parameter_recovery.py

def attack(p, x1, y1, x2, y2):
    """
    Recovers the a and b parameters from an elliptic curve when two points are known.
    :param p: the prime of the curve base ring
    :param x1: the x coordinate of the first point
    :param y1: the y coordinate of the first point
    :param x2: the x coordinate of the second point
    :param y2: the y coordinate of the second point
    :return: a tuple containing the a and b parameters of the elliptic curve
    """
    a = pow(x1 - x2, -1, p) * (pow(y1, 2, p) - pow(y2, 2, p) - (pow(x1, 3, p) - pow(x2, 3, p))) % p
    b = (pow(y1, 2, p) - pow(x1, 3, p) - a * x1) % p
    return int(a), int(b)