Finite Fields

Author by : Gary L. Mullen
Languange : en
Publisher by : American Mathematical Soc.
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Description : 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 continue to grow in importance. This volume contains the refereed proceedings of a conference entitled Finite Fields: Theory, Applications and Algorithms, held in August 1993 at the University of Nevada at Las Vegas. Among the topics treated are theoretical aspects of finite fields, coding theory, cryptology, combinatorial design theory, and algorithms related to finite fields. Also included is a list of open problems and conjectures. This volume is an excellent reference for applied and research mathematicians as well as specialists and graduate students in information theory, computer science, and electrical engineering.


Finite Fields

Author by : Ronald Cleveland Mullin
Languange : en
Publisher by : American Mathematical Soc.
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Description : 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. The conference drew workers in theoretical, applied, and algorithmic finite field theory. All papers were refereed. They are loosely classified as theoretical and applied and are listed under these general headings. The work contains up-to-date results from leading experts in the field.


Finite Fields Theory Applications And Algorithms

Author by : Ronald Cleveland Mullin
Languange : en
Publisher by : American Mathematical Soc.
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Description : 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 particularly important roles in number theory, algebra, and algebraic geometry. They also play a crucial role in computer science, statistics, and engineering. Areas of application include but are not limited to algebraic coding theory, cryptology, and combinatorial design theory. Computational and algorithmic aspects of finite field problems are also growing in significance. The conference drew workers in theoretical, applied, and algorithmic finite field theory. All papers were refereed. They are loosely classified as theoretical and applied and are listed under these general headings. The work contains up-to-date results from leading experts in the field.


Applications Of Finite Fields

Author by : Alfred J. Menezes
Languange : en
Publisher by : Springer Science & Business Media
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Description : 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 Theory And Computation

Author by : Igor Shparlinski
Languange : en
Publisher by : Springer Science & Business Media
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Description : 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 And Applications

Author by : International Conference on Finite Fields and Applications
Languange : en
Publisher by : Springer Science & Business Media
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Description : This book constitutes the thoroughly refereed post-proceedings of the 7th International Conference on Finite Fields and Applications, Fq7, held in Toulouse, France, in May 2004. The 19 revised full papers presented were carefully selected from around 60 presentations at the conference during two rounds of reviewing and revision. Among the topics addressed are Weierstrass semigroups, Galois rings, hyperelliptic curves, polynomial irreducibility, pseudorandom number sequences, permutation polynomials, random polynomials, matrices, function fields, ramified towers, BCH codes, cyclic codes, primitive polynomials, covering sequences, cyclic decompositions.


Computational And Algorithmic Problems In Finite Fields

Author by : Igor Shparlinski
Languange : en
Publisher by : Springer Science & Business Media
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Description : 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.


Finite Fields And Their Applications

Author by : James A. Davis
Languange : en
Publisher by : Walter de Gruyter GmbH & Co KG
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Description : 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.


Finite Fields With Applications To Coding Theory Cryptography And Related Areas

Author by : Gary L. Mullen
Languange : en
Publisher by : Springer Science & Business Media
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Description : 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 documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.


Finite Fields And Applications

Author by : Dieter Jungnickel
Languange : en
Publisher by : Springer Science & Business Media
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Description : The Fifth International Conference on Finite Fields and Applications Fq5 held at the University of Augsburg, Germany, from August 2-6, 1999 continued a series of biennial international conferences on finite fields. The proceedings document the steadily increasing interest in this topic. Finite fields have an inherently fascinating structure and are important tools in discrete mathematics. Their applications range from combinatorial design theory, finite geometries, and algebraic geometry to coding theory, cryptology, and scientific computing. A particularly fruitful aspect is the interplay between theory and applications which has led to many new perspectives in research on finite fields. This interplay has always been a dominant theme in Fq conferences and was very much in evidence at Fq5. The proceedings reflect this, and offer an up-to-date collection of surveys and original research articles by leading experts in the area.


Finite Fields And Applications

Author by : Stephen D. Cohen
Languange : en
Publisher by : Cambridge University Press
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Description : Finite fields are algebraic structures in which there is much research interest. This book gives a state-of-the-art account of finite fields and their applications in communications (coding theory, cryptology), combinatorics, design theory, quasirandom points, algorithms and their complexity. Typically, theory and application are tightly interwoven in the survey articles and original research papers included here. The book also demonstrates interconnections with other branches of pure mathematics such as number theory, group theory and algebraic geometry. This volume is an invaluable resource for any researcher in finite fields or related areas.


Handbook Of Finite Fields

Author by : Gary L. Mullen
Languange : en
Publisher by : CRC Press
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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. Edited by two renowned researchers, the book uses a uniform style and format throughout and


Topics In Galois Fields

Author by : Dirk Hachenberger
Languange : en
Publisher by : Unknown
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Description : 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.--


Topics In Finite Fields

Author by : Gohar Kyureghyan
Languange : en
Publisher by : American Mathematical Soc.
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Description : 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.


