Finite Fields: Theory and Computation - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Fields: Theory and Computation write by Igor Shparlinski. This book was released on 2013-03-09. Finite Fields: Theory and Computation available in PDF, EPUB and Kindle. 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
Finite Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Fields write by Igor Shparlinski. This book was released on 2014-01-15. Finite Fields available in PDF, EPUB and Kindle.
Computational and Algorithmic Problems in Finite Fields
Computational and Algorithmic Problems in Finite Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Computational and Algorithmic Problems in Finite Fields write by Igor Shparlinski. This book was released on 2012-12-06. Computational and Algorithmic Problems in Finite Fields available in PDF, EPUB and Kindle. This volume presents an exhaustive treatment of computation and algorithms for finite fields. Topics covered include polynomial factorization, finding irreducible and primitive polynomials, 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 araes of mathematics. For completeness, also included are two special chapters on some recent advances and applications of the theory of congruences (optimal coefficients, congruential pseudo-random number generators, modular arithmetic etc.), and computational number theory (primality testing, factoring integers, computing in algebraic number theory, etc.) The problems considered here have many applications in computer science, coding theory, cryptography, number theory and discrete mathematics. The level of discussion presuppose only a knowledge of the basic facts on finite fields, and the book can be recommended as supplementary graduate text. For researchers and students interested in computational and algorithmic problems in finite fields.
Applications of Finite Fields
Applications of Finite Fields - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Applications of Finite Fields write by Alfred J. Menezes. This book was released on 2013-04-17. Applications of Finite Fields available 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.
Finite Fields and their Applications
Finite Fields and their Applications - read free eBook in online reader or directly download on the web page. Select files or add your book in reader. Download and read online ebook Finite Fields and their Applications write by James A. Davis. This book was released on 2020-10-26. Finite Fields and their Applications available in PDF, EPUB and Kindle. 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.
