Computational and Algorithmic Problems in Finite Fields (Mathematics and its Applications)

Shparlinski, Igor

ISBN 10: 0792320573 / ISBN 13: 9780792320579

Editore: Springer, 1992

In. Codice articolo ria9780792320579_new

Riassunto:

This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, distribution of these primitive polynomials and of primitive points on elliptic curves, constructing bases of various types, and new applications of finite fields to other areas of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc). The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presupposes only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.

Contenuti: Series Editor's Preface. Preface. Notations. Introduction. 1. Polynomial Factorization. 2. Finding Irreducible and Primitive Polynomials. 3. The Distribution of Irreducible and Primitive Polynomials. 4. Bases and Computation in Finite Fields. 5. Coding Theory and Algebraic Curves. 6. Elliptic Curves. 7. Recurrent Sequences in Finite Fields and Linear Cyclic Codes. 8. Finite Fields and Discreate Mathematics. 9. Congruences. 10. Some Related Problems. Appendix 1. Appendix 2. Appendix 3. Addendum. References. Index.

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Titolo: Computational and Algorithmic Problems in ...
Casa editrice: Springer
Data di pubblicazione: 1992
Legatura: Rilegato
Condizione: New