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Author | : Alfred J. Menezes |
Publisher | : Springer Science & Business Media |
Total Pages | : 229 |
Release | : 2013-04-17 |
Genre | : Technology & Engineering |
ISBN | : 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.
Author | : Rudolf Lidl |
Publisher | : Cambridge University Press |
Total Pages | : 784 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780521392310 |
Download Finite Fields Book in PDF, ePub and Kindle
This book is devoted entirely to the theory of finite fields.
Author | : Gary L. Mullen |
Publisher | : American Mathematical Soc. |
Total Pages | : 190 |
Release | : 2007 |
Genre | : Computers |
ISBN | : 0821844180 |
Download Finite Fields and Applications Book in PDF, ePub and Kindle
Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
Author | : Rudolf Lidl |
Publisher | : Cambridge University Press |
Total Pages | : 446 |
Release | : 1994-07-21 |
Genre | : Mathematics |
ISBN | : 9780521460941 |
Download Introduction to Finite Fields and Their Applications Book in PDF, ePub and Kindle
Presents an introduction to the theory of finite fields and some of its most important applications.
Author | : Gary L. Mullen |
Publisher | : CRC Press |
Total Pages | : 1048 |
Release | : 2013-06-17 |
Genre | : Computers |
ISBN | : 1439873828 |
Download Handbook of Finite Fields Book in PDF, ePub and Kindle
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 | : Pascale Charpin |
Publisher | : Walter de Gruyter |
Total Pages | : 288 |
Release | : 2013-05-28 |
Genre | : Mathematics |
ISBN | : 3110283603 |
Download Finite Fields and Their Applications Book in PDF, ePub and Kindle
This book is based on the invited talks of the "RICAM-Workshop on Finite Fields and Their Applications: Character Sums and Polynomials" held at the Federal Institute for Adult Education (BIfEB) in Strobl, Austria, from September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.
Author | : Kai-Uwe Schmidt |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 506 |
Release | : 2019-07-08 |
Genre | : Mathematics |
ISBN | : 3110641968 |
Download Combinatorics and Finite Fields Book in PDF, ePub and Kindle
The series is devoted to the publication of high-level monographs, surveys and proceedings which cover the whole spectrum of computational and applied mathematics. The books of this series are addressed to both specialists and advanced students. Interested authors may submit book proposals to the Managing Editor or to any member of the Editorial Board. Managing EditorUlrich Langer, Johannes Kepler University Linz, Austria Editorial BoardHansj rg Albrecher, University of Lausanne, SwitzerlandRonald H. W. Hoppe, University of Houston, USAKarl Kunisch, RICAM, Linz, Austria; University of Graz, AustriaHarald Niederreiter, RICAM, Linz, AustriaChristian Schmeiser, University of Vienna, Austria
Author | : Xiang-dong Hou |
Publisher | : American Mathematical Soc. |
Total Pages | : 240 |
Release | : 2018-06-07 |
Genre | : Finite fields (Algebra) |
ISBN | : 1470442892 |
Download Lectures on Finite Fields Book in PDF, ePub and Kindle
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 |
Total Pages | : 532 |
Release | : 2013-03-09 |
Genre | : Mathematics |
ISBN | : 940159239X |
Download Finite Fields: Theory and Computation Book in PDF, ePub and Kindle
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 | : Robert J. McEliece |
Publisher | : Springer Science & Business Media |
Total Pages | : 212 |
Release | : 2012-12-06 |
Genre | : Technology & Engineering |
ISBN | : 1461319838 |
Download Finite Fields for Computer Scientists and Engineers Book in PDF, ePub and Kindle
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.