Handbook of Elliptic and Hyperelliptic Curve Cryptography (Discrete Mathematics and Its Applications)
by Henri CohenThe 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 level.
This makes them particularly attractive for implementations on memory-restricted devices like smart cards and in high-security applications.
The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography.
After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the group operations and computation of pairings.
It explores methods for point counting and constructing curves with the complex multiplication method and provides the algorithms in an explicit manner.
It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves.
For some special curves the discrete logarithm problem can be transferred to an easier one; the consequences are explained and suggestions for good choices are given.
The authors present applications to protocols for discrete-logarithm-based systems (including bilinear structures) and explain the use of elliptic and hyperelliptic curves in factorization and primality proving.
Two chapters explore their design and efficient implementations in smart cards.
Practical and theoretical aspects of side-channel attacks and countermeasures and a chapter devoted to (pseudo-)random number generation round off the exposition.
The broad coverage of all- important areas makes this book a complete handbook of elliptic and hyperelliptic curve cryptography and an invaluable reference to anyone interested in this exciting field.
- Format
- 848 pages, Hardcover
- First published
- July 19, 2005
- Publishers
- Chapman & Hall/CRC
- Subjects
- Data security·Data encryption·Handbooks·Manuals·Etc·Chemistry·General·Language arts·Disciplines·Mathematics·Geometry·Algebraic·Language·Curves·Elliptic·Communication·Mathematics·Combinatorics·Machine theory·Cryptograph
- Language
- English
The book is a collection of algorithms without a central logical thought. It would be more helpful if an effort was made to justify some of the developments from the mathematical point of view.
Don't be fooled: This is a book written by experts, for professionals. The introductory chapters "cover" the mathematical preliminaries, but if you're not already familiar with the concepts, you won't get enough help there to be able to digest the real content of the book, which is very detailed, and looks to be very complete.
When I first opened this book, a tear fell from my eye. Never in my life have I seen such mathematical beauty as summarized from this book.
About Henri Cohen
French numismatist, composer and writer...
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