Algebraic Geometry Modeling in Information Theory


Author: Edgar Martínez-Moro

Publisher: World Scientific

ISBN: 9814335754

Category: Mathematics

Page: 325

View: 383

Algebraic & geometry methods have constituted a basic background and tool for people working on classic block coding theory and cryptography. Nowadays, new paradigms on coding theory and cryptography have arisen such as: Network coding, S-Boxes, APN Functions, Steganography and decoding by linear programming. Again understanding the underlying procedure and symmetry of these topics needs a whole bunch of non trivial knowledge of algebra and geometry that will be used to both, evaluate those methods and search for new codes and cryptographic applications. This book shows those methods in a self-contained form.

Codes for Error Detection


Author: Torleiv Kl?ve

Publisher: World Scientific

ISBN: 9812705864

Category: Mathematics

Page: 201

View: 7739

There are two basic methods of error control for communication, both involving coding of the messages. With forward error correction, the codes are used to detect and correct errors. In a repeat request system, the codes are used to detect errors and, if there are errors, request a retransmission. Error detection is usually much simpler to implement than error correction and is widely used. However, it is given a very cursory treatment in almost all textbooks on coding theory. Only a few older books are devoted to error detecting codes. This book begins with a short introduction to the theory of block codes with emphasis on the parts important for error detection. The weight distribution is particularly important for this application and is treated in more detail than in most books on error correction. A detailed account of the known results on the probability of undetected error on the q-ary symmetric channel is also given.

Information, Coding and Mathematics

Proceedings of Workshop honoring Prof. Bob McEliece on his 60th birthday


Author: Mario Blaum,Patrick G. Farrell,Henk C.A. van Tilborg

Publisher: Springer Science & Business Media

ISBN: 1475735855

Category: Technology & Engineering

Page: 378

View: 1436

Information, Coding and Mathematics is a classic reference for both professional and academic researchers working in error-correction coding and decoding, Shannon theory, cryptography, digital communications, information security, and electronic engineering. The work represents a collection of contributions from leading experts in turbo coding, cryptography and sequences, Shannon theory and coding bounds, and decoding theory and applications. All of the contributors have individually and collectively dedicated their work as a tribute to the outstanding work of Robert J. McEliece. Information, Coding and Mathematics covers the latest advances in the widely used and rapidly developing field of information and communication technology.

Coding Theory and Cryptology


Author: Harald Niederreiter

Publisher: World Scientific

ISBN: 981448766X

Category: Mathematics

Page: 460

View: 3411

The inaugural research program of the Institute for Mathematical Sciences at the National University of Singapore took place from July to December 2001 and was devoted to coding theory and cryptology. As part of the program, tutorials for graduate students and junior researchers were given by world-renowned scholars. These tutorials covered fundamental aspects of coding theory and cryptology and were designed to prepare for original research in these areas. The present volume collects the expanded lecture notes of these tutorials. The topics range from mathematical areas such as computational number theory, exponential sums and algebraic function fields through coding-theory subjects such as extremal problems, quantum error-correcting codes and algebraic-geometry codes to cryptologic subjects such as stream ciphers, public-key infrastructures, key management, authentication schemes and distributed system security. Contents:Extremal Problems of Coding Theory (A Barg)Analysis and Design Issues for Synchronous Stream Ciphers (E Dawson & L Simpson)Quantum Error-Correcting Codes (K Feng)Public Key Infrastructures (D Gollmann)Computational Methods in Public Key Cryptology (A K Lenstra)Detecting and Revoking Compromised Keys (T Matsumoto)Algebraic Function Fields Over Finite Fields (H Niederreiter)Authentication Schemes (D Y Pei)Exponential Sums in Coding Theory, Cryptology and Algorithms (I E Shparlinski)Distributed Authorization: Principles and Practice (V Varadharajan)Introduction to Algebraic Geometry Codes (C P Xing) Readership: Graduate students and researchers in number theory, discrete mathematics, coding theory, cryptology and IT security. Keywords:Coding Theory;Cryptology;Number Theory;Algebraic-Geometry Codes;Public-Key Infrastructures;Error-Correcting Codes

