def test_on_curve(self):
prime = 223
field = generate_finite_field(prime)
a = field(0)
b = field(7)
valid_points = [
(192, 105),
(17, 56),
(1, 193),
]
invalid_points = [(200, 119), (42, 99)]
# valid test
for x_raw, y_raw in valid_points:
x = field(x_raw)
y = field(y_raw)
Point(x, y, a, b)
# invalid test
for x_raw, y_raw in invalid_points:
x = field(x_raw)
y = field(y_raw)
with self.assertRaises(ValueError):
Point(x, y, a, b)
def example1():
field = generate_finite_field(223)
a = field(0)
b = field(7)
x = field(47)
y = field(71)
p = Point(x, y, a, b)
for s in range(1, 21):
result = s * p
print("{}*(47, 71) = ({}, {})".format(s, result.x.num, result.y.num))
def exercise1():
finite223 = generate_finite_field(223)
point_list = [(192, 105), (17, 56), (200, 119), (1, 193), (42, 99)]
point_field_list = [(finite223(point[0]), finite223(point[1]))
for point in point_list]
a = finite223(0)
b = finite223(7)
for point in point_field_list:
try:
print(Point(*point, a, b))
except ValueError as e:
print(e)
def exercise2():
finite223 = generate_finite_field(223)
point_list = [(170, 142), (60, 139), (47, 71), (17, 56), (143, 98),
(76, 66)]
points = [(finite223(point[0]), finite223(point[1]))
for point in point_list]
a = finite223(0)
b = finite223(7)
for i in range(3):
point1 = Point(*points[2 * i], a, b)
point2 = Point(*points[2 * i + 1], a, b)
print("{} + {} = ".format(point_list[2 * i], point_list[2 * i + 1]))
print(point1 + point2)
def exercise5():
field = generate_finite_field(223)
a = field(0)
b = field(7)
x = field(15)
y = field(86)
p = Point(x, y, a, b)
gen_p = p
print("{} generates...".format(p))
while True:
print(gen_p)
gen_p += p
if gen_p == p:
break
def exercise4():
finite223 = generate_finite_field(223)
point_list_raw = [(192, 105), (143, 98), (47, 71), (47, 71), (47, 71),
(47, 71)]
scalar_list = [2, 2, 2, 4, 8, 21]
points = [(finite223(point[0]), finite223(point[1]))
for point in point_list_raw]
a = finite223(0)
b = finite223(7)
for i in range(len(points)):
print("{}*{} = ".format(scalar_list[i], point_list_raw[i]))
point = Point(*points[i], a, b)
print(scalar_list[i] * point)
def test_add(self):
finite223 = generate_finite_field(223)
point_list = [(170, 142), (60, 139), (47, 71), (17, 56), (143, 98),
(76, 66)]
points = [(finite223(point[0]), finite223(point[1]))
for point in point_list]
a = finite223(0)
b = finite223(7)
answer_list_raw = [(220, 181), (215, 68), (47, 71)]
answer_elements = [(finite223(point[0]), finite223(point[1]))
for point in answer_list_raw]
answer_list = [Point(*point, a, b) for point in answer_elements]
for i in range(3):
point1 = Point(*points[2 * i], a, b)
point2 = Point(*points[2 * i + 1], a, b)
self.assertEqual(point1 + point2, answer_list[i])
def example1():
# 타원 곡선 정보
a = 0
b = 7
# 유한체 정보
p = 2**256 - 2**32 - 977
# 유한군 정보
gx = 0x79be667ef9dcbbac55a06295ce870b07029bfcdb2dce28d959f2815b16f81798
gy = 0x483ada7726a3c4655da4fbfc0e1108a8fd17b448a68554199c47d08ffb10d4b8
n = 0xfffffffffffffffffffffffffffffffebaaedce6af48a03bbfd25e8cd0364141
print("Validate generator point(i.e point is on the curve : {}".format(
gy**2 % p == (gx**3 + a * gx + b) % p))
field = generate_finite_field(p)
x = field(gx)
y = field(gy)
a = field(a)
b = field(b)
generotor = Point(x, y, a, b)
print("Validate the order of group(i.e n*g == 0) : {}".format(n *
generotor))