Contemporary Developments In Finite Fields And Applications

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Contemporary Developments In Finite Fields And Applications

Author : Gove Effinger
Publisher : World Scientific
ISBN 13 : 9814719277
Total Pages : 373 pages
Book Rating : 4.8/5 (147 download)

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Book Synopsis Contemporary Developments In Finite Fields And Applications by : Gove Effinger

Download or read book Contemporary Developments In Finite Fields And Applications written by Gove Effinger and published by World Scientific. This book was released on 2016-06-15 with total page 373 pages. Available in PDF, EPUB and Kindle. Book excerpt: The volume is a collection of 20 refereed articles written in connection with lectures presented at the 12th International Conference on Finite Fields and Their Applications ('Fq12') at Skidmore College in Saratoga Springs, NY in July 2015. Finite fields are central to modern cryptography and secure digital communication, and hence must evolve rapidly to keep pace with new technologies. Topics in this volume include cryptography, coding theory, structure of finite fields, algorithms, curves over finite fields, and further applications.Contributors will include: Antoine Joux (Fondation Partenariale de l'UPMC, France); Gary Mullen (Penn State University, USA); Gohar Kyureghyan (Otto-von-Guericke Universität, Germany); Gary McGuire (University College Dublin, Ireland); Michel Lavrauw (Università degli Studi di Padova, Italy); Kirsten Eisentraeger (Penn State University, USA); Renate Scheidler (University of Calgary, Canada); Michael Zieve (University of Michigan, USA).

Applications of Finite Fields

Author : Alfred J. Menezes
Publisher : Springer Science & Business Media
ISBN 13 : 1475722265
Total Pages : 229 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Applications of Finite Fields by : Alfred J. Menezes

Download or read book Applications of Finite Fields written by Alfred J. Menezes and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 229 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Finite Fields and Applications

Author : Gary L. Mullen
Publisher : American Mathematical Soc.
ISBN 13 : 0821844180
Total Pages : 190 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Finite Fields and Applications by : Gary L. Mullen

Download or read book Finite Fields and Applications written by Gary L. Mullen and published by American Mathematical Soc.. This book was released on 2007 with total page 190 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.

Finite Fields

Author : Janet Simmons
Publisher : Nova Publishers
ISBN 13 : 9781536104004
Total Pages : 125 pages
Book Rating : 4.1/5 (4 download)

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Book Synopsis Finite Fields by : Janet Simmons

Download or read book Finite Fields written by Janet Simmons and published by Nova Publishers. This book was released on 2017 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Author : Rudolf Lidl
Publisher : Cambridge University Press
ISBN 13 : 9780521392310
Total Pages : 784 pages
Book Rating : 4.3/5 (923 download)

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Book Synopsis Finite Fields by : Rudolf Lidl

Download or read book Finite Fields written by Rudolf Lidl and published by Cambridge University Press. This book was released on 1997 with total page 784 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted entirely to the theory of finite fields.

Combinatorics and Finite Fields

Author : Kai-Uwe Schmidt
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110641968
Total Pages : 459 pages
Book Rating : 4.1/5 (16 download)

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Book Synopsis Combinatorics and Finite Fields by : Kai-Uwe Schmidt

Download or read book Combinatorics and Finite Fields written by Kai-Uwe Schmidt and published by Walter de Gruyter GmbH & Co KG. This book was released on 2019-07-08 with total page 459 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.

Algebraic Curves and Finite Fields

Author : Harald Niederreiter
Publisher : Walter de Gruyter GmbH & Co KG
ISBN 13 : 3110317915
Total Pages : 254 pages
Book Rating : 4.1/5 (13 download)

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Book Synopsis Algebraic Curves and Finite Fields by : Harald Niederreiter

Download or read book Algebraic Curves and Finite Fields written by Harald Niederreiter and published by Walter de Gruyter GmbH & Co KG. This book was released on 2014-08-20 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebra and number theory have always been counted among the most beautiful and fundamental mathematical areas with deep proofs and elegant results. However, for a long time they were not considered of any substantial importance for real-life applications. This has dramatically changed with the appearance of new topics such as modern cryptography, coding theory, and wireless communication. Nowadays we find applications of algebra and number theory frequently in our daily life. We mention security and error detection for internet banking, check digit systems and the bar code, GPS and radar systems, pricing options at a stock market, and noise suppression on mobile phones as most common examples. This book collects the results of the workshops "Applications of algebraic curves" and "Applications of finite fields" of the RICAM Special Semester 2013. These workshops brought together the most prominent researchers in the area of finite fields and their applications around the world. They address old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

Lectures on Finite Fields and Galois Rings

Author : Zhe-Xian Wan
Publisher : World Scientific
ISBN 13 : 9789812385703
Total Pages : 360 pages
Book Rating : 4.3/5 (857 download)

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Book Synopsis Lectures on Finite Fields and Galois Rings by : Zhe-Xian Wan

Download or read book Lectures on Finite Fields and Galois Rings written by Zhe-Xian Wan and published by World Scientific. This book was released on 2003 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fields are emphasised. In particular, the construction of irreducible polynomials and the normal basis of finite fields are included. The essentials of Galois rings are also presented. This invaluable book has been written in a friendly style, so that lecturers can easily use it as a text and students can use it for self-study. A great number of exercises have been incorporated.

