Elliptic Curves in Cryptography (London Mathematical Society Lecture Note Series, Series Number 265)

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. 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. Elliptic Curve Cryptography Is A Major Challenger To The Dominant Rsa/dsa Systems, With Increased Speed, Less Memory Required And Smaller Key Sizes. This Book Summarises Knowledge Built Up Within Hewlett Packard Over A Number Of Years. Ch. I. Introduction -- Ch. Ii. Finite Field Arithmetic -- Ch. Iii. Arithmetic On An Elliptic Curve -- Ch. Iv. Efficient Implementation Of Elliptic Curves -- Ch. V. The Elliptic Curve Discrete Logarithm Problem -- Ch. Vi. Determining The Group Order -- Ch. Vii. Schoof's Algorithm And Extensions -- Ch. Viii. Generating Curves Using Complex Multiplication -- Ch. Ix. Other Applications Of Elliptic Curves -- Ch. X. Hyperelliptic Cryptosystems -- App. A. Curve Examples. I.f. Blake, G. Seroussi, And N.p. Smart. Includes Bibliographical References And Index.