def test_mul():
with pytest.raises(TypeError):
a = FieldElement(number=2, prime=31)
b = FieldElement(number=2, prime=32)
a * b
a = FieldElement(24, 31)
b = FieldElement(19, 31)
assert a * b == FieldElement(22, 31)
def test_div():
with pytest.raises(TypeError):
a = FieldElement(number=2, prime=31)
b = FieldElement(number=2, prime=32)
a / b
a = FieldElement(3, 31)
b = FieldElement(24, 31)
assert a / b == FieldElement(4, 31)
def test_ne():
with pytest.raises(NotImplementedError):
FieldElement(number=2, prime=31) == 0
a = FieldElement(2, 31)
b = FieldElement(2, 31)
c = FieldElement(15, 31)
assert a == b
assert a != c
assert not (a != b)
def test_add():
# tests the following additions on curve y^2=x^3-7 over F_223:
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),
)
for x1, y1, x2, y2, x3, y3 in additions:
p1 = Point(x=FieldElement(x1, prime),
y=FieldElement(y1, prime),
a=a,
b=b)
p2 = Point(x=FieldElement(x2, prime),
y=FieldElement(y2, prime),
a=a,
b=b)
p3 = Point(x=FieldElement(x3, prime),
y=FieldElement(y3, prime),
a=a,
b=b)
assert p1 + p2 == p3
def test_pow():
a = FieldElement(17, 31)
assert a ** 3 == FieldElement(15, 31)
a = FieldElement(5, 31)
assert a ** 5 == FieldElement(25, 31)
a = FieldElement(17, 31)
assert a ** -3 == FieldElement(29, 31)
a = FieldElement(4, 31)
assert a ** -4 == FieldElement(4, 31)
def test_sub():
with pytest.raises(TypeError):
a = FieldElement(number=2, prime=31)
b = FieldElement(number=2, prime=32)
a - b
a = FieldElement(29, 31)
b = FieldElement(4, 31)
assert a - b == FieldElement(25, 31)
a = FieldElement(15, 31)
b = FieldElement(30, 31)
assert a - b == FieldElement(16, 31)
def test_add():
with pytest.raises(TypeError):
a = FieldElement(number=2, prime=31)
b = FieldElement(number=2, prime=32)
a + b
a = FieldElement(2, 31)
b = FieldElement(15, 31)
assert a + b == FieldElement(17, 31)
a = FieldElement(17, 31)
b = FieldElement(21, 31)
assert a + b == FieldElement(7, 31)
def test_rmul():
prime = 223
a = FieldElement(0, prime)
b = FieldElement(7, prime)
multiplications = (
# scalar, 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),
)
for scalar, x1, y1, x2, y2 in multiplications:
x1_el = FieldElement(x1, prime)
y1_el = FieldElement(y1, prime)
x2_el = x2 and FieldElement(x2, prime)
y2_el = y2 and FieldElement(y2, prime)
p = Point(x1_el, y1_el, a, b)
assert scalar * p == Point(x2_el, y2_el, a, b)
def test_on_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))
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 pytest.raises(ValueError):
Point(x, y, a, b)
def test_rmul():
assert 5 * FieldElement(number=18, prime=31) == FieldElement(number=28, prime=31)
assert -4 * FieldElement(number=11, prime=31) == FieldElement(number=18, prime=31)
def test_number_range():
with pytest.raises(ValueError):
FieldElement(number=7, prime=3)