Algebraic Geometric Codes

Author by : Michael A. Tsfasman
Languange : en
Publisher by : American Mathematical Soc.
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Description : This book focuses on the theory of algebraic geometry codes, a subject that has emerged at the meeting point of several fields of mathematics. Unlike other texts, it consistently seeks interpretations that connect coding theory to algebraic geometry and number theory. This approach makes the book useful for both coding experts and experts in algebraic geometry.


Modular Algorithms In Symbolic Summation And Symbolic Integration

Author by : Jürgen Gerhard
Languange : en
Publisher by : Springer
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Description : This work brings together two streams in computer algebra: symbolic integration and summation on the one hand, and fast algorithmics on the other hand. In many algorithmically oriented areas of computer science, theanalysisof- gorithms–placedintothe limelightbyDonKnuth’stalkat the 1970ICM –provides a crystal-clear criterion for success. The researcher who designs an algorithmthat is faster (asymptotically, in the worst case) than any previous method receives instant grati?cation: her result will be recognized as valuable. Alas, the downside is that such results come along quite infrequently, despite our best efforts. An alternative evaluation method is to run a new algorithm on examples; this has its obvious problems, but is sometimes the best we can do. George Collins, one of the fathers of computer algebra and a great experimenter,wrote in 1969: “I think this demonstrates again that a simple analysis is often more revealing than a ream of empirical data (although both are important). ” Within computer algebra, some areas have traditionally followed the former methodology, notably some parts of polynomial algebra and linear algebra. Other areas, such as polynomial system solving, have not yet been amenable to this - proach. The usual “input size” parameters of computer science seem inadequate, and although some natural “geometric” parameters have been identi?ed (solution dimension, regularity), not all (potential) major progress can be expressed in this framework. Symbolic integration and summation have been in a similar state.


Modern Computer Algebra

Author by : Joachim von zur Gathen
Languange : en
Publisher by : Cambridge University Press
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Description : Computer algebra systems are now ubiquitous in all areas of science and engineering. This highly successful textbook, widely regarded as the 'bible of computer algebra', gives a thorough introduction to the algorithmic basis of the mathematical engine in computer algebra systems. Designed to accompany one- or two-semester courses for advanced undergraduate or graduate students in computer science or mathematics, its comprehensiveness and reliability has also made it an essential reference for professionals in the area. Special features include: detailed study of algorithms including time analysis; implementation reports on several topics; complete proofs of the mathematical underpinnings; and a wide variety of applications (among others, in chemistry, coding theory, cryptography, computational logic, and the design of calendars and musical scales). A great deal of historical information and illustration enlivens the text. In this third edition, errors have been corrected and much of the Fast Euclidean Algorithm chapter has been renovated.


Arithmetic Of Finite Fields

Author by : Çetin Kaya Koç
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the 5th International Workshop on the Arithmetic of Finite Field, WAIFI 2014, held in Gebze, Turkey, in September 2014. The 9 revised full papers and 43 invited talks presented were carefully reviewed and selected from 27 submissions. This workshop is a forum of mathematicians, computer scientists, engineers and physicists performing research on finite field arithmetic, interested in communicating the advances in the theory, applications, and implementations of finite fields. The workshop will help to bridge the gap between the mathematical theory of finite fields and their hardware/software implementations and technical applications.


Self Dual Codes And Invariant Theory

Author by : Gabriele Nebe
Languange : en
Publisher by : Springer Science & Business Media
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Description : One of the most remarkable and beautiful theorems in coding theory is Gleason's 1970 theorem about the weight enumerators of self-dual codes and their connections with invariant theory, which has inspired hundreds of papers about generalizations and applications of this theorem to different types of codes. This self-contained book develops a new theory which is powerful enough to include all the earlier generalizations.


Algorithms And Theory Of Computation Handbook Second Edition Volume 1

Author by : Mikhail J. Atallah
Languange : en
Publisher by : CRC Press
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Description : Algorithms and Theory of Computation Handbook, Second Edition: General Concepts and Techniques provides an up-to-date compendium of fundamental computer science topics and techniques. It also illustrates how the topics and techniques come together to deliver efficient solutions to important practical problems. Along with updating and revising many of the existing chapters, this second edition contains four new chapters that cover external memory and parameterized algorithms as well as computational number theory and algorithmic coding theory. This best-selling handbook continues to help computer professionals and engineers find significant information on various algorithmic topics. The expert contributors clearly define the terminology, present basic results and techniques, and offer a number of current references to the in-depth literature. They also provide a glimpse of the major research issues concerning the relevant topics.


