Algebraic Curves and Cryptography (Fields Institute Communications)

V. Kumar Murty

ISBN 10: 0821843117 / ISBN 13: 9780821843116

Published by Amer Mathematical Society, 2010

Focusing on the theme of point counting and explicit arithmetic on the Jacobians of curves over finite fields the topics covered in this volume 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. Editor(s): Murty, V. Kumar. Series: Fields Institute Communications. Num Pages: 133 pages, Illustrations. BIC Classification: PBF. Category: (P) Professional & Vocational. Dimension: 229 x 152. . . 2010. Hardcover. . . . . Seller Inventory # V9780821843116

Synopsis:

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).

Bibliographic Details

Title: Algebraic Curves and Cryptography (Fields ...
Publisher: Amer Mathematical Society
Publication Date: 2010
Binding: Hardcover
Condition: New