Handbook of Finite Fields

Handbook of Finite Fields
Author: Gary L. Mullen,Daniel Panario
Publsiher: CRC Press
Total Pages: 1068
Release: 2013-06-17
ISBN: 1439873828
Category: Computers
Language: EN, FR, DE, ES & NL

Handbook of Finite Fields Book Excerpt:

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

Finite Fields and Their Applications

Finite Fields and Their Applications
Author: Pascale Charpin,Alexander Pott,Arne Winterhof
Publsiher: Walter de Gruyter
Total Pages: 285
Release: 2013-05-28
ISBN: 3110283603
Category: Mathematics
Language: EN, FR, DE, ES & NL

Finite Fields and Their Applications Book Excerpt:

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 September 2-7, 2012. Finite fields play important roles in many application areas such as coding theory, cryptography, Monte Carlo and quasi-Monte Carlo methods, pseudorandom number generation, quantum computing, and wireless communication. In this book we will focus on sequences, character sums, and polynomials over finite fields in view of the above mentioned application areas: Chapters 1 and 2 deal with sequences mainly constructed via characters and analyzed using bounds on character sums. Chapters 3, 5, and 6 deal with polynomials over finite fields. Chapters 4 and 9 consider problems related to coding theory studied via finite geometry and additive combinatorics, respectively. Chapter 7 deals with quasirandom points in view of applications to numerical integration using quasi-Monte Carlo methods and simulation. Chapter 8 studies aspects of iterations of rational functions from which pseudorandom numbers for Monte Carlo methods can be derived. The goal of this book is giving an overview of several recent research directions as well as stimulating research in sequences and polynomials under the unified framework of character theory.

Lectures on Finite Fields

Lectures on Finite Fields
Author: Xiang-dong Hou
Publsiher: American Mathematical Soc.
Total Pages: 240
Release: 2018-06-07
ISBN: 1470442892
Category: Finite fields (Algebra)
Language: EN, FR, DE, ES & NL

Lectures on Finite Fields Book Excerpt:

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 topics include basic facts about finite fields, polynomials over finite fields, Gauss sums, algebraic number theory and cyclotomic fields, zeros of polynomials over finite fields, and classical groups over finite fields. The book is mostly self-contained, and the material covered is accessible to readers with the knowledge of graduate algebra; the only exception is a section on function fields. Each chapter is supplied with a set of exercises. The book can be adopted as a text for a second year graduate course or used as a reference by researchers.

Finite Fields

Finite Fields
Author: Rudolf Lidl,Harald Niederreiter
Publsiher: Cambridge University Press
Total Pages: 755
Release: 1997
ISBN: 9780521392310
Category: Mathematics
Language: EN, FR, DE, ES & NL

Finite Fields Book Excerpt:

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

Topics in Finite Fields

Topics in Finite Fields
Author: Gohar Kyureghyan, Gary L. Mullen,Alexander Pott
Publsiher: American Mathematical Soc.
Total Pages: 371
Release: 2015-01-29
ISBN: 0821898604
Category: Mathematics
Language: EN, FR, DE, ES & NL

Topics in Finite Fields Book Excerpt:

This volume contains the proceedings of the 11th International Conference on Finite Fields and their Applications (Fq11), held July 22-26, 2013, in Magdeburg, Germany. Finite Fields are fundamental structures in mathematics. They lead to interesting deep problems in number theory, play a major role in combinatorics and finite geometry, and have a vast amount of applications in computer science. Papers in this volume cover these aspects of finite fields as well as applications in coding theory and cryptography.

