Gerhard Frey – författare
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4 produkter
4 produkter
3 325 kr
Skickas inom 10-15 vardagar
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 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.
Algebra and Number Theory
Proceedings of a Conference held at the Institute of Experimental Mathematics, University of Essen (Germany), December 2-4, 1992
Inbunden, Engelska, 1994
2 516 kr
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No detailed description available for "Algebra and Number Theory".
603 kr
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Del 1585 - Lecture Notes in Mathematics
On Artin's Conjecture for Odd 2-dimensional Representations
Häftad, Engelska, 1994
379 kr
Skickas inom 10-15 vardagar
The aim of this volume is to develop efficient algorithms by which one can verify Artin's conjecture for odd two-dimensional representations in a fairly wide range. It describes how to determine the number of all representations with given Artin conductor and determinant, and how to compute the dimension of a corresponding space of cusp forms of weight 1, which is done by exploiting the explicit knowledge of the operation of Hecke operators on modular symbols. It is hoped that the algorithms developed in the volume can be of use for many other problems related to modular forms.