Skip to main content
SpringerLink
Log in

Finite Fields: Theory and Computation

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

  • Conference proceedings
  • © 1999

Overview

Authors:
  1. Igor E. Shparlinski

    1. School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, Australia

    View author publications

    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 477)

This is a preview of subscription content, log in via an institution to check access.

Access this book

Log in via an institution
eBook USD 169.00
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book USD 219.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book USD 219.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Other ways to access

Licence this eBook for your library

Institutional subscriptions

Table of contents (12 papers)

  1. Front Matter

    Pages i-xiv
    Download chapter PDF

  2. Introduction

    • Igor E. Shparlinski
    Pages 1-11

  3. Links Flowchart

    • Igor E. Shparlinski
    Pages 13-15

  4. Polynomial Factorization

    • Igor E. Shparlinski
    Pages 17-44

  5. Finding Irreducible and Primitive Polynomials

    • Igor E. Shparlinski
    Pages 45-64

  6. The Distribution of Irreducible, Primitive and Other Special Polynomials and Matrices

    • Igor E. Shparlinski
    Pages 65-98

  7. Bases and Computation in Finite Fields

    • Igor E. Shparlinski
    Pages 99-148

  8. Coding Theory and Algebraic Curves

    • Igor E. Shparlinski
    Pages 149-213

  9. Elliptic Curves

    • Igor E. Shparlinski
    Pages 215-237

  10. Recurrence Sequences in Finite Fields and Cyclic Linear Codes

    • Igor E. Shparlinski
    Pages 239-264

  11. Finite Fields and Discrete Mathematics

    • Igor E. Shparlinski
    Pages 265-324

  12. Congruences

    • Igor E. Shparlinski
    Pages 325-359

  13. Some Related Problems

    • Igor E. Shparlinski
    Pages 361-401

  14. Back Matter

    Pages 403-528
    Download chapter PDF
Back to top

Keywords

About this book

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

`...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)

Authors and Affiliations

  • School of Mathematics, Physics, Computing and Electronics, Macquarie University, Sydney, Australia

    Igor E. Shparlinski

Bibliographic Information

Publish with us

Policies and ethics

Back to top

Search

Navigation