Pollard Rho碰撞的非简并性
Non-degeneracy of Pollard Rho Collisions
摘要：
Pollard Rho算法是一种广泛应用于求解包括椭圆曲线在内的一般循环群上的离散曲线的算法。最近，第一个非平凡的运行时间估计提供了它，最终在一个尖锐的O（sqrt（n））的碰撞时间限制在一个循环群的顺序n。在本文中，我们表明，对于n满足一个温和的算术条件，这些结果所保证的碰撞是非退化的高概率：即，Pollard Rho算法成功地找到了离散对数。
英文摘要：
The Pollard Rho algorithm is a widely used algorithm for solving discrete logarithms on general cyclic groups, including elliptic curves. Recently the first nontrivial runtime estimates were provided for it, culminating in a sharp O(sqrt(n)) bound for the collision time on a cyclic group of order n. In this paper we show that for n satisfying a mild arithmetic condition, the collisions guaranteed by these results are nondegenerate with high probability: that is, the Pollard Rho algorithm successfully finds the discrete logarithm.
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