Finite Fields For Computer Scientists And Engineers

Finite Fields For Computer Scientists And Engineers Book in PDF, ePub and Kindle version is available to download in english. Read online anytime anywhere directly from your device. Click on the download button below to get a free pdf file of Finite Fields For Computer Scientists And Engineers book. This book definitely worth reading, it is an incredibly well-written.

Finite Fields for Computer Scientists and Engineers

Robert J. McEliece
Finite Fields for Computer Scientists and Engineers Book PDF

Author : Robert J. McEliece
Publisher : Springer Science & Business Media
Page : 212 pages
File Size : 48,9 Mb
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 9781461319832

Get Book

Finite Fields for Computer Scientists and Engineers by Robert J. McEliece Pdf

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.

Arithmetic of Finite Fields

Çetin Kaya Koç,Sihem Mesnager,Erkay Savaş
Arithmetic of Finite Fields Book PDF

Author : Çetin Kaya Koç,Sihem Mesnager,Erkay Savaş
Publisher : Springer
Page : 213 pages
File Size : 43,7 Mb
Release : 2015-02-21
Category : Computers
ISBN : 9783319162775

Get Book

Arithmetic of Finite Fields by Çetin Kaya Koç,Sihem Mesnager,Erkay Savaş Pdf

This book constitutes the refereed proceedings of the 5th International Workshop on the Arithmetic of Finite Field, WAIFI 2014, held in Gebze, Turkey, in September 2014. The 9 revised full papers and 43 invited talks presented were carefully reviewed and selected from 27 submissions. This workshop is a forum of mathematicians, computer scientists, engineers and physicists performing research on finite field arithmetic, interested in communicating the advances in the theory, applications, and implementations of finite fields. The workshop will help to bridge the gap between the mathematical theory of finite fields and their hardware/software implementations and technical applications.

Computer and Cyber Security

Brij B. Gupta
Computer and Cyber Security Book PDF

Author : Brij B. Gupta
Publisher : CRC Press
Page : 666 pages
File Size : 50,7 Mb
Release : 2018-11-19
Category : Business & Economics
ISBN : 9780429756313

Get Book

Computer and Cyber Security by Brij B. Gupta Pdf

This is a monumental reference for the theory and practice of computer security. Comprehensive in scope, this text covers applied and practical elements, theory, and the reasons for the design of applications and security techniques. It covers both the management and the engineering issues of computer security. It provides excellent examples of ideas and mechanisms that demonstrate how disparate techniques and principles are combined in widely-used systems. This book is acclaimed for its scope, clear and lucid writing, and its combination of formal and theoretical aspects with real systems, technologies, techniques, and policies.

Applications of Finite Fields

Alfred J. Menezes,Ian F. Blake,XuHong Gao,Ronald C. Mullin,Scott A. Vanstone,Tomik Yaghoobian
Applications of Finite Fields Book PDF

Author : Alfred J. Menezes,Ian F. Blake,XuHong Gao,Ronald C. Mullin,Scott A. Vanstone,Tomik Yaghoobian
Publisher : Springer Science & Business Media
Page : 229 pages
File Size : 55,7 Mb
Release : 2013-04-17
Category : Technology & Engineering
ISBN : 9781475722260

Get Book

Applications of Finite Fields by Alfred J. Menezes,Ian F. Blake,XuHong Gao,Ronald C. Mullin,Scott A. Vanstone,Tomik Yaghoobian Pdf

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.

Arithmetic of Finite Fields

Joachim von zur Gathen,José Luis Imana,Cetin Kaya Koc
Arithmetic of Finite Fields Book PDF

Author : Joachim von zur Gathen,José Luis Imana,Cetin Kaya Koc
Publisher : Springer
Page : 205 pages
File Size : 54,5 Mb
Release : 2008-07-08
Category : Computers
ISBN : 9783540694991

Get Book

Arithmetic of Finite Fields by Joachim von zur Gathen,José Luis Imana,Cetin Kaya Koc Pdf

This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully reviewed and selected from 34 submissions. The papers are organized in topical sections on structures in finite fields, efficient finite field arithmetic, efficient implementation and architectures, classification and construction of mappings over finite fields, and codes and cryptography.

Arithmetic of Finite Fields

Claude Carlet
Arithmetic of Finite Fields Book PDF

Author : Claude Carlet
Publisher : Springer Science & Business Media
Page : 364 pages
File Size : 43,5 Mb
Release : 2007-06-11
Category : Computers
ISBN : 9783540730736

Get Book

Arithmetic of Finite Fields by Claude Carlet Pdf

This book constitutes the refereed proceedings of the First International Workshop on the Arithmetic of Finite Fields, WAIFI 2007, held in Madrid, Spain in June 2007. It covers structures in finite fields, efficient implementation and architectures, efficient finite field arithmetic, classification and construction of mappings over finite fields, curve algebra, cryptography, codes, and discrete structures.

