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Finite Fields: Theory and Computation : The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography - Igor Shparlinski

Finite Fields: Theory and Computation

The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography

Hardcover Published: 31st May 1999
ISBN: 9780792356622
Number Of Pages: 528

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This book is mainly devoted to some computational and algorithmic problems in finite fields such as, for example, polynomial factorization, finding irreducible and primitive polynomials, the 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 we in­ clude two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number gener­ ators, modular arithmetic, etc.) and computational number theory (primality testing, factoring integers, computation in algebraic number theory, etc.). The problems considered here have many applications in Computer Science, Cod­ ing Theory, Cryptography, Numerical Methods, and so on. There are a few books devoted to more general questions, but the results contained in this book have not till now been collected under one cover. In the present work the author has attempted to point out new links among different areas of the theory of finite fields. It contains many very important results which previously could be found only in widely scattered and hardly available conference proceedings and journals. In particular, we extensively review results which originally appeared only in Russian, and are not well known to mathematicians outside the former USSR.

`...the book can yet be highly recommended as encyclopaedia on these topics, in particular because many Russian papers are incorporated which are hardly accessible.' Monatschafte fur Mathematik, 132:1 (2001)

Preface
Acknowledgments
Notation
Introduction
Links flowchart
Polynomial Factorization
Finding Irreducible and Primitive Polynomials
The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices
Bases and Computation in Finite Fields
Coding Theory and Algebraic Curves
Elliptic Curves
Recurrence Sequences in Finite Fields and Cyclic Linear Codes
Finite Fields and Discrete Mathematics
Congruences
Some Related Problems
References
Index.
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780792356622
ISBN-10: 0792356624
Series: MATHEMATICS AND ITS APPLICATIONS (KLUWER )
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 528
Published: 31st May 1999
Publisher: Springer
Country of Publication: NL
Dimensions (cm): 25.4 x 16.51  x 3.81
Weight (kg): 0.93