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Handbook of Elliptic and Hyperelliptic Curve Cryptography book cover

1st Edition

Handbook of Elliptic and Hyperelliptic Curve Cryptography

Edited By Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, Frederik Vercauteren Copyright 2005
842 Pages 44 B/W Illustrations
by Chapman & Hall

The discrete logarithm problem based on elliptic and hyperelliptic curves has gained a lot of popularity as a cryptographic primitive. The main reason is that no subexponential algorithm for computing discrete logarithms on small genus curves is currently available, except in very special cases. Therefore curve-based cryptosystems require much smaller key sizes than RSA to attain the same security... Read more
Preface
Introduction to Public-Key Cryptography
Mathematical Background
Algebraic Background
Background on p-adic Numbers
Background on Curves and Jacobians
Varieties Over Special Fields
Background on Pairings
Background on Weil Descent
Cohomological Background on Point Counting
Elementary Arithmetic
Exponentiation
Integer Arithmetic
Finite Field Arithmetic
Arithmetic of p-adic Numbers
Arithmetic of Curves
Arithmetic of Elliptic Curves
Arithmetic of Hyperelliptic Curves
Arithmetic of Special Curves
Implementation of Pairings
Point Counting
Point Counting on Elliptic and Hyperelliptic Curves
Complex Multiplication
Computation of Discrete Logarithms
Generic Algorithms for Computing Discrete Logarithms
Index Calculus
Index Calculus for Hyperelliptic Curves
Transfer of Discrete Logarithms
Applications
Algebraic Realizations of DL Systems
Pairing-Based Cryptography
Compositeness and Primality Testing-Factoring
Realizations of DL Systems
Fast Arithmetic Hardware
Smart Cards
Practical Attacks on Smart Cards
Mathematical Countermeasures Against Side-Channel Attacks
Random Numbers—Generation and Testing
References

Biography

Henri Cohen, Gerhard Frey, Roberto Avanzi, Christophe Doche, Tanja Lange, Kim Nguyen, Frederik Vercauteren

… very comprehensive coverage of this vast subject area … a useful and essential treatise for anyone involved in elliptic curve algorithms … this book offers the opportunity to grasp the ECC technology with a diversified and comprehensive perspective. … This book will remain on my shelf for a long time and will land on my desk on many occasions, if only because the coverage of the issues common to factoring and discrete log cryptosystems is excellent.
—IACR Book Reviews, June 2011

… the book is designed for people who are working in the area and want to learn more about a specific issue. The chapters are written to be relatively independent so that readers can focus on the part of interest for them. Such readers will be grateful for the excellent index and extensive bibliography. … the handbook covers a wide range of topics and will be a valuable reference for researchers in curve-based cryptography.
—Steven D. Galbraith, Mathematical Reviews, Issue 2007f

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