1 edition of **Applications of Finite Fields** found in the catalog.

- 269 Want to read
- 21 Currently reading

Published
**1993**
by Springer US in Boston, MA
.

Written in English

- Computer engineering,
- Computational complexity,
- Coding theory,
- Engineering

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.

**Edition Notes**

Statement | by Ian F. Blake, XuHong Gao, Ronald C. Mullin, Scott A. Vanstone, Tomik Yaghoobian ; edited by Alfred J. Menezes |

Series | The Springer International Series in Engineering and Computer Science, Communications and Information Theory -- 199, Springer International Series in Engineering and Computer Science, Communications and Information Theory -- 199. |

Contributions | Gao, XuHong, Mullin, Ronald C., Vanstone, Scott A., Yaghoobian, Tomik, Menezes, Alfred J. |

Classifications | |
---|---|

LC Classifications | TK1-9971 |

The Physical Object | |

Format | [electronic resource] / |

Pagination | 1 online resource (xiii, 218 pages). |

Number of Pages | 218 |

ID Numbers | |

Open Library | OL27017471M |

ISBN 10 | 144195130X, 1475722265 |

ISBN 10 | 9781441951304, 9781475722260 |

OCLC/WorldCa | 851823504 |

For finite fields, there is Lidl and Niederreiter, Finite Fields, which is Volume 20 in the Encyclopedia of Mathematics and its Applications. There are also a couple of conference proceedings: Finite Fields and Applications, the proceedings of the 3rd international conference on finite fields and applications, edited by Cohen and Niederreiter, and Finite Fields: Theory, Applications. The arithmetic of finite fields is used extensively in cryptographic applications, including elliptic curve public-key cryptography and the AES (Advanced Encryption Standard) for the encryption of electronic data, which uses the arithmetic in F {\mathbb F}_{}.

The first part of this book presents an introduction to this theory, emphasizing those aspects that are relevant for application. The second part is devoted to a discussion of the most important applications of finite fields, especially to information theory, algebraic coding theory, and Author: Rudolf Lidl, Harald Niederreiter. Finite fields have widespread application in combinatorics, two well known examples being the definition of Paley Graphs and the related construction for Hadamard Matrices. In arithmetic combinatorics finite fields and finite field models are used extensively, such as in Szemerédi's theorem on arithmetic progressions. Extensions.

Chapter 7 covers some of the applications of finite fields to other areas of mathematics, notably affine and projective geometry, combinatorics, linear modular systems, and simulation of randomness. Applications to coding theory are discussed in Chapter 8, including cyclic codes, Bose-Ray-Chaudhuri-Hocquenghem codes, and Goppa codes. This book presents an introduction to this theory, and contains a discussion of the most important applications of finite fields. From the Back Cover The theory of finite fields is a branch of modern algebra that has come to the fore in recent years because of its diverse applications in such areas as combinatorics, coding theory, cryptology Author: Rudolf Lidl, Harald Niederreiter.

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About this book 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 theory of finite fields is a branch of algebra that has come to the fore becasue of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching ciruits. This book is devoted entirely to the theory of finite fields, and it provides comprehensive coverage Applications of Finite Fields book the literature/5(6).

Book Description The theory of finite fields is a branch of modern algebra that has come to the fore in recent years because of its diverse applications in such areas as combinatorics, coding theory, cryptology and the mathematical study of switching by: 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. Introduction to Finite Fields and Their Applications book. Read reviews from world’s largest community for readers.

The first part of this book presents 5/5(1). Chapter 9 - Applications of Finite Fields Rudolf Lidl, University of Tasmania, Harald Niederreiter, National University of Singapore Publisher: Cambridge University Press.

The book provides a brief introduction to the theory of finite fields and to some of their applications. It is accessible for advanced undergraduate students EMS Newsletter.

This book gives a quick, clear introduction to finite fields and discusses applications in combinatorics, algebraic coding theory, and cryptography. This book provides a brief and accessible introduction to the theory of finite fields and to some of their many fascinating and practical applications.

The first chapter is devoted to the theory of finite fields. Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science.

Gary L. Mullen and Carl Mummert's "Finite Field and Applications" introduces the error-correcting codes (algebraic coding theory) and the related mathematics. The book has four chapters. They are: finite fields, combinatorics, algebraic coding theory, and cryptography.5/5(1).

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.

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.

Proceedings of The Fifth International Conference on Finite Fields and Applications Fq5, held at the University of Augsburg, Germany, August 2–6, Editors.

Focuses attention on some specific developments in the theory and applications of finite fields. This book studies topics such as the different methods of representing the elements of a finite field, algorithms for factoring polynomials over finite. Applications of Finite Fields by Alfred John Menezes,available at Book Depository with free delivery worldwide.

The theory of finite fields is a branch of algebra that has come to the fore because of its diverse applications in such areas as combinatorics, coding theory and the mathematical study of switching ciruits.

This book is devoted entirely to the theory of finite fields, and it provides comprehensive coverage of the literature. Read the latest articles of Finite Fields and Their Applications atElsevier’s leading platform of peer-reviewed scholarly literature. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite.

INTRODUCTION TO FINITE FIELDS of some number of repetitions of g. Thus each element of Gappears in the sequence of elements fg;g'g;g'g'g;g. ; Theorem (Finite cyclic groups) A ﬂnite group Gof order nis cyclic if and only if it is a single-generator group with generator gand with elements f0g;1g;2g;;(n¡1) Size: KB.

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. This book, the first one devoted entirely to this theory, provides comprehensive coverage of the literature on finite fields and their applications.

Extensive bibliographical notes at the end of each chapter give a historical survey of the development of the subject.Finite Fields and Applications Book Subtitle Proceedings of The Fifth International Conference on Finite Fields and Applications Fq 5, held at the University of .Field-like structures 27 Galois rings 28 Finite field related books 31 Textbooks 31 Finite field theory 31 Applications 31 Algorithms 31 Conference proceedings 31 Tables David Thomson 32 Low-weight irreducible and primitive polynomials 32 Low-complexity normal bases