def test_add1(self):
# tests the following additions on curve y^2=x^3-7 over F_223:
# (192,105) + (17,56)
# (47,71) + (117,141)
# (143,98) + (76,66)
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
additions = (
# (x1, y1, x2, y2, x3, y3)
(192, 105, 17, 56, 170, 142),
(47, 71, 117, 141, 60, 139),
(143, 98, 76, 66, 47, 71),
)
# iterate over the additions
# Initialize points this way:
# x1 = FieldElement(x1_raw, prime)
# y1 = FieldElement(y1_raw, prime)
# p1 = Point(x1, y1, a, b)
# x2 = FieldElement(x2_raw, prime)
# y2 = FieldElement(y2_raw, prime)
# p2 = Point(x2, y2, a, b)
# x3 = FieldElement(x3_raw, prime)
# y3 = FieldElement(y3_raw, prime)
# p3 = Point(x3, y3, a, b)
# check that p1 + p2 == p3
raise NotImplementedError
def test_ne(self):
a = FieldElement(2, 31)
b = FieldElement(2, 31)
c = FieldElement(15, 31)
self.assertEqual(a, b)
self.assertTrue(a != c)
self.assertFalse(a != b)
def test_add_FE(self):
a = FieldElement(5, 7)
b = FieldElement(4, 7)
c = FieldElement(2, 11)
self.assertEqual(a + b, FieldElement(2, 7))
with self.assertRaises(RuntimeError):
b + c
def test_exercise_1(self):
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
points = ((192, 105), (17, 56), (200, 119), (1, 193), (42, 99))
expected = [True, True, False, True, False]
for x_raw, y_raw in points:
x = FieldElement(x_raw, prime)
y = FieldElement(y_raw, prime)
if expected.pop(0):
self.assertTrue(Point(x, y, a, b))
else:
with self.assertRaises(ValueError):
Point(x, y, a, b)
def test_example_2(self):
prime = 137
a = FieldElement(0, prime)
b = FieldElement(7, prime)
p1 = Point(FieldElement(73, prime), FieldElement(128, prime), a, b)
p2 = Point(FieldElement(46, prime), FieldElement(22, prime), a, b)
p3 = p1 + p2
self.assertEqual(p3.x.num, 99)
self.assertEqual(p3.y.num, 49)
def test_Point_scalar_multiply(self):
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
x = FieldElement(47, prime)
y = FieldElement(71, prime)
p = Point(x, y, a, b)
x6 = FieldElement(139, prime)
y6 = FieldElement(137, prime)
p6 = Point(x6, y6, a, b)
result = 6 * p
self.assertEqual(result, p6)
result = 21 * p
self.assertEqual(result.x, None)
self.assertEqual(result.y, None)
def test_rmul(self):
# tests the following scalar multiplications
# 2*(192,105)
# 2*(143,98)
# 2*(47,71)
# 4*(47,71)
# 8*(47,71)
# 21*(47,71)
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
multiplications = (
# (coefficient, x1, y1, x2, y2)
(2, 192, 105, 49, 71),
(2, 143, 98, 64, 168),
(2, 47, 71, 36, 111),
(4, 47, 71, 194, 51),
(8, 47, 71, 116, 55),
(21, 47, 71, None, None),
)
# iterate over the multiplications
for s, x1_raw, y1_raw, x2_raw, y2_raw in multiplications:
# Initialize points this way:
# x = FieldElement(192, prime)
# y = FieldElement(105, prime)
# p = Point(x, y, a, b)
x1 = FieldElement(x1_raw, prime)
y1 = FieldElement(y1_raw, prime)
p1 = Point(x1, y1, a, b)
# initialize the second point based on whether it's the point at infinity
if x2_raw is None:
p2 = Point(None, None, a, b)
else:
x2 = FieldElement(x2_raw, prime)
y2 = FieldElement(y2_raw, prime)
p2 = Point(x2, y2, a, b)
# check that the product is equal to the expected point
self.assertEqual(s * p1, p2)
def test_on_curve(self):
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
valid_points = ((192, 105), (17, 56), (1, 193))
invalid_points = ((200, 119), (42, 99))
# iterate over valid points
for x_raw, y_raw in valid_points:
x = FieldElement(x_raw, prime)
y = FieldElement(y_raw, prime)
# Creating the point should not result in an error
Point(x, y, a, b)
# iterate over invalid points
for x_raw, y_raw in invalid_points:
x = FieldElement(x_raw, prime)
y = FieldElement(y_raw, prime)
# check that creating the point results in a ValueError
with self.assertRaises(ValueError):
Point(x, y, a, b)
