Non-degeneracy of Pollard Rho Collisions

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dc.creatorMiller, Stephen D.
dc.creatorVenkatesan, Ramarathnam
dc.date2008-08-04
dc.date2008-08-31
dc.date.accessioned2026-07-07T09:59:17Z
dc.date.available2026-07-07T09:59:17Z
dc.descriptionThe 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.
dc.description10 pages
dc.identifierhttps://arxiv.org/abs/0808.0469
dc.identifierhttp://arxiv.org/abs/0808.0469
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/167966
dc.subjectNumber Theory
dc.subjectCryptography and Security
dc.subjectDiscrete Mathematics
dc.subjectCombinatorics
dc.titleNon-degeneracy of Pollard Rho Collisions
dc.typetext

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