Computational and Algorithmic Problems in Finite Fields
Computational and Algorithmic Problems in Finite Fields

Author: Igor Shparlinski

Publisher: Springer Science & Business Media

Published: 2012-12-06

Total Pages: 253

ISBN-13: 940111806X

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This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, 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 araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.

Finite Fields: Theory, Applications and Algorithms
Finite Fields: Theory, Applications and Algorithms

Author: Ronald Cleveland Mullin

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 258

ISBN-13: 0821808176

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The Ontario conference drew workers from theoretical, applied, and algorithm finite field theory to share their recent findings applying finite fields to such areas as number theory, algebra, and algebraic geometry. The 21 topics include actions of linearized polynomials on the algebraic closure of a finite field, kernels and defaults, computing zeta functions over finite fields, and the state complexity of some long codes. No index. Member prices are $39 for institutions and $29 for individuals. Annotation copyrighted by Book News, Inc., Portland, OR

Finite Fields and Applications
Finite Fields and Applications

Author: Gary L. Mullen

Publisher: American Mathematical Soc.

Published: 2007

Total Pages: 190

ISBN-13: 0821844180

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Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.

Finite Fields: Theory, Applications, and Algorithms
Finite Fields: Theory, Applications, and Algorithms

Author: Gary L. Mullen

Publisher: American Mathematical Soc.

Published: 1994

Total Pages: 434

ISBN-13: 0821851837

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Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.

Applications of Finite Fields
Applications of Finite Fields

Author: Alfred J. Menezes

Publisher: Springer Science & Business Media

Published: 2013-04-17

Total Pages: 229

ISBN-13: 1475722265

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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.

Handbook of Finite Fields
Handbook of Finite Fields

Author: Gary L. Mullen

Publisher: CRC Press

Published: 2013-06-17

Total Pages: 1048

ISBN-13: 1439873828

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Poised to become the leading reference in the field, the Handbook of Finite Fields is exclusively devoted to the theory and applications of finite fields. More than 80 international contributors compile state-of-the-art research in this definitive handbook. Edited by two renowned researchers, the book uses a uniform style and format throughout and

Finite Fields
Finite Fields

Author: Ronald Cleveland Mullin

Publisher: American Mathematical Soc.

Published: 1999

Total Pages: 260

ISBN-13: 9780821855614

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The Fourth International Conference on "Finite Fields: Theory, Applications, and Algorithms" was held at the University of Waterloo in August 1997. This volume presents the refereed proceedings. The conference drew workers in theoretical, applied, and algorithmic finite field theory. All papers were refereed. They are loosely classified as theoretical and applied and are listed under these general headings. The work contains up-to-date results from leading experts in the field.

Finite Fields
Finite Fields

Author: Rudolf Lidl

Publisher: Cambridge University Press

Published: 1997

Total Pages: 784

ISBN-13: 9780521392310

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This book is devoted entirely to the theory of finite fields.

Finite Fields
Finite Fields

Author: Janet Simmons

Publisher: Nova Publishers

Published: 2017

Total Pages: 125

ISBN-13: 9781536104004

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This book provides new research in finite fields. Chapter One presents some techniques that rely on a combination of results from graph theory, finite fields, matrix theory, and finite geometry to researchers working in the area of preserver problems. It also gives a brief presentation of this research field to other mathematicians. Chapter Two contains a basic and self-contained introduction to classical coherent state transforms, namely classical wavelet and classical wave-packet transforms, on finite fields. Chapter Three proposes an intrinsic representation of finite m? extension as this is a tradition for finite extension fields. Chapter Four reviews m? cyclic codes on a m? field. Chapter Five discusses two problems of Carlitz and their generalizations.

Finite Fields and Applications
Finite Fields and Applications

Author: Dieter Jungnickel

Publisher: Springer Science & Business Media

Published: 2001-03-20

Total Pages: 514

ISBN-13: 9783540411093

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This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department of Mathematics. The conference continued a series of biennial international conferences on finite fields, following earlier conferences at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University ofGlasgow (Scotland) in July 1995, and the University ofWaterloo (Canada) in August 1997. The Organizing Committee of F q5 comprised Thomas Beth (University ofKarlsruhe), Stephen D. Cohen (University of Glasgow), Dieter Jungnickel (University of Augsburg, Chairman), Alfred Menezes (University of Waterloo), Gary L. Mullen (Pennsylvania State University), Ronald C. Mullin (University of Waterloo), Harald Niederreiter (Austrian Academy of Sciences), and Alexander Pott (University of Magdeburg). The program ofthe conference consisted offour full days and one halfday ofsessions, with 11 invited plenary talks andover80contributedtalks that re- quired three parallel sessions. This documents the steadily increasing interest in finite fields and their applications. Finite fields have an inherently fasci- nating structure and they are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields.