Non-degeneracy of Pollard Rho Collisions

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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.
10 pages

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Number Theory, Cryptography and Security, Discrete Mathematics, Combinatorics

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http://salesiana.dossiersoluciones.com/handle/123456789/167966

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0808.0469
 http://arxiv.org/abs/0808.0469

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arXiv