A Birthday Paradox for Markov Chains, with an Optimal Bound for Collision in the Pollard Rho Algorithm for Discrete Loga
We show a Birthday Paradox for self-intersections of Markov chains with uniform stationary distribution. As an application, we analyze Pollard’s Rho algorithm for finding the discrete logarithm in a cyclic group G and find that, if the partition in the al
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Editorial Board David Hutchison Lancaster University, UK Takeo Kanade Carnegie Mellon University, Pittsburgh, PA, USA Josef Kittler University of Surrey, Guildford, UK Jon M. Kleinberg Cornell University, Ithaca, NY, USA Alfred Kobsa University of California, Irvine, CA, USA Friedemann Mattern ETH Zurich, Switzerland John C. Mitchell Stanford University, CA, USA Moni Naor Weizmann Institute of Science, Rehovot, Israel Oscar Nierstrasz University of Bern, Switzerland C. Pandu Rangan Indian Institute of Technology, Madras, India Bernhard Steffen University of Dortmund, Germany Madhu Sudan Massachusetts Institute of Technology, MA, USA Demetri Terzopoulos University of California, Los Angeles, CA, USA Doug Tygar University of California, Berkeley, CA, USA Gerhard Weikum Max-Planck Institute of Computer Science, Saarbruecken, Germany
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Alfred J. van der Poorten Andreas Stein (Eds.)
Algorithmic Number Theory 8th International Symposium, ANTS-VIII Banff, Canada, May 17-22, 2008 Proceedings
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Volume Editors Alfred J. van der Poorten ceNTRe for Number Theory Research 1 Bimbil Place, Killara, NSW 2071, Australia E-mail: [email protected] Andreas Stein Carl von Ossietzky Universität Oldenburg Institut für Mathematik 26111 Oldenburg, Germany E-mail: [email protected]
Library of Congress Control Number: 2008925108 CR Subject Classification (1998): F.2, G.2, E.3, I.1 LNCS Sublibrary: SL 1 – Theoretical Computer Science and General Issues ISSN ISBN-10 ISBN-13
0302-9743 3-540-79455-7 Springer Berlin Heidelberg New York 978-3-540-79455-4 Springer Berlin Heidelberg New York
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Preface
The first Algorithmic Number Theory Symposium took place in May 1994 at Cornell University. The preface to its proceedings has the organizers expressing the hope that the meeting would be “the first in a long series of international conferences on the algorithmic, computational, and complexity theoretic aspects of number theory.” ANTS VIII was held May 17–22, 2008 at the Banff Centre in Banff, Alberta, Canada. It was the eighth in this lengthening series. The conference included four invited talks, by Johannes Buchmann (TU ´ Darmstadt), Andrew Granville (Universit´e de Mont
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