def pointAddition(P, Q):
gradient: int
# check whether addition is possible
if P == Q:
print(
"you can't do addition with the same point, you need to perform point duplication"
)
else:
isPointOfInfinity = False
if P[0] == Q[0]:
isPointOfInfinity = True
else:
# perform the addition
divident = turnPositive(curve.p, Q[1] - P[1] % curve.p)
diviser = Q[0] - P[0] % curve.p
inverse = extendedEuclidian.getInverse(curve.p, diviser)
gradient = divident * inverse % curve.p
x = (gradient**2 - P[0] - Q[0]) % curve.p
y = turnPositive(curve.p,
((gradient * (P[0] - x) - P[1]) % curve.p))
# print out the new point
if isPointOfInfinity:
print(f"\n{P} + {P} is the point of infinity!")
else:
print(f"\n{P} + {Q} is ({x}, {y})!")
def pointDuplication(self, P: Point) -> Point:
if P.isPointOfInfinity():
return P
elif P.y == 0:
return Point()
else:
divident = (3 * ((P.x**2) % self.p) + self.a) % self.p
diviser = 2 * P.y % self.p
inverse = getInverse(self.p, diviser)
gradient = divident * inverse % self.p
x = turnPositive(self.p,
((gradient**2 % self.p) - P.x - P.x) % self.p)
y = turnPositive(self.p, ((gradient * (P.x - x) - P.y) % self.p))
return Point(x, y)
def pointDuplication(P):
isPointOfInfinity = False
if P[1] == 0:
isPointOfInfinity = True
else:
gradient: int
divident = (3 * (P[0]**2) + curve.a) % curve.p
diviser = 2 * P[1] % curve.p
inverse = extendedEuclidian.getInverse(curve.p, diviser)
gradient = divident * inverse % curve.p
x = turnPositive(curve.p, (gradient**2 - P[0] - P[0]) % curve.p)
y = turnPositive(curve.p,
((gradient * (P[0] - x) - P[1]) % curve.p))
# print out the new point
if isPointOfInfinity:
print(f"\n{P} + {P} is the point of infinity!")
else:
print(f"\n{P} + {P} is ({x}, {y})!")
def calculate(self):
isPointOfInfinity = False
if self.P[1] == 0:
isPointOfInfinity = True
else:
gradient: int
divident = (3 * (self.P[0]**2) + curve.a) % curve.p
diviser = 2 * self.P[1] % curve.p
inverse = extendedEuclidian.getInverse(curve.p, diviser)
gradient = divident * inverse % curve.p
x = turnPositive(curve.p,
(gradient**2 - self.P[0] - self.P[0]) % curve.p)
y = turnPositive(
curve.p, ((gradient * (self.P[0] - x) - self.P[1]) % curve.p))
# print out the new point
if isPointOfInfinity:
print(f"\n{self.P} + {self.P} is the point of infinity!")
else:
print(f"\n{self.P} + {self.P} is ({x}, {y})!")
def pointAddition(self, P: Point, Q: Point) -> Point:
# is one of them the point of infinity?
if P.isPointOfInfinity() or Q.isPointOfInfinity():
if P.isPointOfInfinity():
return Q
else:
return P
# are they identical? perform duplication
elif P == Q:
return self.pointDuplication(P)
elif P.x == Q.x:
return Point()
else:
# perform the addition
divident = Q.y - P.y % self.p
diviser = Q.x - P.x % self.p
inverse = getInverse(self.p, diviser)
gradient = divident * inverse % self.p
x = turnPositive(self.p,
((gradient**2 % self.p) - P.x - Q.x) % self.p)
y = turnPositive(self.p, ((gradient * (P.x - x) - P.y) % self.p))
return Point(x, y)