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Author: Alfred J. Menezes
Publisher: Springer Science & Business Media
ISBN: 9780792392828
Category : Computers
Languages : en
Pages : 242
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Book Description
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 of mathematics, in recent years there has been a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. Applications of Finite Fields introduces some of these recent developments. This book focuses attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, Applications of Finite Fields does not attempt 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. This book is developed from a seminar held at the University of Waterloo. The purpose of the seminar was to bridge the knowledge of the participants whose expertise and interests ranged from the purely theoretical to the applied. As a result, this book will be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. Applications of Finite Fields is an excellent reference and may be used as a text for a course on the subject.
Author: Alfred J. Menezes
Publisher: Springer Science & Business Media
ISBN: 9780792392828
Category : Computers
Languages : en
Pages : 242
Get Book Here
Book Description
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 of mathematics, in recent years there has been a resurgence of interest in finite fields, and this is partly due to important applications in coding theory and cryptography. Applications of Finite Fields introduces some of these recent developments. This book focuses attention on some specific recent developments in the theory and applications of finite fields. While the topics selected are treated in some depth, Applications of Finite Fields does not attempt 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. This book is developed from a seminar held at the University of Waterloo. The purpose of the seminar was to bridge the knowledge of the participants whose expertise and interests ranged from the purely theoretical to the applied. As a result, this book will be of interest to a wide range of students, researchers and practitioners in the disciplines of computer science, engineering and mathematics. Applications of Finite Fields is an excellent reference and may be used as a text for a course on the subject.
Author: Rudolf Lidl
Publisher: Cambridge University Press
ISBN: 9780521392310
Category : Mathematics
Languages : en
Pages : 784
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Book Description
This book is devoted entirely to the theory of finite fields.
Author: Gary L. Mullen
Publisher: American Mathematical Soc.
ISBN: 0821844180
Category : Computers
Languages : en
Pages : 190
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Book Description
Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
Author: Gary L. Mullen
Publisher: Springer
ISBN: 3540246339
Category : Mathematics
Languages : en
Pages : 271
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Book Description
Thisvolumerepresentstherefereedproceedingsofthe7thInternationalC- ference on Finite Fields and Applications (F 7) held during May 5-9, q 2003, in Toulouse, France. The conference was hosted by the Pierre Baudis C- gress Center, downtown, and held at the excellent conference facility. This event continued a series of biennial international conferences on Finite Fields and - plications, following earlier meetings at the University of Nevada at Las Vegas (USA) in August 1991 and August 1993, the University of Glasgow (UK) in July 1995, the University of Waterloo (Canada) in August 1997, the Univ- sity of Augsburg (Germany) in August 1999, and the Universidad Aut ́ onoma Metropolitana-Iztapalapa, in Oaxaca (Mexico) in 2001. The Organizing Committee of F 7 consisted of Claude Carlet (INRIA, Paris, q France), Dieter Jungnickel (University of Augsburg, Germany), Gary Mullen (Pennsylvania State University, USA), Harald Niederreiter (National University of Singapore, Singapore), Alain Poli, Chair (Paul Sabatier University, Toulouse, France), Henning Stichtenoth (Essen University, Germany), and Horacio Tapia- Recillas (Universidad Aut ́ onoma Metropolitan-Iztapalapa, Mexico). The program of the conference consisted of four full days and one half day of sessions, with eight invited plenary talks, and close to 60 contributed talks.
Author: Alfred J. Menezes
Publisher: Springer Science & Business Media
ISBN: 1475722265
Category : Technology & Engineering
Languages : en
Pages : 229
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Book Description
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.
Author: Gary L. Mullen
Publisher: CRC Press
ISBN: 1439873828
Category : Computers
Languages : en
Pages : 1048
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Book Description
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
Author: Xiang-dong Hou
Publisher: American Mathematical Soc.
ISBN: 1470442892
Category : Mathematics
Languages : en
Pages : 242
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Book Description
The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science. This book is a collection of selected topics in the theory of finite fields and related areas. The topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.
Author: Igor Shparlinski
Publisher: Springer Science & Business Media
ISBN: 940159239X
Category : Mathematics
Languages : en
Pages : 532
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Book Description
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.
Author: Rudolf Lidl
Publisher: Cambridge University Press
ISBN: 9780521460941
Category : Mathematics
Languages : en
Pages : 446
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Book Description
Presents an introduction to the theory of finite fields and some of its most important applications.
Author: Robert J. McEliece
Publisher: Springer Science & Business Media
ISBN: 1461319838
Category : Technology & Engineering
Languages : en
Pages : 212
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Book Description
This book developed from a course on finite fields I gave at the University of Illinois at Urbana-Champaign in the Spring semester of 1979. The course was taught at the request of an exceptional group of graduate students (includ ing Anselm Blumer, Fred Garber, Evaggelos Geraniotis, Jim Lehnert, Wayne Stark, and Mark Wallace) who had just taken a course on coding theory from me. The theory of finite fields is the mathematical foundation of algebraic coding theory, but in coding theory courses there is never much time to give more than a "Volkswagen" treatment of them. But my 1979 students wanted a "Cadillac" treatment, and this book differs very little from the course I gave in response. Since 1979 I have used a subset of my course notes (correspond ing roughly to Chapters 1-6) as the text for my "Volkswagen" treatment of finite fields whenever I teach coding theory. There is, ironically, no coding theory anywhere in the book! If this book had a longer title it would be "Finite fields, mostly of char acteristic 2, for engineering and computer science applications. " It certainly does not pretend to cover the general theory of finite fields in the profound depth that the recent book of Lidl and Neidereitter (see the Bibliography) does.
