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Applications of Finite Fields

  • Ian F. Blake
  • XuHong Gao
  • Ronald C. Mullin
  • Scott A. Vanstone
  • Tomik Yaghoobian
  • Editors
  • Alfred J. Menezes

Table of contents

  1. Front Matter
    Pages i-xiii
  2. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 1-16
  3. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 17-38
  4. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 39-68
  5. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 69-92
  6. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 93-114
  7. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 115-138
  8. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 139-150
  9. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 151-171
  10. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 173-190
  11. Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian
    Pages 191-209
  12. Back Matter
    Pages 211-218

About this book

Introduction

The theory of finite fields, whose origins can be traced back to the works of Gauss and Galois, has played a part in various branches in mathematics. Inrecent years we have witnessed a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. The purpose of this book is to introduce the reader to some of these recent developments. It should be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. We shall focus our attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, we have not attempted to be encyclopedic. Among the topics studied are different methods of representing the elements of a finite field (including normal bases and optimal normal bases), algorithms for factoring polynomials over finite fields, methods for constructing irreducible polynomials, the discrete logarithm problem and its implications to cryptography, the use of elliptic curves in constructing public key cryptosystems, and the uses of algebraic geometry in constructing good error-correcting codes. To limit the size of the volume we have been forced to omit some important applications of finite fields. Some of these missing applications are briefly mentioned in the Appendix along with some key references.

Keywords

algorithms coding theory computer computer science cryptography error-correcting code finite field geometry

Authors and affiliations

  • Ian F. Blake
    • 1
  • XuHong Gao
    • 1
  • Ronald C. Mullin
    • 1
  • Scott A. Vanstone
    • 1
  • Tomik Yaghoobian
    • 1
  1. 1.University of WaterlooCanada

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-2226-0
  • Copyright Information Springer-Verlag US 1993
  • Publisher Name Springer, Boston, MA
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-5130-4
  • Online ISBN 978-1-4757-2226-0
  • Series Print ISSN 0893-3405
  • Buy this book on publisher's site