Finite fields : theory and computation : the meeting point of number theory, computer science, coding theory and cryptography

Bibliographic Information

Finite fields : theory and computation : the meeting point of number theory, computer science, coding theory and cryptography

by Igor E. Shparlinski

(Mathematics and its applications, v. 477)

Kluwer Academic Publishers, c1999

  • : hb

Available at  / 54 libraries

Search this Book/Journal

Note

Bibliography: p. 409-524

Includes index

Description and Table of Contents

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.

Table of Contents

Preface. Acknowledgments. Notation. Introduction. 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. Index.

by "Nielsen BookData"

Related Books: 1-1 of 1

Details

  • NCID
    BA41334011
  • ISBN
    • 0792356624
  • LCCN
    99018969
  • Country Code
    ne
  • Title Language Code
    eng
  • Text Language Code
    eng
  • Place of Publication
    Dordrecht
  • Pages/Volumes
    xiv, 528 p.
  • Size
    25 cm
  • Classification
  • Subject Headings
  • Parent Bibliography ID
Page Top