Topics in Galois Fields

Topics in Galois Fields
Author: Dirk Hachenberger,Dieter Jungnickel
Publsiher: Springer Nature
Total Pages: 785
Release: 2020-09-29
ISBN: 3030608069
Category: Mathematics
Language: EN, FR, DE, ES & NL

Topics in Galois Fields Book Excerpt:

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 textbooks: the primitive normal basis theorem, the existence of primitive elements in affine hyperplanes, and the Niederreiter method for factoring polynomials over finite fields. We give streamlined and/or clearer proofs for many fundamental results and treat some classical material in an innovative manner. In particular, we emphasize the interplay between arithmetical and structural results, and we introduce Berlekamp algebras in a novel way which provides a deeper understanding of Berlekamp's celebrated factorization algorithm. The book provides a thorough grounding in finite field theory for graduate students and researchers in mathematics. In view of its emphasis on applicable and computational aspects, it is also useful for readers working in information and communication engineering, for instance, in signal processing, coding theory, cryptography or computer science.

Combinatorics and Finite Fields

Combinatorics and Finite Fields
Author: Kai-Uwe Schmidt,Arne Winterhof
Publsiher: Walter de Gruyter GmbH & Co KG
Total Pages: 354
Release: 2019-07-08
ISBN: 3110642093
Category: Mathematics
Language: EN, FR, DE, ES & NL

Combinatorics and Finite Fields Book Excerpt:

Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.

Arithmetic of Finite Fields

Arithmetic of Finite Fields
Author: Sylvain Duquesne,Svetla Petkova-Nikova
Publsiher: Springer
Total Pages: 277
Release: 2017-03-08
ISBN: 3319552279
Category: Computers
Language: EN, FR, DE, ES & NL

Arithmetic of Finite Fields Book Excerpt:

This book constitutes the thoroughly refereed post-workshop proceedings of the 6th International Workshop on the Arithmetic of Finite Field, WAIFI 2016, held in Ghent, Belgium, in July 2016. The 14 revised full papers and 3 invited talks presented were carefully reviewed and selected from 38 submissions. The papers are organized in topical sections on invited talks; elliptic curves; applications; irreducible polynomials; applications to cryptography; Boolean functions; cryptography; cryptography and Boolean functions.

Arithmetic of Finite Fields

Arithmetic of Finite Fields
Author: Jean Claude Bajard,Alev Topuzoğlu
Publsiher: Springer Nature
Total Pages: 273
Release: 2021-02-16
ISBN: 3030688690
Category: Computers
Language: EN, FR, DE, ES & NL

Arithmetic of Finite Fields Book Excerpt:

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 was held online. The 12 revised full papers and 3 invited talks presented were carefully reviewed and selected from 22 submissions. The papers are organized in topical sections on invited talks, Finite Field Arithmetic, Coding Theory, Network Security and much more.

Contemporary Developments in Finite Fields and Applications

Contemporary Developments in Finite Fields and Applications
Author: Anne Canteaut,Gove Effinger,Sophie Huczynska,Daniel Panario,Leo Storme
Publsiher: World Scientific
Total Pages: 372
Release: 2016-06-15
ISBN: 9814719277
Category: Mathematics
Language: EN, FR, DE, ES & NL

Contemporary Developments in Finite Fields and Applications Book Excerpt:

