Non-degeneracy of Pollard Rho Collisions

Details Non-degeneracy of Pollard Rho Collisions Non-degeneracy of Pollard Rho Collisions

2008-08-04

arxiv.org/abs/0808.0469v2

Mathematics

Number Theory

10 pages

Scientific paper

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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