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import pytest
from six import print_
try:
import unittest2 as unittest
except ImportError:
import unittest
from hypothesis import given, settings
import hypothesis.strategies as st
try:
from hypothesis import HealthCheck
HC_PRESENT=True
except ImportError: # pragma: no cover
HC_PRESENT=False
from .numbertheory import inverse_mod
from .ellipticcurve import CurveFp, INFINITY, Point
HYP_SETTINGS={}
if HC_PRESENT: # pragma: no branch
HYP_SETTINGS['suppress_health_check']=[HealthCheck.too_slow]
HYP_SETTINGS['deadline'] = 5000
# NIST Curve P-192:
p = 6277101735386680763835789423207666416083908700390324961279
r = 6277101735386680763835789423176059013767194773182842284081
# s = 0x3045ae6fc8422f64ed579528d38120eae12196d5
# c = 0x3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65
b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
Gx = 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
Gy = 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
c192 = CurveFp(p, -3, b)
p192 = Point(c192, Gx, Gy, r)
c_23 = CurveFp(23, 1, 1)
g_23 = Point(c_23, 13, 7, 7)
HYP_SLOW_SETTINGS=dict(HYP_SETTINGS)
HYP_SLOW_SETTINGS["max_examples"]=10
@settings(**HYP_SLOW_SETTINGS)
@given(st.integers(min_value=1, max_value=r+1))
def test_p192_mult_tests(multiple):
inv_m = inverse_mod(multiple, r)
p1 = p192 * multiple
assert p1 * inv_m == p192
def add_n_times(point, n):
ret = INFINITY
i = 0
while i <= n:
yield ret
ret = ret + point
i += 1
# From X9.62 I.1 (p. 96):
@pytest.mark.parametrize(
"p, m, check",
[(g_23, n, exp) for n, exp in enumerate(add_n_times(g_23, 8))],
ids=["g_23 test with mult {0}".format(i) for i in range(9)])
def test_add_and_mult_equivalence(p, m, check):
assert p * m == check
class TestCurve(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.c_23 = CurveFp(23, 1, 1)
def test_equality_curves(self):
self.assertEqual(self.c_23, CurveFp(23, 1, 1))
def test_inequality_curves(self):
c192 = CurveFp(p, -3, b)
self.assertNotEqual(self.c_23, c192)
def test_usability_in_a_hashed_collection_curves(self):
{self.c_23: None}
def test_hashability_curves(self):
hash(self.c_23)
def test_conflation_curves(self):
ne1, ne2, ne3 = CurveFp(24, 1, 1), CurveFp(23, 2, 1), CurveFp(23, 1, 2)
eq1, eq2, eq3 = CurveFp(23, 1, 1), CurveFp(23, 1, 1), self.c_23
self.assertEqual(len(set((c_23, eq1, eq2, eq3))), 1)
self.assertEqual(len(set((c_23, ne1, ne2, ne3))), 4)
self.assertDictEqual({c_23: None}, {eq1: None})
self.assertTrue(eq2 in {eq3: None})
class TestPoint(unittest.TestCase):
@classmethod
def setUpClass(cls):
cls.c_23 = CurveFp(23, 1, 1)
cls.g_23 = Point(cls.c_23, 13, 7, 7)
p = 6277101735386680763835789423207666416083908700390324961279
r = 6277101735386680763835789423176059013767194773182842284081
# s = 0x3045ae6fc8422f64ed579528d38120eae12196d5
# c = 0x3099d2bbbfcb2538542dcd5fb078b6ef5f3d6fe2c745de65
b = 0x64210519e59c80e70fa7e9ab72243049feb8deecc146b9b1
Gx = 0x188da80eb03090f67cbf20eb43a18800f4ff0afd82ff1012
Gy = 0x07192b95ffc8da78631011ed6b24cdd573f977a11e794811
cls.c192 = CurveFp(p, -3, b)
cls.p192 = Point(cls.c192, Gx, Gy, r)
def test_p192(self):
# Checking against some sample computations presented
# in X9.62:
d = 651056770906015076056810763456358567190100156695615665659
Q = d * self.p192
self.assertEqual(Q.x(), 0x62B12D60690CDCF330BABAB6E69763B471F994DD702D16A5)
k = 6140507067065001063065065565667405560006161556565665656654
R = k * self.p192
self.assertEqual(R.x(), 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD)
self.assertEqual(R.y(), 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835)
u1 = 2563697409189434185194736134579731015366492496392189760599
u2 = 6266643813348617967186477710235785849136406323338782220568
temp = u1 * self.p192 + u2 * Q
self.assertEqual(temp.x(), 0x885052380FF147B734C330C43D39B2C4A89F29B0F749FEAD)
self.assertEqual(temp.y(), 0x9CF9FA1CBEFEFB917747A3BB29C072B9289C2547884FD835)
def test_double_infinity(self):
p1 = INFINITY
p3 = p1.double()
self.assertEqual(p1, p3)
self.assertEqual(p3.x(), p1.x())
self.assertEqual(p3.y(), p3.y())
def test_double(self):
x1, y1, x3, y3 = (3, 10, 7, 12)
p1 = Point(self.c_23, x1, y1)
p3 = p1.double()
self.assertEqual(p3.x(), x3)
self.assertEqual(p3.y(), y3)
def test_multiply(self):
x1, y1, m, x3, y3 = (3, 10, 2, 7, 12)
p1 = Point(self.c_23, x1, y1)
p3 = p1 * m
self.assertEqual(p3.x(), x3)
self.assertEqual(p3.y(), y3)
# Trivial tests from X9.62 B.3:
def test_add(self):
"""We expect that on curve c, (x1,y1) + (x2, y2 ) = (x3, y3)."""
x1, y1, x2, y2, x3, y3 = (3, 10, 9, 7, 17, 20)
p1 = Point(self.c_23, x1, y1)
p2 = Point(self.c_23, x2, y2)
p3 = p1 + p2
self.assertEqual(p3.x(), x3)
self.assertEqual(p3.y(), y3)
def test_add_as_double(self):
"""We expect that on curve c, (x1,y1) + (x2, y2 ) = (x3, y3)."""
x1, y1, x2, y2, x3, y3 = (3, 10, 3, 10, 7, 12)
p1 = Point(self.c_23, x1, y1)
p2 = Point(self.c_23, x2, y2)
p3 = p1 + p2
self.assertEqual(p3.x(), x3)
self.assertEqual(p3.y(), y3)
def test_equality_points(self):
self.assertEqual(self.g_23, Point(self.c_23, 13, 7, 7))
def test_inequality_points(self):
c = CurveFp(100, -3, 100)
p = Point(c, 100, 100, 100)
self.assertNotEqual(self.g_23, p)
def test_inaquality_points_diff_types(self):
c = CurveFp(100, -3, 100)
self.assertNotEqual(self.g_23, c)
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