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Elliptic Curves in Cryptography
About This Book
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.
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Table of contents
- Cover
- Series Page
- Title
- Copyright
- Dedication
- Contents
- Preface
- Abbreviations and Standard Notation
- CHAPTER I Introduction
- CHAPTER II Finite Field Arithmetic
- CHAPTER III Arithmetic on an Elliptic Curve
- CHAPTER IV Efficient Implementation of Elliptic Curves
- CHAPTER V The Elliptic Curve Discrete Logarithm Problem
- CHAPTER VI Determining the Group Order
- CHAPTER VII Schoof's Algorithm and Extensions
- CHAPTER VIII Generating Curves using Complex Multiplication
- CHAPTER IX Other Applications of Elliptic Curves
- CHAPTER X Hyperelliptic Cryptosystems
- APPENDIX A Curve Examples
- Bibliography
- Author Index
- Subject Index