handbook of finite fields discrete mathematics and its applications

Download Book Handbook Of Finite Fields Discrete Mathematics And Its Applications in PDF format. You can Read Online Handbook Of Finite Fields Discrete Mathematics And Its Applications here in PDF, EPUB, Mobi or Docx formats.

Handbook Of Finite Fields

Author : Gary L. Mullen
ISBN : 9781439873823
Genre : Computers
File Size : 59. 96 MB
Format : PDF, Mobi
Download : 528
Read : 984

Download Now


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 each chapter is self contained and peer reviewed. The first part of the book traces the history of finite fields through the eighteenth and nineteenth centuries. The second part presents theoretical properties of finite fields, covering polynomials, special functions, sequences, algorithms, curves, and related computational aspects. The final part describes various mathematical and practical applications of finite fields in combinatorics, algebraic coding theory, cryptographic systems, biology, quantum information theory, engineering, and other areas. The book provides a comprehensive index and easy access to over 3,000 references, enabling you to quickly locate up-to-date facts and results regarding finite fields.

Applications Of Finite Fields

Author : Alfred J. Menezes
ISBN : 0792392825
Genre : Computers
File Size : 57. 56 MB
Format : PDF, Kindle
Download : 497
Read : 687

Download Now


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.

Finite Fields

Author : Rudolf Lidl
ISBN : 0521392314
Genre : Mathematics
File Size : 75. 33 MB
Format : PDF, ePub
Download : 228
Read : 645

Download Now


This book is devoted entirely to the theory of finite fields.

Introduction To Finite Fields And Their Applications

Author : Rudolf Lidl
ISBN : 0521460948
Genre : Mathematics
File Size : 68. 31 MB
Format : PDF, ePub, Mobi
Download : 740
Read : 477

Download Now


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

Finite Fields Theory And Computation

Author : Igor Shparlinski
ISBN : 9789401592390
Genre : Mathematics
File Size : 71. 67 MB
Format : PDF, Kindle
Download : 340
Read : 934

Download Now


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.

Finite Fields With Applications To Coding Theory Cryptography And Related Areas

Author : Gary L. Mullen
ISBN : 9783642594359
Genre : Mathematics
File Size : 64. 21 MB
Format : PDF, ePub
Download : 691
Read : 553

Download Now



Finite Fields And Applications

Author : Gary L. Mullen
ISBN : 9783540246336
Genre : Mathematics
File Size : 48. 33 MB
Format : PDF, ePub, Docs
Download : 858
Read : 761

Download Now



Finite Fields And Applications

Author : Gary L. Mullen
ISBN : 9780821843093
Genre : Mathematics
File Size : 23. 83 MB
Format : PDF
Download : 929
Read : 313

Download Now


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 combinatorial design theory.

Applied Abstract Algebra

Author : Rudolf Lidl
ISBN : 9781475729412
Genre : Mathematics
File Size : 62. 84 MB
Format : PDF, Docs
Download : 245
Read : 315

Download Now


Accessible to junior and senior undergraduate students, this survey contains many examples, solved exercises, sets of problems, and parts of abstract algebra of use in many other areas of discrete mathematics. Although this is a mathematics book, the authors have made great efforts to address the needs of users employing the techniques discussed. Fully worked out computational examples are backed by more than 500 exercises throughout the 40 sections. This new edition includes a new chapter on cryptology, and an enlarged chapter on applications of groups, while an extensive chapter has been added to survey other applications not included in the first edition. The book assumes knowledge of the material covered in a course on linear algebra and, preferably, a first course in (abstract) algebra covering the basics of groups, rings, and fields.

Elliptic Curves

Author : Lawrence C. Washington
ISBN : 1420071475
Genre : Mathematics
File Size : 64. 37 MB
Format : PDF, Docs
Download : 137
Read : 255

Download Now


Like its bestselling predecessor, Elliptic Curves: Number Theory and Cryptography, Second Edition develops the theory of elliptic curves to provide a basis for both number theoretic and cryptographic applications. With additional exercises, this edition offers more comprehensive coverage of the fundamental theory, techniques, and applications of elliptic curves. New to the Second Edition Chapters on isogenies and hyperelliptic curves A discussion of alternative coordinate systems, such as projective, Jacobian, and Edwards coordinates, along with related computational issues A more complete treatment of the Weil and Tate–Lichtenbaum pairings Doud’s analytic method for computing torsion on elliptic curves over Q An explanation of how to perform calculations with elliptic curves in several popular computer algebra systems Taking a basic approach to elliptic curves, this accessible book prepares readers to tackle more advanced problems in the field. It introduces elliptic curves over finite fields early in the text, before moving on to interesting applications, such as cryptography, factoring, and primality testing. The book also discusses the use of elliptic curves in Fermat’s Last Theorem. Relevant abstract algebra material on group theory and fields can be found in the appendices.

Top Download:

Best Books