Elliptic Curves: Number Theory and Cryptography, Second Edition / Edition 2

by Lawrence C. Washington

Overview

Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves.

New to the Second Edition

Chapters on isogenies and hyperelliptic curves

A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues

A more complete treatment of the Weil and Tate–Lichtenbaum pairings

Doud’s analytic method for computing torsion on elliptic curves over Q

An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems

Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

Product Details

ISBN-13:	9781420071467
Publisher:	Taylor & Francis
Publication date:	04/03/2008
Series:	Discrete Mathematics and Its Applications , #43
Edition description:	REV
Pages:	532
Product dimensions:	6.12(w) x 9.19(h) x (d)

Table of Contents

Introduction. The Basic Theory. Torsion Points. Elliptic Curves over Finite Fields. The Discrete Logarithm Problem. Elliptic Curve Cryptography. Other Applications. Elliptic Curves over Q. Elliptic Curves over C. Complex Multiplication. Divisors. Isogenies. Hyperelliptic Curves. Zeta Functions. Fermat’s Last Theorem. Appendices. References. Index.

Editorial Reviews

… the book is well structured and does not waste the reader’s time in dividing cryptography from number theory-only information. This enables the reader just to pick the desired information. … a very comprehensive guide on the theory of elliptic curves. … I can recommend this book for both cryptographers and mathematicians doing either their Ph.D. or Master’s … I enjoyed reading and studying this book and will be glad to have it as a future reference.
—IACR book reviews, April 2010

Praise for the First Edition
There are already a number of books about elliptic curves, but this new offering by Washington is definitely among the best of them. It gives a rigorous though relatively elementary development of the theory of elliptic curves, with emphasis on those aspects of the theory most relevant for an understanding of elliptic curve cryptography. … an excellent companion to the books of Silverman and Blake, Seroussi and Smart. It would be a fine asset to any library or collection.
—Mathematical Reviews, Issue 2004e

Washington … has found just the right level of abstraction for a first book … . Notably, he offers the most lucid and concrete account ever of the perpetually mysterious Shafarevich–Tate group. A pleasure to read! Summing Up: Highly recommended.
—CHOICE, March 2004

… a nice, relatively complete, elementary account of elliptic curves.
—Bulletin of the AMS

From the Publisher