用python编程实现ECC的基本运算规则。

下面是 Python 代码实现 ECC 的基本运算规则，同样假设椭圆曲线方程为 y^2 = x^3 + ax + b，其中 p 是模数。

p = 2333   # 模数p
a = 3      # 曲线系数a
b = 5      # 曲线系数b
Gx = 2     # 生成元G的x坐标
Gy = 6     # 生成元G的y坐标

class Point:
    def __init__(self, x, y):
        self.x = x
        self.y = y

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

    def __add__(self, other):
        if self == other:
            s = (3 * self.x * self.x + a) % p
            t = (2 * self.y) % p
        else:
            s = (other.y - self.y) % p
            t = (other.x - self.x) % p
        inv = pow(t, p - 2, p)
        lambda_ = (s * inv) % p
        x = (lambda_ * lambda_ - self.x - other.x) % p
        y = (lambda_ * (self.x - x) - self.y) % p
        return Point(x, y)

    def __rmul__(self, k):
        R = self
        k -= 1
        while k > 0:
            if k & 1:
                R = R + self
            self = self + self
            k >>= 1
        return R

    def __repr__(self):
        return f"({self.x}, {self.y})"

    def compress(self):
        flag = self.y & 1
        return (flag << 8) | self.x

    @staticmethod
    def decompress(com):
        flag = (com >> 8) & 1
        x = com & 0xff
        y2 = (x * x * x + a * x + b) % p
        if flag != (y2 & 1):
            y2 = p - y2
        y = pow(y2, (p + 1) // 4, p)
        return Point(x, y)

# 测试点加法
P = Point(1, 2)
Q = Point(3, 4)
R = P + Q
print(R)

# 测试倍乘
k = 5
S = k * P
print(S)

# 测试点压缩和解压缩
com = P.compress()
P = Point.decompress(com)
print(P)

上述代码中，pow(x, y, z) 函数是快速幂算法，用于计算 $x^y \bmod z$ 的值。