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Algebraic Curves and Cryptography
Edited by: V. Kumar Murty, University of Toronto, ON, Canada
A co-publication of the AMS and Fields Institute.

Fields Institute Communications
2010; 133 pp; hardcover
Volume: 58
ISBN-10: 0-8218-4311-7
ISBN-13: 978-0-8218-4311-6
List Price: US$83
Member Price: US$66.40
Order Code: FIC/58
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See also:

Cryptography: An Introduction - V V Yaschenko

\(p\)-adic Geometry: Lectures from the 2007 Arizona Winter School - Matthew Baker, Brian Conrad, Samit Dasgupta, Kiran S Kedlaya, Jeremy Teitelbaum, edited by David Savitt and Dinesh S Thakur

It is by now a well-known paradigm that public-key cryptosystems can be built using finite Abelian groups and that algebraic geometry provides a supply of such groups through Abelian varieties over finite fields. Of special interest are the Abelian varieties that are Jacobians of algebraic curves. All of the articles in this volume are centered on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields. The topics covered include Schoof's \(\ell\)-adic point counting algorithm, the \(p\)-adic algorithms of Kedlaya and Denef-Vercauteren, explicit arithmetic on the Jacobians of \(C_{ab}\) curves and zeta functions.

This volume is based on seminars on algebraic curves and cryptography held at the GANITA Lab of the University of Toronto during 2001-2008. The articles are mostly suitable for independent study by graduate students who wish to enter the field, both in terms of introducing basic material as well as guiding them in the literature. The literature in cryptography seems to be growing at an exponential rate. For a new entrant into the subject, navigating through this ocean can seem quite daunting. In this volume, the reader is steered toward a discussion of a few key ideas of the subject, together with some brief guidance for further reading. It is hoped that this approach may render the subject more approachable.

Titles in this series are co-published with the Fields Institute for Research in Mathematical Sciences (Toronto, Ontario, Canada).


Graduate students and research mathematicians interested in cryptography, applications of number theory and algebraic geometry.

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