Applications of Finite Fields

Alfred J. Menezes, Ian F. Blake, Xuhong Gao, Ronald C. Mullin, Scott A. Vanstone (Autoren)

Buch | Softcover

218 Seiten

2010 | Softcover reprint of hardcover 1st ed. 1993
Springer-Verlag New York Inc.
978-1-4419-5130-4 (ISBN)

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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.

1 Introduction to Finite Fields and Bases.- 2 Factoring Polynomials over Finite Fields.- 3 Construction of Irreducible Polynomials.- 4 Normal Bases.- 5 Optimal Normal Bases.- 6 The Discrete Logarithm Problem.- 7 Elliptic Curves over Finite Fields.- 8 Elliptic Curve Cryptosystems.- 9 Introduction to Algebraic Geometry.- 10 Codes From Algebraic Geometry.- Appendix — Other Applications.

Erscheint lt. Verlag	3.12.2010
Reihe/Serie	The Springer International Series in Engineering and Computer Science ; 199
Zusatzinfo	XIV, 218 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	160 x 240 mm
Themenwelt	Informatik ► Theorie / Studium ► Kryptologie
	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Technik ► Elektrotechnik / Energietechnik
ISBN-10	1-4419-5130-X / 144195130X
ISBN-13	978-1-4419-5130-4 / 9781441951304
Zustand	Neuware