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(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
for x1_raw, y1_raw, x2_raw, y2_raw, x3_raw, y3_raw in additions:
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
self.assertEqual(p1 + p2, p3)
def test_div(self):
a = FieldElement(3, 31)
b = FieldElement(24, 31)
self.assertEqual(a / b, FieldElement(4, 31))
a = FieldElement(17, 31)
self.assertEqual(a**-3, FieldElement(29, 31))
a = FieldElement(4, 31)
b = FieldElement(11, 31)
self.assertEqual(a**-4 * b, FieldElement(13, 31))
def test_sub(self):
a = FieldElement(29, 31)
b = FieldElement(4, 31)
self.assertEqual(a - b, FieldElement(25, 31))
a = FieldElement(15, 31)
b = FieldElement(30, 31)
self.assertEqual(a - b, FieldElement(16, 31))
def test_add(self):
a = FieldElement(2, 31)
b = FieldElement(15, 31)
self.assertEqual(a + b, FieldElement(17, 31))
a = FieldElement(17, 31)
b = FieldElement(21, 31)
self.assertEqual(a + b, FieldElement(7, 31))
def test_on_curve(self):
prime = 223
a = FieldElement(0, 223)
b = FieldElement(7, 223)
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.assetRaises(valueError):
Point(x, y, a, b)
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:
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):
# tests whether the given points [(192,105) (17,56) (200,119) (1,193) (42,99)] are on the curve or not
# elliptic curve used: y^2=x^3-7 over F_223
# raise ValueError for the Points that aren't on this curve
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)
with self.assertRaises(ValueError):
Point(x, y, a, b)
def test_pow(self):
a = FieldElement(17, 31)
self.assertEqual(a**3, FieldElement(15, 31))
a = FieldElement(5, 31)
b = FieldElement(18, 31)
self.assertEqual(a**5 * b, FieldElement(16, 31))
def test_rmul(self):
a = FieldElement(24, 31)
b = 2
self.assertEqual(b * a, a + a)
def test_mul(self):
a = FieldElement(24, 31)
b = FieldElement(19, 31)
self.assertEqual(a * b, FieldElement(22, 31))
{self.y!r})"
def __rmul__(self, coef: int):
# point multiplication
current = self
print("**********************")
result = self.__class__(None, None, self.a, self.b)
while coef:
print("++++++++++")
print(current)
if coef & 1:
result += current
print("current***")
current += current
coef >>= 1
return result
if __name__ == "__main__":
from field_element import FieldElement
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
x = FieldElement(47, prime)
y = FieldElement(71, prime)
p = Point(x, y, a, b)
print(p)
for num in range(21):
result = num * p