Elliptic Curves in Cryptography

ISBN-13: 9780521653749 / Angielski / Miękka / 1999 / 224 str.

Ian F. Blake; I. Blake; G. Seroussi

Opis

In the past few years elliptic curve cryptography has moved from a fringe activity to a major system in the commercial world. This timely work summarizes knowledge gathered at Hewlett-Packard over a number of years and explains the mathematics behind practical implementations of elliptic curve systems. Since the mathematics is advanced, a high barrier to entry exists for individuals and companies new to this technology. Hence, this book will be invaluable not only to mathematicians but also to engineers and computer scientists who want to actually implement such systems.

Recenzje

'… 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

Spis treści

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.