Finite Fields With Applications To Coding Theory Cryptography And Related Areas
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Author | : Gary L. Mullen |
Publisher | : Springer Science & Business Media |
Total Pages | : 345 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642594352 |
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The Sixth International Conference on Finite Fields and Applications, Fq6, held in the city of Oaxaca, Mexico, from May 21-25, 2001, continued a series of biennial international conferences on finite fields. This volume documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.
Author | : Alfred J. Menezes |
Publisher | : Springer Science & Business Media |
Total Pages | : 229 |
Release | : 2013-04-17 |
Genre | : Technology & Engineering |
ISBN | : 1475722265 |
Download Applications of Finite Fields Book in PDF, Epub and Kindle
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 | : Gary L. Mullen |
Publisher | : American Mathematical Soc. |
Total Pages | : 190 |
Release | : 2007 |
Genre | : Computers |
ISBN | : 0821844180 |
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Finite fields Combinatorics Algebraic coding theory Cryptography Background in number theory and abstract algebra Hints for selected exercises References Index.
Author | : Pascale Charpin |
Publisher | : Walter de Gruyter |
Total Pages | : 288 |
Release | : 2013-05-28 |
Genre | : Mathematics |
ISBN | : 3110283603 |
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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 | : James A. Davis |
Publisher | : Walter de Gruyter GmbH & Co KG |
Total Pages | : 214 |
Release | : 2020-10-26 |
Genre | : Mathematics |
ISBN | : 3110621738 |
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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.
Author | : Arnaldo Garcia |
Publisher | : Springer Science & Business Media |
Total Pages | : 212 |
Release | : 2006-11-15 |
Genre | : Mathematics |
ISBN | : 1402053347 |
Download Topics in Geometry, Coding Theory and Cryptography Book in PDF, Epub and Kindle
The theory of algebraic function fields over finite fields has its origins in number theory. However, after Goppa`s discovery of algebraic geometry codes around 1980, many applications of function fields were found in different areas of mathematics and information theory. This book presents survey articles on some of these new developments. The topics focus on material which has not yet been presented in other books or survey articles.
Author | : Igor Shparlinski |
Publisher | : |
Total Pages | : 548 |
Release | : 2014-01-15 |
Genre | : |
ISBN | : 9789401592406 |
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Author | : Rudolf Lidl |
Publisher | : Cambridge University Press |
Total Pages | : 784 |
Release | : 1997 |
Genre | : Mathematics |
ISBN | : 9780521392310 |
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This book is devoted entirely to the theory of finite fields.
Author | : Gary L. Mullen |
Publisher | : American Mathematical Soc. |
Total Pages | : 278 |
Release | : 2008 |
Genre | : Computers |
ISBN | : 0821843095 |
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This volume contains the proceedings of the Eighth International Conference on Finite Fields and Applications, held in Melbourne, Australia, July 9-13, 2007. It contains 5 invited survey papers as well as original research articles covering various theoretical and applied areas related to finite fields.Finite fields, and the computational and algorithmic aspects of finite field problems, continue to grow in importance and interest in the mathematical and computer science communities because of their applications in so many diverse areas. In particular, finite fields now play very important roles in number theory, algebra, and algebraic geometry, as well as in computer science, statistics, and engineering. Areas of application include algebraic coding theory, cryptology, and combinatorialdesign theory.
Author | : Harald Niederreiter |
Publisher | : Princeton University Press |
Total Pages | : 272 |
Release | : 2009-09-21 |
Genre | : Mathematics |
ISBN | : 140083130X |
Download Algebraic Geometry in Coding Theory and Cryptography Book in PDF, Epub and Kindle
This textbook equips graduate students and advanced undergraduates with the necessary theoretical tools for applying algebraic geometry to information theory, and it covers primary applications in coding theory and cryptography. Harald Niederreiter and Chaoping Xing provide the first detailed discussion of the interplay between nonsingular projective curves and algebraic function fields over finite fields. This interplay is fundamental to research in the field today, yet until now no other textbook has featured complete proofs of it. Niederreiter and Xing cover classical applications like algebraic-geometry codes and elliptic-curve cryptosystems as well as material not treated by other books, including function-field codes, digital nets, code-based public-key cryptosystems, and frameproof codes. Combining a systematic development of theory with a broad selection of real-world applications, this is the most comprehensive yet accessible introduction to the field available. Introduces graduate students and advanced undergraduates to the foundations of algebraic geometry for applications to information theory Provides the first detailed discussion of the interplay between projective curves and algebraic function fields over finite fields Includes applications to coding theory and cryptography Covers the latest advances in algebraic-geometry codes Features applications to cryptography not treated in other books