## Finite Fields: Theory and Computation

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### Finite Fields: Theory and Computation

• Author : Igor Shparlinski
• ISBN : 940159239X
• Category : Mathematics
• Publisher : Springer Science & Business Media
• Pages : 528
• Release Date : 2013-03-09

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.

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 pol ...

This is a textbook for graduate and upper level undergraduate students in mathematics, computer science, communication engineering and other fields. The explicit construction of finite fields and the computation in finite fie ...

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 referen ...

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 docum ...

This monograph provides a self-contained presentation of the foundations of finite fields, including a detailed treatment of their algebraic closures. It also covers important advanced topics which are not yet found in textbo ...

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 irr ...

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 Septem ...

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 ar ...

This volume represents the refereed proceedings of the Fifth International Conference on Finite Fields and Applications (F q5) held at the University of Augsburg (Germany) from August 2-6, 1999, and hosted by the Department o ...

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, ...

Thisvolumerepresentstherefereedproceedingsofthe7thInternationalC- ference on Finite Fields and Applications (F 7) held during May 5-9, q 2003, in Toulouse, France. The conference was hosted by the Pierre Baudis C- gress Cente ...

This book constitutes the refereed proceedings of the Second International Workshop on the Arithmetic of Finite Fields, WAIFI 2008, held in Siena, Italy, in July 2008. The 16 revised full papers presented were carefully revie ...

Over the last several decades there has been a renewed interest in finite field theory, partly as a result of important applications in a number of diverse areas such as electronic communications, coding theory, combinatorics ...

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 ...

This book constitutes the refereed proceedings of the 4th International Workshop on the Arithmetic of Finite Field, WAIFI 2012, held in Bochum, Germany, in July 2012. The 13 revised full papers and 4 invited talks presented w ...

From Gauss to G|del, mathematicians have sought an efficient algorithm to distinguish prime numbers from composite numbers. This book presents a random polynomial time algorithm for the problem. The methods used are from arit ...

This book constitutes the thoroughly refereed post-workshop proceedings of the 8th International Workshop on the Arithmetic of Finite Field, WAIFI 2020, held in Rennes, France in July 2020. Due to the COVID-19, the workshop w ...

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 resea ...

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 t ...

This volume contains the proceedings of the Ninth International Conference on Finite Fields and Applications, held in Ireland, July 13-17, 2009. It includes survey papers by all invited speakers as well as selected contribute ...

"Number Theory Arising from Finite Fields: Analytic and Probabilistic Theory" offers a discussion of the advances and developments in the field of number theory arising from finite fields. It emphasizes mean-value theorems of ...

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 ...

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 s ...

This book constitutes the thoroughly refereed post-workshop proceedings of the 7th International Workshop on the Arithmetic of Finite Field, WAIFI 2018, held in Bergen, Norway, in June 2018. The 14 revised full papers and six ...

Reviews the fundamental concepts behind the theory and computation of electromagnetic fields The book is divided in two parts. The first part covers both fundamental theories (such as vector analysis, Maxwell’s equations, b ...

Lecture Series on Computer and on Computational Sciences (LSCCS) aims to provide a medium for the publication of new results and developments of high-level research and education in the field of computer and computational sci ...

The book contains 8 detailed expositions of the lectures given at the Kaikoura 2000 Workshop on Computability, Complexity, and Computational Algebra. Topics covered include basic models and questions of complexity theory, the ...

According to the great mathematician Paul Erdös, God maintains perfect mathematical proofs in The Book. This book presents the authors candidates for such "perfect proofs," those which contain brilliant ideas, clever connect ...

Interested readers will find here the thoroughly refereed post-proceedings of the International Workshop of Sequences, Subsequences and Consequences, SSC 2007, held in Los Angeles, USA, in 2007. The 16 revised invited full pa ...

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 ap ...

This is the third supplementary volume to Kluwer's highly acclaimed twelve-volume Encyclopaedia of Mathematics. This additional volume contains nearly 500 new entries written by experts and covers developments and topics not ...

The EUROCRYPT ’96 conference was sponsored by the International Asso- ation for Cryptologic Research (IACR)l, in cooperation with the University of Saragossa. It took place at the Palacio de Congresos in Saragossa, Spain, d ...

Computers have stretched the limits of what is possible in mathematics. More: they have given rise to new fields of mathematical study; the analysis of new and traditional algorithms, the creation of new paradigms for impleme ...

This volume collects together lectures presented at the Sixth International Conference held at the University of Ioannina, Greece, on p-adic functional analysis with applications in the fields of physics, differential equatio ...

This book presents a study on the foundations of a large class of paraconsistent logics from the point of view of the logics of formal inconsistency. It also presents several systems of non-standard logics with paraconsistent ...

This impressive compilation of the material presented at the International Conference on Partial Differential Equations held in Fez, Morocco, represents an integrated discussion of all major topics in the area of partial diff ...

Algebra and number theory have always been counted among the most beautiful mathematical areas with deep proofs and elegant results. However, for a long time they were not considered that important in view of the lack of real ...

This volume contains the proceedings of the 13th $\mathrm{AGC^2T}$ conference, held March 14-18, 2011, in Marseille, France, together with the proceedings of the 2011 Geocrypt conference, held June 19-24, 2011, in Bastia, Fra ...