Elliptic Curves in Cryptography

This book explains the mathematics behind practical implementations of elliptic curve systems.

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.

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.

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. It will be invaluable to mathematicians wanting to see how pure mathematics can be applied, and also engineers and computer scientists wishing to implement such systems.