Elliptic Curves
Number Theory and Cryptography, Second Edition
2nd Edition
Published on 3. April 2008
Book
Hardback
532 pages
978-1-4200-7146-7 (ISBN)
Description
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.
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.
Reviews / Votes
... 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
More details
Series
Edition
2nd edition
Language
English
Place of publication
Oxford
United Kingdom
Publishing group
Taylor & Francis Ltd
Target group
College/higher education
Professional
Illustrations
20 s/w Abbildungen
20 Illustrations, black and white
Dimensions
Height: 240 mm
Width: 161 mm
Thickness: 33 mm
Weight
957 gr
ISBN-13
978-1-4200-7146-7 (9781420071467)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
E-Book
04/2008
2nd Edition
Chapman & Hall/CRC
€264.99
Available for download
E-Book
04/2008
2nd Edition
Chapman and Hall
€264.99
Available for download
Previous edition
Book
05/2003
1st Edition
Chapman & Hall/CRC
€79.41
Article exhausted; check for reprint
Person
Lawrence C. Washington
Content
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.