
The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curvebased cryptography. After a very detailed exposition of the mathematical background, it provides readytoimplement 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 discretelogarithmbased 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 sidechannel 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.
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