Elliptic and Hyperelliptic Curve Cryptography

Henri Cohen, Gerhard Frey - Collection Discrete Mathematics and Its Applications

808 pages, parution le 23/08/2005

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Résumé

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security level. This makes them particularly attractive for implementation on memory-restricted devices like smart cards and in high-security applications.

The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the arithmetic of elliptic and hyperelliptic curves and the computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves as well as transfers of discrete logarithm problems for special curves. It ends up with concrete realizations of cryptosystems in smart cards, including efficient implementation in hardware and side-channel attacks as well as countermeasures.

Authored by an outstanding group of experts, this is the definitive guide to quickly and easily implementing curve-based cryptography for efficient and robust security.

L'auteur - Henri Cohen

Dr. Henri Cohen is Professor of Mathematics at the University of Bordeaux, France. His research interests are number theory in general, and computational number theory in particular.

L'auteur - Gerhard Frey

Dr. Gerhard Frey holds a chair for number theory at the Institute for Experimental Mathematics at the University of Duisburg-Essen, Germany. His research interests are number theory and arithmetical geometry as well as applications to coding theory and cryptography.

Sommaire

List pf Algorithms
Preface
Introduction to Public-Key Cryptography
Mathematical Background
Elementary Arithmetic
Arithmetic of Curves
Point Counting
Computation of Discrete Logarithms
Applications
Realization of Discrete Logarithm Systems
References
Notation Index
General Index

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	PAPIER
Éditeur(s)	Chapman and Hall / CRC
Auteur(s)	Henri Cohen, Gerhard Frey
Collection	Discrete Mathematics and Its Applications
Parution	23/08/2005
Nb. de pages	808
Format	18,5 x 26
Couverture	Relié
Poids	1630g
Intérieur	Noir et Blanc
EAN13	9781584885184
ISBN13	978-1-58488-518-4