The volume is a collection of 20 refereed articles written in connection with lectures presented at the 12th International Conference on Finite Fields and Their Applications ("Fq12") at Skidmore College in Saratoga Springs, NY in July 2015. Finite fields are central to modern cryptography and secure digital communication, and hence must evolve rapidly to keep pace with new technologies. Topics in this volume include cryptography, coding theory, structure of finite fields, algorithms, curves over finite fields, and further applications. Contributors will include: Antoine Joux (Fondation Partenariale de l'UPMC, France); Gary Mullen (Penn State University, USA); Gohar Kyureghyan (Otto-von-Guericke Universität, Germany); Gary McGuire (University College Dublin, Ireland); Michel Lavrauw (Università degli Studi di Padova, Italy); Kirsten Eisentraeger (Penn State University, USA); Renate Scheidler (University of Calgary, Canada); Michael Zieve (University of Michigan, USA). Contents:Divisibility of L-Polynomials for a Family of Curves (I Blanco-Chacón, R Chapman, S Fordham and G McGuire)Divisibility of Exponential Sums Associated to Binomials Over 𝔽p (F Castro, R Figueroa, P Guan and J Ortiz-Ubarri)Dickson Polynomials that are Involutions (P Charpin, S Mesnager and S Sarkar)Constructing Elliptic Curves and Curves of Genus 2 over Finite Fields (K Eisenträger)A Family of Plane Curves with Two or More Galois Points in Positive Characteristic (S Fukasawa)Permutation Polynomials of 𝔽q2 of the Form αX + Xr(q-1)+1 (X-D Hou)Character Sums and Generating Sets (M-D A Huang and L Liu)Nearly Sparse Linear Algebra and Application to Discrete Logarithms Computations (A Joux and C Pierrot)Full Degree Two del Pezzo Surfaces over Small Finite Fields (A Knecht and K Reyes)Diameter of Some Monomial Digraphs (A Kodess, F Lazebnik, S Smith and J Sporre)Permutation Polynomials of the Form X + γTr(Xk) (G Kyureghyan and M Zieve)Scattered Spaces in Galois Geometry (M Lavrauw)On the Value Set of Small Families of Polynomials over a Finite Field, III (G Matera, M Pérez and Melina Privitelli)The Density of Unimodular Matrices over Integrally Closed Subrings of Function Fields (G Micheli and R Schnyder)Some Open Problems Arising from My Recent Finite Field Research (G L Mullen)On Coefficients of Powers of Polynomials and Their Compositions over Finite Fields (G L Mullen, A Muratović-Ribić and Q Wang)On the Structure of Certain Reduced Linear Modular Systems (E Orozco)Finding a Gröbner Basis for the Ideal of Recurrence Relations on m-Dimensional Periodic Arrays (I M Rubio, M Sweedler and C Heegard)An Introduction to Hyperelliptic Curve Arithmetic (R Scheidler)On the Existence of Aperiodic Complementary Hexagonal Lattice Arrays (Y Tan and G Gong) Readership: Researchers in combinatorics and graph theory, numerical analysis and computational mathematics, and coding theory.

Applied Algebra and Number Theory

Applied Algebra and Number Theory
Author: Gerhard Larcher,Friedrich Pillichshammer,Arne Winterhof,Chaoping Xing
Publsiher: Cambridge University Press
Total Pages: 345
Release: 2014-12-11
ISBN: 1107074002
Category: Mathematics
Language: EN, FR, DE, ES & NL

Applied Algebra and Number Theory Book Excerpt:

Survey articles on modern topics related to the work of Harald Niederreiter, written by close colleagues and leading experts.

Open Problems in Mathematics and Computational Science

Open Problems in Mathematics and Computational Science
Author: Çetin Kaya Koç
Publsiher: Springer
Total Pages: 439
Release: 2015-03-25
ISBN: 331910683X
Category: Computers
Language: EN, FR, DE, ES & NL

Open Problems in Mathematics and Computational Science Book Excerpt:

This book presents interesting, important unsolved problems in the mathematical and computational sciences. The contributing authors are leading researchers in their fields and they explain outstanding challenges in their domains, first by offering basic definitions, explaining the context, and summarizing related algorithms, theorems, and proofs, and then by suggesting creative solutions. The authors feel a strong motivation to excite deep research and discussion in the mathematical and computational sciences community, and the book will be of value to postgraduate students and researchers in the areas of theoretical computer science, discrete mathematics, engineering, and cryptology.

Women in Numbers Europe II

Women in Numbers Europe II
Author: Irene I. Bouw,Ekin Ozman,Jennifer Johnson-Leung,Rachel Newton
Publsiher: Springer
Total Pages: 213
Release: 2018-06-01
ISBN: 3319749986
Category: Mathematics
Language: EN, FR, DE, ES & NL

Women in Numbers Europe II Book Excerpt:

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 the conference make up this diverse volume. Topics cover a broad range of topics such as arithmetic dynamics, failure of local-global principles, geometry in positive characteristics, and heights of algebraic integers. The use of tools from algebra, analysis and geometry, as well as computational methods exemplifies the wealth of techniques available to modern researchers in number theory. Exploring connections between different branches of mathematics and combining different points of view, these papers continue the tradition of supporting and highlighting the contributions of women number theorists at a variety of career stages. Perfect for students and researchers interested in the field, this volume provides an easily accessible introduction and has the potential to inspire future work.

