Finite Fields: Theory and Computation

Finite Fields: Theory and Computation

Author: Igor Shparlinski

Publisher: Springer Science & Business Media

ISBN: 9789401592390

Category: Mathematics

Page: 528

View: 531

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: Theory and Computation
Language: en
Pages: 528
Authors: Igor Shparlinski
Categories: Mathematics
Type: BOOK - Published: 2013-03-09 - Publisher: Springer Science & Business Media

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
Finite Fields
Language: en
Pages: 402
Authors: Gary L. Mullen, Peter Jau-Shyong Shiue
Categories: Mathematics
Type: BOOK - Published: 1994 - Publisher: American Mathematical Soc.

Because of their applications in so many diverse areas, finite fields continue to play increasingly important roles in various branches of modern mathematics, including number theory, algebra, and algebraic geometry, as well as in computer science, information theory, statistics, and engineering. Computational and algorithmic aspects of finite field problems also
Cryptography and Computational Number Theory
Language: en
Pages: 378
Authors: Kwok Y. Lam, Igor Shparlinski, Huaxiong Wang, Chaoping Xing
Categories: Computers
Type: BOOK - Published: 2013-03-07 - Publisher: Birkhäuser

This volume contains the refereed proceedings of the Workshop on Cryptography and Computational Number Theory, CCNT'99, which has been held in Singapore during the week of November 22-26, 1999. The workshop was organized by the Centre for Systems Security of the Na tional University of Singapore. We gratefully acknowledge the
Women in Numbers Europe II
Language: en
Pages: 213
Authors: Irene I. Bouw, Ekin Ozman, Jennifer Johnson-Leung, Rachel Newton
Categories: Mathematics
Type: BOOK - Published: 2018-06-01 - Publisher: Springer

Inspired by the September 2016 conference of the same name, this second volume highlights recent research in a wide range of topics in contemporary number theory and arithmetic geometry. Research reports from projects started at the conference, expository papers describing ongoing research, and contributed papers from women number theorists outside
Finite Fields: Theory, Applications and Algorithms
Language: en
Pages: 243
Authors: Ronald Cleveland Mullin, Applications International Conference on Finite Fields: Theory, and Algorithms (4th : 1997 : University of Waterloo), Gary L. Mullen, International Conference on Finite Fields: Theory, Applications, and Algorithms (4th : 1997 : University of Waterloo)
Categories: Mathematics
Type: BOOK - Published: 1999 - Publisher: American Mathematical Soc.

The Fourth International Conference on Finite Fields: Theory, Applications, and Algorithms was held at the University of Waterloo in August 1997. This volume presents the refereed proceedings. Because of its applications in so many diverse areas, finite fields continues to grow in importance in modern mathematics. Finite fields now play