《国密算法》--国产加密算法SM2，椭圆曲线。.zip

#!/usr/bin/python #-*- coding: utf-8 -*- """ Created on 2018-5-17 @author: aozhuo """ class FiniteFieldOperation: # 用扩展欧几里得算法求逆元 def CalculateInverseElement(self, x, p): temp_p = p s1, s2 = 1, 0 t1, t2 = 0, 1 while True: q = int(temp_p / x) #将s、t向下滑，这里就是交换数的位置 s1, s2 = s2, s1 - q * s2 t1, t2 = t2, t1 - q * t2 temp_p, x = x, temp_p % x if x == 1: break return t2 % p # 两个不同的点相加 def DifferentPointAdd(self, P1, P2, p): x1, y1 = P1 x2, y2 = P2 # 这里先判断能否整除，能整除就直接算，不能的话在用扩展欧几里得 if ((y2 - y1) % (x2 - x1)) == 0: t = int((y2 - y1) / (x2 - x1)) %p else: t = (self.CalculateInverseElement(x2 - x1, p) * (y2 - y1)) % p x3 = (t ** 2 - x1 - x2) % p y3 = (t * (x1 - x3) - y1) % p return x3, y3 # 两个相同的点相加 def PointDouble(self, P1, a, p): x1, y1 = P1 # 这个除法应该不是普通的除法吧 if ((3 * (x1 ** 2) + a) % (2 * y1)) == 0: t = int((3 * (x1 ** 2) + a) / (2 * y1)) % p else: t = (self.CalculateInverseElement(2 * y1, p) * (3 * (x1 ** 2) + a)) % p x3 = (t ** 2 - 2 * x1) % p y3 = (t * (x1 - x3) - y1) % p return x3, y3 # 整合一下上面两个函数，计算任意两个点相加的情况 def TwoPointAdd(self, P1, P2, a, p): if P1 == P2: return self.PointDouble(P1, a, p) else: return self.DifferentPointAdd(P1, P2, p) # 计算倍点 def CalculateEllipticPoint(self, k, P, a, p): multiple_P = P for i in range(k): multiple_P = self.TwoPointAdd(multiple_P, P, a, p) return multiple_P test = FiniteFieldOperation() P1 = [10,2] P2 = [9,6] x, y = test.PointDouble(P1, 1, 19) print(x, y)