Information Security and Cryptology

Information Security and Cryptology
Author: Yu Yu,Moti Yung
Publsiher: Springer Nature
Total Pages: 552
Release: 2021-10-17
ISBN: 303088323X
Category: Computers
Language: EN, FR, DE, ES & NL

Information Security and Cryptology Book Excerpt:

This book constitutes the post-conference proceedings of the 17th International Conference on Information Security and Cryptology, Inscrypt 2021, in August 2021. Due the COVID-19, the conference was held online The 28 full papers presented were carefully reviewed and selected from 81 submissions. The papers presents papers about research advances in all areas of information security, cryptology, and their applications.

Computer Algebra and Polynomials

Computer Algebra and Polynomials
Author: Jaime Gutierrez,Josef Schicho,Martin Weimann
Publsiher: Springer
Total Pages: 213
Release: 2015-01-20
ISBN: 3319150812
Category: Computers
Language: EN, FR, DE, ES & NL

Computer Algebra and Polynomials Book Excerpt:

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-life applications. This has dramatically changed: nowadays we find applications of algebra and number theory frequently in our daily life. This book focuses on the theory and algorithms for polynomials over various coefficient domains such as a finite field or ring. The operations on polynomials in the focus are factorization, composition and decomposition, basis computation for modules, etc. Algorithms for such operations on polynomials have always been a central interest in computer algebra, as it combines formal (the variables) and algebraic or numeric (the coefficients) aspects. The papers presented were selected from the Workshop on Computer Algebra and Polynomials, which was held in Linz at the Johann Radon Institute for Computational and Applied Mathematics (RICAM) during November 25-29, 2013, at the occasion of the Special Semester on Applications of Algebra and Number Theory.

Applied Number Theory

Applied Number Theory
Author: Harald Niederreiter,Arne Winterhof
Publsiher: Springer
Total Pages: 442
Release: 2015-09-01
ISBN: 3319223216
Category: Mathematics
Language: EN, FR, DE, ES & NL

Applied Number Theory Book Excerpt:

This textbook effectively builds a bridge from basic number theory to recent advances in applied number theory. It presents the first unified account of the four major areas of application where number theory plays a fundamental role, namely cryptography, coding theory, quasi-Monte Carlo methods, and pseudorandom number generation, allowing the authors to delineate the manifold links and interrelations between these areas. Number theory, which Carl-Friedrich Gauss famously dubbed the queen of mathematics, has always been considered a very beautiful field of mathematics, producing lovely results and elegant proofs. While only very few real-life applications were known in the past, today number theory can be found in everyday life: in supermarket bar code scanners, in our cars’ GPS systems, in online banking, etc. Starting with a brief introductory course on number theory in Chapter 1, which makes the book more accessible for undergraduates, the authors describe the four main application areas in Chapters 2-5 and offer a glimpse of advanced results that are presented without proofs and require more advanced mathematical skills. In the last chapter they review several further applications of number theory, ranging from check-digit systems to quantum computation and the organization of raster-graphics memory. Upper-level undergraduates, graduates and researchers in the field of number theory will find this book to be a valuable resource.

Algebra for Cryptologists

Algebra for Cryptologists
Author: Alko R. Meijer
Publsiher: Springer
Total Pages: 301
Release: 2016-09-01
ISBN: 3319303961
Category: Mathematics
Language: EN, FR, DE, ES & NL

Algebra for Cryptologists Book Excerpt:

This textbook provides an introduction to the mathematics on which modern cryptology is based. It covers not only public key cryptography, the glamorous component of modern cryptology, but also pays considerable attention to secret key cryptography, its workhorse in practice. Modern cryptology has been described as the science of the integrity of information, covering all aspects like confidentiality, authenticity and non-repudiation and also including the protocols required for achieving these aims. In both theory and practice it requires notions and constructions from three major disciplines: computer science, electronic engineering and mathematics. Within mathematics, group theory, the theory of finite fields, and elementary number theory as well as some topics not normally covered in courses in algebra, such as the theory of Boolean functions and Shannon theory, are involved. Although essentially self-contained, a degree of mathematical maturity on the part of the reader is assumed, corresponding to his or her background in computer science or engineering. Algebra for Cryptologists is a textbook for an introductory course in cryptography or an upper undergraduate course in algebra, or for self-study in preparation for postgraduate study in cryptology.

