Theory And Applications Of Finite Fields

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Applications Of Finite Fields

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Author : Alfred J. Menezes
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17

Applications Of Finite Fields written by Alfred J. Menezes and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Technology & Engineering categories.

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.

Introduction To Finite Fields And Their Applications

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Author : Rudolf Lidl
language : en
Publisher: Cambridge University Press
Release Date : 1994-07-21

Introduction To Finite Fields And Their Applications written by Rudolf Lidl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-07-21 with Mathematics categories.

Presents an introduction to the theory of finite fields and some of its most important applications.

Theory And Applications Of Finite Fields

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Author : Michel Lavrauw
language : en
Publisher: American Mathematical Soc.
Release Date : 2012

Theory And Applications Of Finite Fields written by Michel Lavrauw and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012 with Mathematics categories.

This volume contains the proceedings of the 10th International Congress on Finite Fields and their Applications (Fq 10), held July 11-15, 2011, in Ghent, Belgium. Research on finite fields and their practical applications continues to flourish. This volume's topics, which include finite geometry, finite semifields, bent functions, polynomial theory, designs, and function fields, show the variety of research in this area and prove the tremendous importance of finite field theory.

Finite Fields With Applications To Combinatorics

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Author : Kannan Soundararajan
language : en
Publisher: American Mathematical Society
Release Date : 2022-11-09

Finite Fields With Applications To Combinatorics written by Kannan Soundararajan and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-11-09 with Mathematics categories.

This book uses finite field theory as a hook to introduce the reader to a range of ideas from algebra and number theory. It constructs all finite fields from scratch and shows that they are unique up to isomorphism. As a payoff, several combinatorial applications of finite fields are given: Sidon sets and perfect difference sets, de Bruijn sequences and a magic trick of Persi Diaconis, and the polynomial time algorithm for primality testing due to Agrawal, Kayal and Saxena. The book forms the basis for a one term intensive course with students meeting weekly for multiple lectures and a discussion session. Readers can expect to develop familiarity with ideas in algebra (groups, rings and fields), and elementary number theory, which would help with later classes where these are developed in greater detail. And they will enjoy seeing the AKS primality test application tying together the many disparate topics from the book. The pre-requisites for reading this book are minimal: familiarity with proof writing, some linear algebra, and one variable calculus is assumed. This book is aimed at incoming undergraduate students with a strong interest in mathematics or computer science.

Handbook Of Finite Fields

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Author : Gary L. Mullen
language : en
Publisher: CRC Press
Release Date : 2013-06-17

Handbook Of Finite Fields written by Gary L. Mullen and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-06-17 with Computers categories.

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 And Applications

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Author : Gary L. Mullen
language : en
Publisher: American Mathematical Soc.
Release Date : 2007

Finite Fields And Applications written by Gary L. Mullen and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Computers categories.

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

Finite Fields

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Author : Ronald Cleveland Mullin
language : en
Publisher: American Mathematical Soc.
Release Date : 1999

Finite Fields written by Ronald Cleveland Mullin and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

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

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Author : Rudolf Lidl
language : en
Publisher: Cambridge University Press
Release Date : 1997

Finite Fields written by Rudolf Lidl and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997 with Mathematics categories.

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

Rational Points On Curves Over Finite Fields

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Author : Harald Niederreiter
language : en
Publisher: Cambridge University Press
Release Date : 2001-06-14

Rational Points On Curves Over Finite Fields written by Harald Niederreiter and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-06-14 with Computers categories.

Discussion of theory and applications of algebraic curves over finite fields with many rational points.

Finite Fields And Their Applications

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Author : James A. Davis
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2020-10-26

Finite Fields And Their Applications written by James A. Davis and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-10-26 with Mathematics categories.

The volume covers wide-ranging topics from Theory: structure of finite fields, normal bases, polynomials, function fields, APN functions. Computation: algorithms and complexity, polynomial factorization, decomposition and irreducibility testing, sequences and functions. Applications: algebraic coding theory, cryptography, algebraic geometry over finite fields, finite incidence geometry, designs, combinatorics, quantum information science.