Hewlett-Packard Laboratories Palo Alto, California and Bristol, U.K.

Cambridge University Press, Cambridge, 1999

ISBN: 0521653746

Description In the past few years elliptic curve cryptography has moved from a fringe activity to a major challenger to the dominant RSA/DSA systems. Elliptic curves offer major advances on older systems such as increased speed, less memory and smaller key sizes. As digital signatures become more and more important in the commercial world the use of elliptic curve-based signatures will become all pervasive. This book summarizes knowledge built up within Hewlett-Packard over a number of years, and explains the mathematics behind practical implementations of elliptic curve systems. Due to the advanced nature of the mathematics there is a high barrier to entry for individuals and companies to this technology. Hence this book will be invaluable not only to mathematicians wanting to see how pure mathematics can be applied but also to engineers and computer scientists wishing (or needing) to actually implement such systems.

For more information, see http://www.hpl.hp.com/research/itc/csl/vcd/infotheory/ellipbook.htm.

Institut fuer Mathematik, Universitaet Augsburg, Germany

Kluwer Academic Publishers, Boston

Hardbound, ISBN 0-7923-8589-6

August 1999, 184 pp.

NLG 235.00 / USD 115.00 / GBP 74.75

Since their invention in the late seventies, public key cryptosystems have become an indispensable asset in establishing private and secure electronic communication, and this need, given the tremendous growth of the Internet, is likely to continue growing. Elliptic curve cryptosystems represent the state of the art for such systems.

"Elliptic Curves and Their Applications to Cryptography: An Introduction" provides a comprehensive and self-contained introduction to elliptic curves and how they are employed to secure public key cryptosystems. Even though the elegant mathematical theory underlying these cryptosystems is considerably more involved than for other systems, this text requires the reader to have only an elementary knowledge of basic algebra. The text nevertheless leads to problems at the forefront of current research, featuring chapters on point counting algorithms and security issues. The adopted unifying approach treats with equal care elliptic curves over fields of even characteristic, which are especially suited for hardware implementations, and curves over fields of odd characteristic, which have traditionally received more attention.

"Elliptic Curves and Their Applications: An Introduction" has been used successfully for teaching advanced undergraduate courses. It will be of greatest interest to mathematicians, computer scientists, and engineers who are curious about elliptic curve cryptography in practice, without losing the beauty of the underlying mathematics.

For more information, see http://www.wkap.nl/book.htm/0-7923-8589-6.

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