def test_ne(self):
a = FieldElement(11, 71)
b = FieldElement(11, 71)
c = FieldElement(7, 71)
self.assertTrue(a != c)
self.assertFalse(a != b)
def test_eq(self):
a = FieldElement(11, 71)
b = FieldElement(11, 71)
c = FieldElement(7, 71)
self.assertTrue(a == b)
self.assertFalse(a == c)
def test_pow(self):
a = FieldElement(5, 17)
b = FieldElement(8, 17)
self.assertTrue(a ** 2 == b)
a = FieldElement(7, 13)
b = FieldElement(8, 13)
self.assertTrue(a ** -3 == b)
def test_sub(self):
a = FieldElement(13, 17)
b = FieldElement(15, 17)
c = FieldElement(15, 17)
self.assertTrue(a - b == c)
a = FieldElement(13, 17)
b = FieldElement(1, 17)
c = FieldElement(12, 17)
self.assertTrue(a - b == c)
def test_field_elements_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))
for x_raw, y_raw in valid_points:
x = FieldElement(x_raw, prime)
y = FieldElement(y_raw, prime)
Point(x, y, a, b)
for x_raw, y_raw in invalid_points:
x = FieldElement(x_raw, prime)
y = FieldElement(y_raw, prime)
with self.assertRaises(ValueError):
Point(x, y, a, b)
def test_truediv(self):
a = FieldElement(5, 17)
b = FieldElement(8, 17)
c = FieldElement(7, 17)
self.assertTrue(a / b == c)
def test_mul(self):
a = FieldElement(13, 17)
b = FieldElement(3, 17)
c = FieldElement(5, 17)
self.assertTrue(a * b == c)
def test_add(self):
a = FieldElement(14, 17)
b = FieldElement(7, 17)
c = FieldElement(4, 17)
self.assertTrue(a + b == c)
def test_add_for_field_points(self):
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
p1 = Point(FieldElement(170, prime), FieldElement(142, prime), a, b)
p2 = Point(FieldElement(60, prime), FieldElement(139, prime), a, b)
p_result = Point(FieldElement(220, prime), FieldElement(181, prime), a,
b)
self.assertTrue(p1 + p2 == p_result)
p1 = Point(FieldElement(47, prime), FieldElement(71, prime), a, b)
p2 = Point(FieldElement(17, prime), FieldElement(56, prime), a, b)
p_result = Point(FieldElement(215, prime), FieldElement(68, prime), a,
b)
self.assertTrue(p1 + p2 == p_result)
p1 = Point(FieldElement(143, prime), FieldElement(98, prime), a, b)
p2 = Point(FieldElement(76, prime), FieldElement(66, prime), a, b)
p_result = Point(FieldElement(47, prime), FieldElement(71, prime), a,
b)
self.assertTrue(p1 + p2 == p_result)