Algebraic Curves over a Finite Field

Author : J. W. P. Hirschfeld
Publisher : Princeton University Press
ISBN 13 : 1400847419
Total Pages : 717 pages
Book Rating : 4.4/5 (8 download)

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Book Synopsis Algebraic Curves over a Finite Field by : J. W. P. Hirschfeld

Download or read book Algebraic Curves over a Finite Field written by J. W. P. Hirschfeld and published by Princeton University Press. This book was released on 2013-03-25 with total page 717 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an accessible and self-contained introduction to the theory of algebraic curves over a finite field, a subject that has been of fundamental importance to mathematics for many years and that has essential applications in areas such as finite geometry, number theory, error-correcting codes, and cryptology. Unlike other books, this one emphasizes the algebraic geometry rather than the function field approach to algebraic curves. The authors begin by developing the general theory of curves over any field, highlighting peculiarities occurring for positive characteristic and requiring of the reader only basic knowledge of algebra and geometry. The special properties that a curve over a finite field can have are then discussed. The geometrical theory of linear series is used to find estimates for the number of rational points on a curve, following the theory of Stöhr and Voloch. The approach of Hasse and Weil via zeta functions is explained, and then attention turns to more advanced results: a state-of-the-art introduction to maximal curves over finite fields is provided; a comprehensive account is given of the automorphism group of a curve; and some applications to coding theory and finite geometry are described. The book includes many examples and exercises. It is an indispensable resource for researchers and the ideal textbook for graduate students.

Finite Fields for Computer Scientists and Engineers

Author : Robert J. McEliece
Publisher : Springer Science & Business Media
ISBN 13 : 1461319838
Total Pages : 212 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Finite Fields for Computer Scientists and Engineers by : Robert J. McEliece

Download or read book Finite Fields for Computer Scientists and Engineers written by Robert J. McEliece and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Algebraic Curves Over Finite Fields

Author : Carlos Moreno
Publisher : Cambridge University Press
ISBN 13 : 9780521459013
Total Pages : 264 pages
Book Rating : 4.4/5 (59 download)

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Book Synopsis Algebraic Curves Over Finite Fields by : Carlos Moreno

Download or read book Algebraic Curves Over Finite Fields written by Carlos Moreno and published by Cambridge University Press. This book was released on 1993-10-14 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Develops the theory of algebraic curves over finite fields, their zeta and L-functions and the theory of algebraic geometric Goppa codes.

Arithmetic of Finite Fields

Author : Jean Claude Bajard
Publisher : Springer Nature
ISBN 13 : 3030688690
Total Pages : 273 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Arithmetic of Finite Fields by : Jean Claude Bajard

Download or read book Arithmetic of Finite Fields written by Jean Claude Bajard and published by Springer Nature. This book was released on 2021-02-16 with total page 273 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2020, held in Rennes, France in July 2020. Due to the COVID-19, the workshop was held online. The 12 revised full papers and 3 invited talks presented were carefully reviewed and selected from 22 submissions. The papers are organized in topical sections on invited talks, Finite Field Arithmetic, Coding Theory, Network Security and much more.

Hardware Implementation of Finite-Field Arithmetic

Author : Jean-Pierre Deschamps
Publisher : McGraw Hill Professional
ISBN 13 : 0071545824
Total Pages : 364 pages
Book Rating : 4.0/5 (715 download)

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Book Synopsis Hardware Implementation of Finite-Field Arithmetic by : Jean-Pierre Deschamps

Download or read book Hardware Implementation of Finite-Field Arithmetic written by Jean-Pierre Deschamps and published by McGraw Hill Professional. This book was released on 2009-01-14 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Implement Finite-Field Arithmetic in Specific Hardware (FPGA and ASIC) Master cutting-edge electronic circuit synthesis and design with help from this detailed guide. Hardware Implementation of Finite-Field Arithmetic describes algorithms and circuits for executing finite-field operations, including addition, subtraction, multiplication, squaring, exponentiation, and division. This comprehensive resource begins with an overview of mathematics, covering algebra, number theory, finite fields, and cryptography. The book then presents algorithms which can be executed and verified with actual input data. Logic schemes and VHDL models are described in such a way that the corresponding circuits can be easily simulated and synthesized. The book concludes with a real-world example of a finite-field application--elliptic-curve cryptography. This is an essential guide for hardware engineers involved in the development of embedded systems. Get detailed coverage of: Modulo m reduction Modulo m addition, subtraction, multiplication, and exponentiation Operations over GF(p) and GF(pm) Operations over the commutative ring Zp[x]/f(x) Operations over the binary field GF(2m) using normal, polynomial, dual, and triangular

