[Bitcoin] 楕円曲線:点の加算

class Point:

	def __init__(self, x, y, a, b):
		self.a = a
		self.b = b
		self.x = x
		self.y = y
		if self.x is None and self.y is None:
			return
		if self.y**2 != self.x**3 + a * x + b:
			raise ValueError('({},{}) is not on the curve'.format(x, y))

	def __add__(self, other):
		if self.a != other.a or self.b != other.b:
			raise TypeError('Points {}, {} are not on the same curve'.format(self, other))

		if self.x == other.x and self.y != other.y:
			return self.__class__(None, None, self.a, self.b)

		if self.x is None:
			return other
		if other.x is None:
			return self

	def __eq__(self, other):
		return self.x == other.x and self.y == other.y \
			and self.a == other.a and self.b == other.b

	def __ne__(self, other):
		return not (self == other)

p1 = Point(-1, -1, 5, 7)
p2 = Point(-1, 1, 5, 7)
inf = Point(None, None, 5, 7)
print(p1 + inf)
print(inf + p2)
print(p1 + p2)

$ python3 app.py
<__main__.Point object at 0x7f014fc2fbb0>
<__main__.Point object at 0x7f014fbf07f0>
None

### x1 != x2 の点の加算
P1 = (x1,y1), P2 = (x2, y2), P3 = (x3, y3)
s = (y2 – y1)/(x2 – x1)
x3 = s^2 – x1 – x2
y3 = s(x1 – x3) – y1

x1, y1 = 2, 5
x2, y2 = -1, -1
s = (y2 - y1) / (x2 - x1)
x3 = s**2 - x1 - x2
y3 = s * (x1 - x3) - y1
print(x3, y3)

		if self.x != other.x:
			s = (other.y - self.y) / (other.x - self.x)
			x = s**2 - self.x - other.x
			y = s * (self.x - x) - self.y
			return self.__class__(x, y, self.a, self.b)

### P1 = P2 の時の点の加算
x3 = s^2 – 2×1
y3 = s(x1 – x3) – y1

a, x1, y1 = 5, -1, -1
s = (3 * x1**2 + a) / (2 * y1)
x3 = s**2 - 2*x1
y3 = s * (x1 - x3) - y1
print(x3, y3)

		if self == other:
			s = (3 * self.x**2 + self.a) / (2 * self.y)
			x = s**2 - 2 * self.x
			y = s * (self.x - x) - self.y
			return self.__class__(x, y, self.a, self.b)

		if self == other and self.y == 0 * self.x:
			return self.__class__(None, None, self.a, self.b)

なるほどー