Finite Fields: Theory and Applications

Gary McGuire
Finite Fields Theory and Applications Book PDF

Author : Gary McGuire
Publisher : American Mathematical Soc.
Page : 394 pages
File Size : 54,8 Mb
Release : 2010
Category : Computers
ISBN : 9780821847862

Get Book

Finite Fields: Theory and Applications by Gary McGuire Pdf

This volume contains the proceedings of the Ninth International Conference on Finite Fields and Applications, held in Ireland, July 13-17, 2009. It includes survey papers by all invited speakers as well as selected contributed papers. Finite fields continue to grow in mathematical importance due to applications in many diverse areas. This volume contains a variety of results advancing the theory of finite fields and connections with, as well as impact on, various directions in number theory, algebra, and algebraic geometry. Areas of application include algebraic coding theory, cryptology, and combinatorial design theory.

Infinite Algebraic Extensions of Finite Fields

Joel V. Brawley,George E. Schnibben
Infinite Algebraic Extensions of Finite Fields Book PDF

Author : Joel V. Brawley,George E. Schnibben
Publisher : American Mathematical Soc.
Page : 104 pages
File Size : 48,9 Mb
Release : 1989
Category : Mathematics
ISBN : 9780821851012

Get Book

Infinite Algebraic Extensions of Finite Fields by Joel V. Brawley,George E. Schnibben Pdf

Over the last several decades there has been a renewed interest in finite field theory, partly as a result of important applications in a number of diverse areas such as electronic communications, coding theory, combinatorics, designs, finite geometries, cryptography, and other portions of discrete mathematics. In addition, a number of recent books have been devoted to the subject. Despite the resurgence in interest, it is not widely known that many results concerning finite fields have natural generalizations to abritrary algebraic extensions of finite fields. The purpose of this book is to describe these generalizations. After an introductory chapter surveying pertinent results about finite fields, the book describes the lattice structure of fields between the finite field $GF(q)$ and its algebraic closure $\Gamma (q)$. The authors introduce a notion, due to Steinitz, of an extended positive integer $N$ which includes each ordinary positive integer $n$ as a special case. With the aid of these Steinitz numbers, the algebraic extensions of $GF(q)$ are represented by symbols of the form $GF(q^N)$. When $N$ is an ordinary integer $n$, this notation agrees with the usual notation $GF(q^n)$ for a dimension $n$ extension of $GF(q)$. The authors then show that many of the finite field results concerning $GF(q^n)$ are also true for $GF(q^N)$. One chapter is devoted to giving explicit algorithms for computing in several of the infinite fields $GF(q^N)$ using the notion of an explicit basis for $GF(q^N)$ over $GF(q)$. Another chapter considers polynomials and polynomial-like functions on $GF(q^N)$ and contains a description of several classes of permutation polynomials, including the $q$-polynomials and the Dickson polynomials. Also included is a brief chapter describing two of many potential applications. Aimed at the level of a beginning graduate student or advanced undergraduate, this book could serve well as a supplementary text for a course in finite field theory.

Introduction to Finite Fields and Their Applications

Rudolf Lidl,Harald Niederreiter
Introduction to Finite Fields and Their Applications Book PDF

Author : Rudolf Lidl,Harald Niederreiter
Publisher : Cambridge University Press
Page : 446 pages
File Size : 54,7 Mb
Release : 1994-07-21
Category : Mathematics
ISBN : 0521460948

Get Book

Introduction to Finite Fields and Their Applications by Rudolf Lidl,Harald Niederreiter Pdf

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

Cryptographic Engineering

Cetin Kaya Koc
Cryptographic Engineering Book PDF

Author : Cetin Kaya Koc
Publisher : Springer Science & Business Media
Page : 528 pages
File Size : 43,9 Mb
Release : 2008-12-11
Category : Technology & Engineering
ISBN : 9780387718170

Get Book

Cryptographic Engineering by Cetin Kaya Koc Pdf

This book is for engineers and researchers working in the embedded hardware industry. This book addresses the design aspects of cryptographic hardware and embedded software. The authors provide tutorial-type material for professional engineers and computer information specialists.

Topics in Galois Fields

Dirk Hachenberger,Dieter Jungnickel
Topics in Galois Fields Book PDF

Author : Dirk Hachenberger,Dieter Jungnickel
Publisher : Springer Nature
Page : 785 pages
File Size : 40,7 Mb
Release : 2020-09-29
Category : Mathematics
ISBN : 9783030608064

Get Book

Topics in Galois Fields by Dirk Hachenberger,Dieter Jungnickel Pdf

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.

Handbook of Algebra

Anonim
Handbook of Algebra Book PDF

Author : Anonim
Publisher : Elsevier
Page : 936 pages
File Size : 49,8 Mb
Release : 1995-12-18
Category : Mathematics
ISBN : 9780080532950

Get Book

Handbook of Algebra by Anonim Pdf

Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.

