Elliptic Curves in Cryptography

London Mathematical Society Lecture Note #265

by Ian F. Blake, Gadiel Seroussi, Nigel P. Smart

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.

224 pages, ebook

First published January 1, 1999

Reviews

[Dan · Rating 4 out of 5]

This is a good book for a high level introduction to the Mathematics behind Elliptic Curve Cryptography.

It does not go into a great amount of detail, but it is relatively clearly written, and that definitely counts for a lot. Also, it has a very comprehensive list of references, and cites them well, so it is easy to track down the details.

So far I have used this book to learn about:

1) Isogenies - a high level introduction / definitions.
2) Complex Multiplication - I got introduced to the subject here.

I read this book because my boss Kristin Lauter suggested it was a good place to start learning about ECC.