Non-degeneracy of Pollard Rho Collisions
Number Theory
2008-08-31 v2 Cryptography and Security
Discrete Mathematics
Combinatorics
Abstract
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.
Keywords
Cite
@article{arxiv.0808.0469,
title = {Non-degeneracy of Pollard Rho Collisions},
author = {Stephen D. Miller and Ramarathnam Venkatesan},
journal= {arXiv preprint arXiv:0808.0469},
year = {2008}
}
Comments
10 pages