Towards A Quarter Century Of Public Key Cryptography

Author by : Neal Koblitz
Languange : en
Publisher by : Springer Science & Business Media
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Description : Dept. of Mathematics, University of Washington, Seattle, USA This book brings together in one place important contributions and up-to-date research results in this fast moving area. Reprinted from Designs, Codes and Cryptography, 19:2/3.


Computational Invariant Theory

Author by : Harm Derksen
Languange : en
Publisher by : Springer
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Description : This book is about the computational aspects of invariant theory. Of central interest is the question how the invariant ring of a given group action can be calculated. Algorithms for this purpose form the main pillars around which the book is built. There are two introductory chapters, one on Gröbner basis methods and one on the basic concepts of invariant theory, which prepare the ground for the algorithms. Then algorithms for computing invariants of finite and reductive groups are discussed. Particular emphasis lies on interrelations between structural properties of invariant rings and computational methods. Finally, the book contains a chapter on applications of invariant theory, covering fields as disparate as graph theory, coding theory, dynamical systems, and computer vision. The book is intended for postgraduate students as well as researchers in geometry, computer algebra, and, of course, invariant theory. The text is enriched with numerous explicit examples which illustrate the theory and should be of more than passing interest. More than ten years after the first publication of the book, the second edition now provides a major update and covers many recent developments in the field. Among the roughly 100 added pages there are two appendices, authored by Vladimi r Popov, and an addendum by Norbert A'Campo and Vladimir Popov.


Unsolved Problems In Number Theory

Author by : Richard Guy
Languange : en
Publisher by : Springer Science & Business Media
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Description : Mathematics is kept alive by the appearance of new, unsolved problems. This book provides a steady supply of easily understood, if not easily solved, problems that can be considered in varying depths by mathematicians at all levels of mathematical maturity. This new edition features lists of references to OEIS, Neal Sloane’s Online Encyclopedia of Integer Sequences, at the end of several of the sections.


Public Key Cryptography Pkc 2006

Author by : Moti Yung
Languange : en
Publisher by : Springer Science & Business Media
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Description : Here are the refereed proceedings of the 9th International Conference on Theory and Practice in Public-Key Cryptography, PKC 2006, held in New York City in April 2006. The 34 revised full papers presented are organized in topical sections on cryptanalysis and protocol weaknesses, distributed crypto-computing, encryption methods, cryptographic hash and applications, number theory algorithms, pairing-based cryptography, cryptosystems design and analysis, signature and identification, authentication and key establishment, multi-party computation, and PKI techniques.


Cryptographic Hardware And Embedded Systems

Author by : Cetin K. Koc
Languange : en
Publisher by : Springer
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Description : This book constitutes the refereed proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems, CHES'99, held in Worcester, MA, USA in August 1999. The 27 revised papers presented together with three invited contributions were carefully reviewed and selected from 42 submissions. The papers are organized in sections on cryptographic hardware, hardware architectures, smartcards and embedded systems, arithmetic algorithms, power attacks, true random numbers, cryptographic algorithms on FPGAs, elliptic curve implementations, new cryptographic schemes and modes of operation.


Cryptographic Hardware And Embedded Systems

Author by : CHES
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 66
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Description : This book constitutes the refereed proceedings of the First International Workshop on Cryptographic Hardware and Embedded Systems, CHES'99, held in Worcester, MA, USA in August 1999. The 27 revised papers presented together with three invited contributions were carefully reviewed and selected from 42 submissions. The papers are organized in sections on cryptographic hardware, hardware architectures, smartcards and embedded systems, arithmetic algorithms, power attacks, true random numbers, cryptographic algorithms on FPGAs, elliptic curve implementations, new cryptographic schemes and modes of operation.


Public Key Cryptography

Author by : Hideki Imai
Languange : en
Publisher by : Springer Science & Business Media
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Total Read : 56
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Description : The intricate 3D structure of the CNS lends itself to multimedia presentation, and is depicted here by way of dynamic 3D models that can be freely rotated, and in over 200 illustrations taken from the successful book 'The Human Central Nervous System' by R. Nieuwenhuys et al, allowing the user to explore all aspects of this complex and fascinating subject. All this fully hyperlinked with over 2000 specialist terms. Optimal exam revision is guaranteed with the self-study option. For further information please contact: http://www.brainmedia.de/html/frames/pr/pr 5/pr 5 02.html


Quadratic Forms And Their Applications

Author by : Eva Bayer-Fluckiger
Languange : en
Publisher by : American Mathematical Soc.
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Description : This volume outlines the proceedings of the conference on 'Quadratic Forms and Their Applications' held at University College Dublin. It includes survey articles and research papers ranging from applications in topology and geometry to the algebraic theory of quadratic forms and its history. Various aspects of the use of quadratic forms in algebra, analysis, topology, geometry, and number theory are addressed. Special features include the first published proof of the Conway-Schneeberger Fifteen Theorem on integer-valued quadratic forms and the first English-language biography of Ernst Witt, founder of the theory of quadratic forms.