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 explains the mathematics behind practical implementations of elliptic curve systems.
'... gives a comprehensive explanation of elliptic curve cryptography. It is clearly written and is appropriate for both computer scientists and mathematicians interested in the field.' E. Schaefer, Niew Archief voor Wiskunde '... a very well written description of the use of elliptic curves in public key cryptography.' Franck Leprevost, Zentralblatt fur Mathematik 'An excellent new book on elliptic curve theory and practical implementation.' Dr Dobb's Journal Online '... a good introduction to the mathematics behind the design of elliptic-curve cryptosystems and their implementation ... this work is an important addition to the literature.' Jonathan Golan, Computing Reviews '... 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
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