Surveys in Combinatorics 2021

Author : Konrad K. Dabrowski
Publisher : Cambridge University Press
ISBN 13 : 1009041819
Total Pages : 380 pages
Book Rating : 4.0/5 (9 download)

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Book Synopsis Surveys in Combinatorics 2021 by : Konrad K. Dabrowski

Download or read book Surveys in Combinatorics 2021 written by Konrad K. Dabrowski and published by Cambridge University Press. This book was released on 2021-06-24 with total page 380 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume contains nine survey articles based on plenary lectures given at the 28th British Combinatorial Conference, hosted online by Durham University in July 2021. This biennial conference is a well-established international event, attracting speakers from around the world. Written by some of the foremost researchers in the field, these surveys provide up-to-date overviews of several areas of contemporary interest in combinatorics. Topics discussed include maximal subgroups of finite simple groups, Hasse–Weil type theorems and relevant classes of polynomial functions, the partition complex, the graph isomorphism problem, and Borel combinatorics. Representing a snapshot of current developments in combinatorics, this book will be of interest to researchers and graduate students in mathematics and theoretical computer science.

Progress in Cryptology – INDOCRYPT 2019

Author : Feng Hao
Publisher : Springer Nature
ISBN 13 : 3030354237
Total Pages : 589 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Progress in Cryptology – INDOCRYPT 2019 by : Feng Hao

Download or read book Progress in Cryptology – INDOCRYPT 2019 written by Feng Hao and published by Springer Nature. This book was released on 2019-12-09 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 20th International Conference on Cryptology in India, INDOCRYPT 2019, held in Hyderabad, India, in December 2019. The 28 revised full papers presented in this book were carefully reviewed and selected from 110 submissions (of which 20 were either rejected without being reviewed or withdrawn before the deadline). The focus of the conference includes works on signatures and filter permutators; symmetric key ciphers and hash functions; blockchain, secure computation and blind coupon mechanism; oblivious transfer, obfuscation and privacy amplification; Boolean functions, elliptic curves and lattices; algorithms, attacks and distribution; and efficiency, side-channel resistance and PUFs.

Handbook of Finite Fields

Author : Gary L. Mullen
Publisher : CRC Press
ISBN 13 : 1439873828
Total Pages : 1048 pages
Book Rating : 4.4/5 (398 download)

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Book Synopsis Handbook of Finite Fields by : Gary L. Mullen

Download or read book Handbook of Finite Fields written by Gary L. Mullen and published by CRC Press. This book was released on 2013-06-17 with total page 1048 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Mathematical Principles of the Internet, Two Volume Set

Author : Nirdosh Bhatnagar
Publisher : CRC Press
ISBN 13 : 1351379216
Total Pages : 1773 pages
Book Rating : 4.3/5 (513 download)

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Book Synopsis Mathematical Principles of the Internet, Two Volume Set by : Nirdosh Bhatnagar

Download or read book Mathematical Principles of the Internet, Two Volume Set written by Nirdosh Bhatnagar and published by CRC Press. This book was released on 2019-03-18 with total page 1773 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two-volume set on Mathematical Principles of the Internet provides a comprehensive overview of the mathematical principles of Internet engineering. The books do not aim to provide all of the mathematical foundations upon which the Internet is based. Instead, these cover only a partial panorama and the key principles. Volume 1 explores Internet engineering, while the supporting mathematics is covered in Volume 2. The chapters on mathematics complement those on the engineering episodes, and an effort has been made to make this work succinct, yet self-contained. Elements of information theory, algebraic coding theory, cryptography, Internet traffic, dynamics and control of Internet congestion, and queueing theory are discussed. In addition, stochastic networks, graph-theoretic algorithms, application of game theory to the Internet, Internet economics, data mining and knowledge discovery, and quantum computation, communication, and cryptography are also discussed. In order to study the structure and function of the Internet, only a basic knowledge of number theory, abstract algebra, matrices and determinants, graph theory, geometry, analysis, optimization theory, probability theory, and stochastic processes, is required. These mathematical disciplines are defined and developed in the books to the extent that is needed to develop and justify their application to Internet engineering.