The Springer International Series in Engineering and Computer Science

Applications of Finite Fields

Authors: Menezes, A.J., Blake, I.F., XuHong Gao, Mullin, R.C., Vanstone, S.A., Yaghoobian, T.

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eBook 142,79 €
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  • ISBN 978-1-4757-2226-0
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Hardcover 176,79 €
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  • ISBN 978-0-7923-9282-8
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Softcover 176,79 €
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  • ISBN 978-1-4419-5130-4
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About this book

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.

Table of contents (10 chapters)

  • Introduction to Finite Fields and Bases

    Blake, Ian F. (et al.)

    Pages 1-16

    Preview Buy Chapter 30,19 €
  • Factoring Polynomials over Finite Fields

    Blake, Ian F. (et al.)

    Pages 17-38

    Preview Buy Chapter 30,19 €
  • Construction of Irreducible Polynomials

    Blake, Ian F. (et al.)

    Pages 39-68

    Preview Buy Chapter 30,19 €
  • Normal Bases

    Blake, Ian F. (et al.)

    Pages 69-92

    Preview Buy Chapter 30,19 €
  • Optimal Normal Bases

    Blake, Ian F. (et al.)

    Pages 93-114

    Preview Buy Chapter 30,19 €

Buy this book

eBook 142,79 €
price for Spain (gross)
valid through November 5, 2017
  • ISBN 978-1-4757-2226-0
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover 176,79 €
price for Spain (gross)
valid through November 5, 2017
  • ISBN 978-0-7923-9282-8
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
Softcover 176,79 €
price for Spain (gross)
valid through November 5, 2017
  • ISBN 978-1-4419-5130-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
  • The final prices may differ from the prices shown due to specifics of VAT rules
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Bibliographic Information

Bibliographic Information
Book Title
Applications of Finite Fields
Authors
Series Title
The Springer International Series in Engineering and Computer Science
Series Volume
199
Copyright
1993
Publisher
Springer US
Copyright Holder
Springer-Verlag US
eBook ISBN
978-1-4757-2226-0
DOI
10.1007/978-1-4757-2226-0
Hardcover ISBN
978-0-7923-9282-8
Softcover ISBN
978-1-4419-5130-4
Series ISSN
0893-3405
Edition Number
1
Number of Pages
XIV, 218
Topics