
Finite Fields: Theory and Computation
The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography
Igor Shparlinski(Author)
Springer (Publisher)
Published on 7. December 2010
Book
Paperback/Softback
XIV, 528 pages
978-90-481-5203-2 (ISBN)
Description
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.
Reviews / Votes
` ...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 für Mathematik, 132:1 (2001)
More details
Series
Edition
Softcover reprint of hardcover 1st ed. 1999
Language
English
Place of publication
Dordrecht
Netherlands
Target group
Professional and scholarly
Research
Illustrations
XIV, 528 p.
Dimensions
Height: 235 mm
Width: 155 mm
Thickness: 30 mm
Weight
814 gr
ISBN-13
978-90-481-5203-2 (9789048152032)
DOI
10.1007/978-94-015-9239-0
Schweitzer Classification
Other editions
Additional editions

Igor Shparlinski
Finite Fields: Theory and Computation
The Meeting Point of Number Theory, Computer Science, Coding Theory and Cryptography
Book
05/1999
Kluwer Academic Publishers
€213.99
Shipment within 15-20 days
Content
Links flowchart.- 1. Polynomial Factorization.- 2. Finding Irreducible and Primitive Polynomials.- 3. The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices.- 4. Bases and Computation in Finite Fields.- 5. Coding Theory and Algebraic Curves.- 6. Elliptic Curves.- 7. Recurrence Sequences in Finite Fields and Cyclic Linear Codes.- 8. Finite Fields and Discrete Mathematics.- 9. Congruences.- 10. Some Related Problems.- Appendix 1.- Appendix 2.- Appendix 3.- References.