def test_add(self):
i1 = ecc.ECPoint(0, 0, 1)
i2 = ecc.ECPoint(1, 2, 1)
assert (self.ec.add(i1, i2) == i1)
assert (self.ec.add(i1, i2) == i2)
p1 = ecc.ECPoint(4, 1)
p2 = ecc.ECPoint(6, 6)
p3 = ecc.ECPoint(5, 0)
assert (self.ec.add(p1, p1) == p2)
assert (self.ec.add(p1, p2) == p3)
assert (self.ec.add(p2, p1) == p3)
class TestBasic:
""" Create the curve Y^2 = X^3 + X + 3. """
g = ecc.ECPoint(4, 1) # generator
ec = ecc.EllipticCurve(7, g, 1, 3)
def test_generator(self):
s = set()
p = self.g
for i in range(12):
s.add(p)
p = self.ec.add(p, self.g)
assert (len(s) == 6)
def test_add(self):
i1 = ecc.ECPoint(0, 0, 1)
i2 = ecc.ECPoint(1, 2, 1)
assert (self.ec.add(i1, i2) == i1)
assert (self.ec.add(i1, i2) == i2)
p1 = ecc.ECPoint(4, 1)
p2 = ecc.ECPoint(6, 6)
p3 = ecc.ECPoint(5, 0)
assert (self.ec.add(p1, p1) == p2)
assert (self.ec.add(p1, p2) == p3)
assert (self.ec.add(p2, p1) == p3)
def test_mul(self):
p1 = ecc.ECPoint(4, 1)
assert (self.ec.mul(p1, 2) == self.ec.add(p1, p1))
# the order of P1 is 6
assert (self.ec.mul(p1, 7) == p1)
class TestSecp256k1:
""" Create the secp256k1 curve Y^2 = X^3 + 7. """
p = int('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEFFFFFC2F',
16)
a = 0
b = 7
g = ecc.ECPoint(
int('79BE667EF9DCBBAC55A06295CE870B07029BFCDB2DCE28D959F2815B16F81798',
16),
int('483ADA7726A3C4655DA4FBFC0E1108A8FD17B448A68554199C47D08FFB10D4B8',
16))
ec = ecc.EllipticCurve(p, g, a, b)
# order of group
n = int('FFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFEBAAEDCE6AF48A03BBFD25E8CD0364141',
16)
def test_generator(self):
# the order is such that nP = 0
assert self.ec.mul(self.g, self.n) == ecc.ECPoint(0, 0, 1)
def test_arithmetic(self):
p1 = self.ec.random_point()
assert self.ec.add(p1, self.ec.neg(p1)) == self.ec.identity()
p2 = self.ec.random_point()
p3 = self.ec.add(p1, p2)
assert self.ec.is_valid(p3) == True
def test_mul(self):
p1 = ecc.ECPoint(4, 1)
assert (self.ec.mul(p1, 2) == self.ec.add(p1, p1))
# the order of P1 is 6
assert (self.ec.mul(p1, 7) == p1)
def test_generator(self):
# the order is such that nP = 0
assert self.ec.mul(self.g, self.n) == ecc.ECPoint(0, 0, 1)