Finite fields theory and computation : the meeting point of number theory, computer science, coding theory, and cryptography by Igor E. Shparlinski

Cover of: Finite fields | Igor E. Shparlinski

Published by Kluwer Academic Publishers in Dordrecht, Boston .

Written in English

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Subjects:

  • Finite fields (Algebra)

Edition Notes

Includes bibliographical references (p. 409-524) and index.

Book details

Statementby Igor E. Shparlinski.
SeriesMathematics and its applications ;, v. 477, Mathematics and its applications (Kluwer Academic Publishers) ;, v. 477.
Classifications
LC ClassificationsQA247.3 .S477 1999
The Physical Object
Paginationxiv, 528 p. :
Number of Pages528
ID Numbers
Open LibraryOL34744M
ISBN 100792356624
LC Control Number99018969

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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 of the literature/5(6).

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

This book, the first one devoted entirely to this theory, provides comprehensive coverage /5(4). 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 circuits. The first part of this book presents an introduction to this theory, Cited by: "Preface The CRC Handbook of Finite fields book Fields (hereafter referred to as the Handbook) is a reference book for the theory and applications of nite elds.

It is not intended to be an introductory textbook. Our goal is to compile in one volume the state of the art in. A look at the topics of the proceed­ ings volume of the Third International Conference on Finite Fields and Their Applications (Glasgow, ) (see [18]), or at the list of references in I.

Shparlinski's book [47] (a recent extensive survey on the Theory of Finite Fields with particular emphasis on computational aspects), shows that the Brand: Springer US. 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. 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. 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.

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.

Finite fields I talked in class about the field with two elements F2 = {0,1} and we’ve used it in various examples and homework problems. In these notes I will introduce Finite fields book finite fields F p = {0,1,p−1} for every prime number p.

I’ll say a little about what linear Finite fields book looks like over these fields, and why you might Size: 66KB.

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. Finite fields book   The theory of finite fields encompasses algebra, combinatorics, and number theory and has furnished widespread applications in other areas of mathematics and computer science.

This book is a collection of selected topics in the theory of finite fields and related areas. 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 Reviews: 1.

A look at the topics of the proceed­ ings volume of the Third International Conference on Finite Fields and Their Applications (Glasgow, ) (see [18]), or at the list of references in I.

Shparlinski's book [47] (a recent extensive survey on the Theory of Finite Fields with particular emphasis on computational aspects), shows that the.

Finite Fields and Applications Buy Physical Book Learn about institutional subscriptions. Papers Table of contents (36 papers) About About these Galois field Graph Permutation algebra algorithms coding theory finite field scientific computing.

Editors and affiliations. A finite field is a finite set which is a field; this means that multiplication, addition, subtraction and division (excluding division by zero) are defined and satisfy the rules of arithmetic known as the field axioms.

The number of elements of a finite field is called its order or, sometimes, its size. This book provides an exhaustive survey of the most recent achievements in the theory and applications of finite fields and in many related areas such as algebraic number theory, theoretical computer science, coding theory and cryptography.

of finite fields, we refer to the books by Lidl and Niederreiter [71, 72]. Structure of Finite Fields For a prime number p, the residue class ring Z/pZ of the ring Z of integers forms a field.

We also denote Z/pZ by F p. It is a prime field in the sense that there are no proper subfields of F p. There are exactly p elements in F Size: KB.

Although the universal property of a completely free element used to accelerate arithmetic computation in finite fields has not been ascertained, this volume represents the search for such elements and leads to a deeper insight of the finite fields structure.

Annotation c. by Book News, Inc., Portland, Or. BooknewsPrice: $ 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.

For finite fields, there is Lidl and Niederreiter, Finite Fields, which is Volume 20 in the Encyclopedia of Mathematics and its Applications.

The theory of polynomials over finite fields is important for investigating the algebraic structure of finite fields as well as for many applications.

Above all, irreducible polynomials—the prime elements of the polynomial ring over a finite field—are indispensable for constructing finite fields and computing with the elements of a finite.

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.

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 circuits.

The first part of this book presents an introduction to this theory, emphasizing those aspects that are relevant for application.5/5(1).

The theory of finite fields is a key part of number theory, abstract algebra, arithmetic algebraic geometry, and cryptography, among others.

Many questions about the integers or the rational numbers can be translated into questions about the arithmetic in. 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 circuits.

This book is devoted entirely to the theory of finite fields, and it provides comprehensive coverage of the literature. 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.4/5(2).

Additional Physical Format: Online version: Lidl, Rudolf. Finite fields. Reading, Mass.: Addison-Wesley Pub. Co., Advanced Book Program/World Science Division,   xiv, p.: 25 cm Includes bibliographical references (p. ) and indexes 11 07Pages: 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). Finite fields as splitting fields We can describe every nite eld as a splitting eld of a polynomial depending only on the size of the eld. Lemma A eld of prime power order pn is a splitting eld over F p of xp n x.

Proof. Let F be a eld of order pn. From the proof of Theorem, F contains a sub eld isomorphic to Z=(p) = F p. Explicitly File Size: KB. Ri W, Myong G, Kim R and Rim C () The number of irreducible polynomials over finite fields of characteristic 2 with given trace and subtrace, Finite Fields and Their Applications, 29, (), Online publication date: 1-Sep   A large portion of the book can be used as a textbook for graduate and upper level undergraduate students in mathematics, communication engineering, computer science and other fields.

The remaining part can be used as references for specialists. Explicit construction and computation of finite Pages: A finite field must be a finite dimensional vector space, so all finite fields have degrees. The number of elements in a finite field is the order of that field.

The order of a finite field A finite field, since it cannot contain ℚ, must have a prime subfieldFile Size: KB. Applications of finite fields introduce some of these developments in cryptography, computer algebra and coding theory. A finite field or Galois field is a field with a finite order (number of elements).

The order of a finite field is always a prime or a power of prime. 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. Finite Field Definition. Mathematically, a finite field is defined as a finite set of numbers and two operations + (addition) and ⋅ (multiplication) that satisfy the following: If a and b are in the set, a + b and a ⋅ b are in the set.

We call this property closed. 0 exists and has the property a + 0 = call this the additive identity. 1 exists and has the property a ⋅ 1 = a. A Course in Finite Group Representation Theory Peter Webb Febru Preface The representation theory of nite groups has a long history, going back to the 19th century and earlier.

A milestone in the subject was the de nition of characters of nite This book is written for students who are studying nite group representationFile Size: 1MB. This section sets up many of the basic notions used in this book.

Finite Fields. This chapter starts out with a discussion of the structure of finite fields. Given a field its characteristic is defined as the smallest number such that ⋅ is congruent to zero in. All the things that are genuinely linear, like basis, matricial representations for finite dimensional spaces, dual and bi-dual, Gaussian elimination, determinants, Rouché-Capelli theorem carry on verbatim or with very obvious adjustments.

The results around Jordan normal form stay unchanged for algebraically closed fields. 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.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.Orders of Gauß Periods in Finite Fields Article (PDF Available) in Applicable Algebra in Engineering Communication and Computing 9(1) .

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