Handbook of Algebra

Handbook of Algebra
Author: Anonim
Publsiher: Elsevier
Total Pages: 912
Release: 1995-12-18
ISBN: 9780080532950
Category: Mathematics
Language: EN, FR, DE, ES & NL

Handbook of Algebra Book Excerpt:

Handbook of Algebra defines algebra as consisting of many different ideas, concepts and results. Even the nonspecialist is likely to encounter most of these, either somewhere in the literature, disguised as a definition or a theorem or to hear about them and feel the need for more information. Each chapter of the book combines some of the features of both a graduate-level textbook and a research-level survey. This book is divided into eight sections. Section 1A focuses on linear algebra and discusses such concepts as matrix functions and equations and random matrices. Section 1B cover linear dependence and discusses matroids. Section 1D focuses on fields, Galois Theory, and algebraic number theory. Section 1F tackles generalizations of fields and related objects. Section 2A focuses on category theory, including the topos theory and categorical structures. Section 2B discusses homological algebra, cohomology, and cohomological methods in algebra. Section 3A focuses on commutative rings and algebras. Finally, Section 3B focuses on associative rings and algebras. This book will be of interest to mathematicians, logicians, and computer scientists.

Introduction to Combinatorics

Introduction to Combinatorics
Author: Walter D. Wallis,John C. George
Publsiher: CRC Press
Total Pages: 424
Release: 2016-12-12
ISBN: 1498777635
Category: Mathematics
Language: EN, FR, DE, ES & NL

Introduction to Combinatorics Book Excerpt:

What Is Combinatorics Anyway? Broadly speaking, combinatorics is the branch of mathematics dealing with different ways of selecting objects from a set or arranging objects. It tries to answer two major kinds of questions, namely, counting questions: how many ways can a selection or arrangement be chosen with a particular set of properties; and structural questions: does there exist a selection or arrangement of objects with a particular set of properties? The authors have presented a text for students at all levels of preparation. For some, this will be the first course where the students see several real proofs. Others will have a good background in linear algebra, will have completed the calculus stream, and will have started abstract algebra. The text starts by briefly discussing several examples of typical combinatorial problems to give the reader a better idea of what the subject covers. The next chapters explore enumerative ideas and also probability. It then moves on to enumerative functions and the relations between them, and generating functions and recurrences., Important families of functions, or numbers and then theorems are presented. Brief introductions to computer algebra and group theory come next. Structures of particular interest in combinatorics: posets, graphs, codes, Latin squares, and experimental designs follow. The authors conclude with further discussion of the interaction between linear algebra and combinatorics. Features Two new chapters on probability and posets. Numerous new illustrations, exercises, and problems. More examples on current technology use A thorough focus on accuracy Three appendices: sets, induction and proof techniques, vectors and matrices, and biographies with historical notes, Flexible use of MapleTM and MathematicaTM

Graphs Algorithms and Optimization

Graphs  Algorithms  and Optimization
Author: William Kocay,Donald L. Kreher
Publsiher: CRC Press
Total Pages: 546
Release: 2016-11-03
ISBN: 1482251183
Category: Mathematics
Language: EN, FR, DE, ES & NL

Graphs Algorithms and Optimization Book Excerpt:

The second edition of this popular book presents the theory of graphs from an algorithmic viewpoint. The authors present the graph theory in a rigorous, but informal style and cover most of the main areas of graph theory. The ideas of surface topology are presented from an intuitive point of view. We have also included a discussion on linear programming that emphasizes problems in graph theory. The text is suitable for students in computer science or mathematics programs.