如何测试SageMath中求解小整数ECDL的算法？

Question

我的问题是在SageMath或Python中实现baby-step-giant-step或Pollard-Rho，为给定的p生成一个G的小乘数x，这样p=x*G

这是一个大项目的任务部分

modi =  115792089237316195423570985008687907853269984665640564039457584007908834671663

E=EllipticCurve(GF(modi), [0,7])

G=E(55066263022277343669578718895168534326250603453777594175500187360389116729240, 32670510020758816978083085130507043184471273380659243275938904335757337482424)

P=E(69335761065767984070318781108127416310968753866933119760392423089576366173459, 113425617697416972613102767146321902225172329004525144463444008550345431352693)

x=2473426105351567

搜索应限制在x的2^54点空间内，并求解p=x*G，保留上面的所有其他参数

我尝试了https://github.com/qubd/mini_ecdsa，得到了下面的错误

>>>C = CurveOverFp(0, 0, 7, 2**256-2**32-2**9-2**8-2**7-2**6-2**4-1)
y^2 = x^3 + 7 over F_115792089237316195423570985008687907853269984665640564039457584007908834671663

>>> P = Point(55066263022277343669578718895168534326250603453777594175500187360389116729240,
... 32670510020758816978083085130507043184471273380659243275938904335757337482424)

>>> n = 2^54

>>> Q = (69335761065767984070318781108127416310968753866933119760392423089576366173459, 113425617697416972613102767146321902225172329004525144463444008550345431352693)

>>>crack_baby_giant(C, P, n, Q)

Traceback (most recent call last):
  File "<stdin>", line 1, in <module>
  File "mini_ecdsa.py", line 470, in crack_baby_giant
    R = curve.add(Q, curve.invert(curve.mult(P, g*m)))
  File "mini_ecdsa.py", line 321, in add
    y_diff = (P_2.y - P_1.y) % self.char
AttributeError: 'tuple' object has no attribute 'y'

Answer 1

您正在尝试对Q使用元组。但是如果需要一个Point，这就行不通了，正如Github链接中的文档所示。试着做Q = Point(... , ...)，希望这能奏效

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顺便说一句，可能您应该自己实现它，而不是用其他代码实现-或者这是作为一个例子提供的？祝你好运