Elliptic Curves in Cryptography
Elliptic Curves in Cryptography
G. Seroussi, Hewlett-Packard Laboratories, Palo Alto, California
N. Smart, Hewlett-Packard Laboratories, Bristol
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.
- Indispensable for researchers in this area
- Authors are top names
- Covers state of the art results
Reviews & endorsements
'… gives a comprehensive explanation of elliptic curve cryptography. It is clearly written and is appropriate for both computer scientists and mathematicians interested in the field.' E. Schaefer, Niew Archief voor Wiskunde
'… a very well written description of the use of elliptic curves in public key cryptography.' Franck Leprévost, Zentralblatt für Mathematik
'An excellent new book on elliptic curve theory and practical implementation.' Dr Dobb's Journal Online
'… a good introduction to the mathematics behind the design of elliptic-curve cryptosystems and their implementation … this work is an important addition to the literature.' Jonathan Golan, Computing Reviews
'… written in a very readable form and thus can be consulted and used both by mathematicians and by anybody wishing to learn more about the mathematics behind the implementations of elliptic curve cryptosystems.' European Maths Society Journal
Product details
No date availablePaperback
9780521653749
224 pages
229 × 153 × 15 mm
0.326kg
Table of Contents
- Preface
- 1. Introduction
- 2. Finite field arithmetic
- 3. Arithmetic on an elliptic curve
- 4. Efficient implementation of elliptic curves
- 5. The elliptic curve discrete logarithm problem
- 6. Determining the group order
- 7. Schoof's algorithm and extensions
- 8. Generating curves using complex multiplication
- 9. Other applications of elliptic curves
- 10. Hyperelliptic curves
- Appendix A. Curve examples
- Bibliography
- Author index
- Subject index.
