# stark curve https://docs.starkware.co/starkex/crypto/stark-curve.html

import random


p = 3618502788666131213697322783095070105623107215331596699973092056135872020481
alpha = 1
# $$y^2 = x^3 + \alpha \dot x + \beta$$  (mod p)
beta = 3141592653589793238462643383279502884197169399375105820974944592307816406665
F = GF(p)
E = EllipticCurve(F, [alpha,beta])
ec_order = E.order()
# ECDSA scheme generator
G_generator = E(874739451078007766457464989774322083649278607533249481151382481072868806602, 152666792071518830868575557812948353041420400780739481342941381225525861407)
p_scalar = 3618502788666131213697322783095070105526743751716087489154079457884512865583
K = GF(p_scalar)


class CurvePoint():
      def __init__(self, x=None, y=None):
          if x==None or y==None:
             self.point = CurvePoint.random()
          else:
                self.point = E(x,y)
          self.x = self.point[0]
          self.y = self.point[1]

      def zero():
            return G_generator * 0

      def __repr__(self):
          return bytes("[ x: {}, y: {}, z: 1]".format(self.x, self.y), encoding='utf-8')

      def __str__(self):
          return self.__repr__()

      def random(max=p):
          return G_generator * random.randint(0, max)

      def __add__(self, rhs):
          return self.point + rhs.point

      def __sub__(self, rhs):
          return self.point - rhs.point

      def __neg__(self):
          return -1 * self.point

      def generator():
          return G_generator

      def __mul__(self, factor):
          return factor * self.point

      def msm(points, scalars):
          assert len(points) == len(scalars), 'len(p): {}, len(s): {}'.format(len(points), len(scalars))
          return sum([s*p for (s, p) in zip(points, scalars)])