(
self.secp128r1.curve.prime, other, **self.secp128r1.curve.parameters
)
self.assertIsNotNone(pt)
def test_parameters(self):
res = self.jac_dbl(
self.secp128r1.curve.prime,
self.jac_secp128r1.generator,
**self.jac_secp128r1.curve.parameters
)
self.assertIsNotNone(res)
def test_symbolic(self):
p = self.secp128r1.curve.prime
k = FF(p)
coords = self.secp128r1.curve.coordinate_model
sympy_params = {
key: SymbolicMod(k(int(value)), p)
for key, value in self.secp128r1.curve.parameters.items()
}
symbolic_point = Point(
coords, **{key: SymbolicMod(symbols(key), p) for key in coords.variables}
)
symbolic_double = self.dbl(p, symbolic_point, **sympy_params)[0]
generator_double = self.dbl(
p, self.secp128r1.generator, **self.secp128r1.curve.parameters
)[0]
for outer_var in coords.variables:
symbolic_val = getattr(symbolic_double, outer_var).x
generator_val = getattr(generator_double, outer_var).x
for inner_var in coords.variables:
symbolic_val = symbolic_val.subs(
inner_var, k(getattr(self.secp128r1.generator, inner_var).x)
)
self.assertEqual(Mod(int(symbolic_val), p), Mod(generator_val, p))
|