Galois Fields and Galois Rings Made Easy

Maurice Kibler
Galois Fields and Galois Rings Made Easy Book PDF

Author : Maurice Kibler
Publisher : Elsevier
Page : 270 pages
File Size : 55,5 Mb
Release : 2017-09-22
Category : Mathematics
ISBN : 9780081023518

Get Book

Galois Fields and Galois Rings Made Easy by Maurice Kibler Pdf

This book constitutes an elementary introduction to rings and fields, in particular Galois rings and Galois fields, with regard to their application to the theory of quantum information, a field at the crossroads of quantum physics, discrete mathematics and informatics. The existing literature on rings and fields is primarily mathematical. There are a great number of excellent books on the theory of rings and fields written by and for mathematicians, but these can be difficult for physicists and chemists to access. This book offers an introduction to rings and fields with numerous examples. It contains an application to the construction of mutually unbiased bases of pivotal importance in quantum information. It is intended for graduate and undergraduate students and researchers in physics, mathematical physics and quantum chemistry (especially in the domains of advanced quantum mechanics, quantum optics, quantum information theory, classical and quantum computing, and computer engineering). Although the book is not written for mathematicians, given the large number of examples discussed, it may also be of interest to undergraduate students in mathematics. Contains numerous examples that accompany the text Includes an important chapter on mutually unbiased bases Helps physicists and theoretical chemists understand this area of mathematics

Advances in Information Security and Assurance

James (Jong Hyuk) Park,Hsiao-Hwa Chen,Mohammed Atiquzzaman,Changhoon Lee,Sang-Soo Yeo
Advances in Information Security and Assurance Book PDF

Author : James (Jong Hyuk) Park,Hsiao-Hwa Chen,Mohammed Atiquzzaman,Changhoon Lee,Sang-Soo Yeo
Publisher : Springer
Page : 841 pages
File Size : 41,7 Mb
Release : 2009-06-18
Category : Computers
ISBN : 9783642026171

Get Book

Advances in Information Security and Assurance by James (Jong Hyuk) Park,Hsiao-Hwa Chen,Mohammed Atiquzzaman,Changhoon Lee,Sang-Soo Yeo Pdf

Welcome to the Third International Conference on Information Security and Ass- ance (ISA 2009). ISA 2009 was the most comprehensive conference focused on the various aspects of advances in information security and assurance. The concept of security and assurance is emerging rapidly as an exciting new paradigm to provide reliable and safe life services. Our conference provides a chance for academic and industry professionals to discuss recent progress in the area of communication and networking including modeling, simulation and novel applications associated with the utilization and acceptance of computing devices and systems. ISA 2009 was a succ- sor of the First International Workshop on Information Assurance in Networks (IAN 2007, Jeju-island, Korea, December, 2007), and the Second International Conference on Information Security and Assurance (ISA 2008, Busan, Korea, April 2008). The goal of this conference is to bring together researchers from academia and industry as well as practitioners to share ideas, problems and solutions relating to the multifaceted aspects of information technology. ISA 2009 contained research papers submitted by researchers from all over the world. In order to guarantee high-quality proceedings, we put extensive effort into reviewing the papers. All submissions were peer reviewed by at least three Program Committee members as well as external reviewers. As the quality of the submissions was quite high, it was extremely difficult to select the papers for oral presentation and publication in the proceedings of the conference.

Algorithms for Computer Algebra

Keith O. Geddes,Stephen R. Czapor,George Labahn
Algorithms for Computer Algebra Book PDF

Author : Keith O. Geddes,Stephen R. Czapor,George Labahn
Publisher : Springer Science & Business Media
Page : 594 pages
File Size : 42,7 Mb
Release : 2007-06-30
Category : Computers
ISBN : 9780585332475

Get Book

Algorithms for Computer Algebra by Keith O. Geddes,Stephen R. Czapor,George Labahn Pdf

Algorithms for Computer Algebra is the first comprehensive textbook to be published on the topic of computational symbolic mathematics. The book first develops the foundational material from modern algebra that is required for subsequent topics. It then presents a thorough development of modern computational algorithms for such problems as multivariate polynomial arithmetic and greatest common divisor calculations, factorization of multivariate polynomials, symbolic solution of linear and polynomial systems of equations, and analytic integration of elementary functions. Numerous examples are integrated into the text as an aid to understanding the mathematical development. The algorithms developed for each topic are presented in a Pascal-like computer language. An extensive set of exercises is presented at the end of each chapter. Algorithms for Computer Algebra is suitable for use as a textbook for a course on algebraic algorithms at the third-year, fourth-year, or graduate level. Although the mathematical development uses concepts from modern algebra, the book is self-contained in the sense that a one-term undergraduate course introducing students to rings and fields is the only prerequisite assumed. The book also serves well as a supplementary textbook for a traditional modern algebra course, by presenting concrete applications to motivate the understanding of the theory of rings and fields.