Cryptography, Information Theory, and Error-Correction

A Handbook for the 21st Century


Author: Aiden A. Bruen,Mario A. Forcinito

Publisher: John Wiley & Sons

ISBN: 1118031385

Category: Mathematics

Page: 496

View: 5932

Discover the first unified treatment of today's most essentialinformation technologies— Compressing, Encrypting, andEncoding With identity theft, cybercrime, and digital file sharingproliferating in today's wired world, providing safe and accurateinformation transfers has become a paramount concern. The issuesand problems raised in this endeavor are encompassed within threedisciplines: cryptography, information theory, anderror-correction. As technology continues to develop, these fieldshave converged at a practical level, increasing the need for aunified treatment of these three cornerstones of the informationage. Stressing the interconnections of the disciplines, Cryptography,Information Theory, and Error-Correction offers a complete, yetaccessible account of the technologies shaping the 21st century.This book contains the most up-to-date, detailed, and balancedtreatment available on these subjects. The authors draw on theirexperience both in the classroom and in industry, giving the book'smaterial and presentation a unique real-world orientation. With its reader-friendly style and interdisciplinary emphasis,Cryptography, Information Theory, and Error-Correction serves asboth an admirable teaching text and a tool for self-learning. Thechapter structure allows for anyone with a high school mathematicseducation to gain a strong conceptual understanding, and provideshigher-level students with more mathematically advanced topics. Theauthors clearly map out paths through the book for readers of alllevels to maximize their learning. This book: Is suitable for courses in cryptography, information theory, orerror-correction as well as courses discussing all three areas Provides over 300 example problems with solutions Presents new and exciting algorithms adopted by industry Discusses potential applications in cell biology Details a new characterization of perfect secrecy Features in-depth coverage of linear feedback shift registers(LFSR), a staple of modern computing Follows a layered approach to facilitate discussion, withsummaries followed by more detailed explanations Provides a new perspective on the RSA algorithm Cryptography, Information Theory, and Error-Correction is anexcellent in-depth text for both graduate and undergraduatestudents of mathematics, computer science, and engineering. It isalso an authoritative overview for IT professionals, statisticians,mathematicians, computer scientists, electrical engineers,entrepreneurs, and the generally curious.

Codes: An Introduction to Information Communication and Cryptography


Author: Norman L. Biggs

Publisher: Springer Science & Business Media

ISBN: 9781848002739

Category: Computers

Page: 274

View: 2074

Many people do not realise that mathematics provides the foundation for the devices we use to handle information in the modern world. Most of those who do know probably think that the parts of mathematics involvedare quite ‘cl- sical’, such as Fourier analysis and di?erential equations. In fact, a great deal of the mathematical background is part of what used to be called ‘pure’ ma- ematics, indicating that it was created in order to deal with problems that originated within mathematics itself. It has taken many years for mathema- cians to come to terms with this situation, and some of them are still not entirely happy about it. Thisbookisanintegratedintroductionto Coding.Bythis Imeanreplacing symbolic information, such as a sequence of bits or a message written in a naturallanguage,byanother messageusing (possibly) di?erentsymbols.There are three main reasons for doing this: Economy (data compression), Reliability (correction of errors), and Security (cryptography). I have tried to cover each of these three areas in su?cient depth so that the reader can grasp the basic problems and go on to more advanced study. The mathematical theory is introduced in a way that enables the basic problems to bestatedcarefully,butwithoutunnecessaryabstraction.Theprerequisites(sets andfunctions,matrices,?niteprobability)shouldbefamiliartoanyonewhohas taken a standard course in mathematical methods or discrete mathematics. A course in elementary abstract algebra and/or number theory would be helpful, but the book contains the essential facts, and readers without this background should be able to understand what is going on. vi Thereareafewplaceswherereferenceismadetocomputeralgebrasystems.

Research EU.

Results magazine


Author: N.A

Publisher: N.A


Category: Research

Page: N.A

View: 2597

Foundations of Coding

Compression, Encryption, Error Correction


Author: Jean-Guillaume Dumas,Jean-Louis Roch,Éric Tannier,Sébastien Varrette

Publisher: John Wiley & Sons

ISBN: 1118960521

Category: Computers

Page: 376

View: 7094

Offers a comprehensive introduction to the fundamentalstructures and applications of a wide range of contemporary codingoperations This book offers a comprehensive introduction to the fundamentalstructures and applications of a wide range of contemporary codingoperations. This text focuses on the ways to structure informationso that its transmission will be in the safest, quickest, and mostefficient and error-free manner possible. All coding operations arecovered in a single framework, with initial chapters addressingearly mathematical models and algorithmic developments which led tothe structure of code. After discussing the general foundations ofcode, chapters proceed to cover individual topics such as notionsof compression, cryptography, detection, and correction codes. Bothclassical coding theories and the most cutting-edge models areaddressed, along with helpful exercises of varying complexities toenhance comprehension. Explains how to structure coding information so that itstransmission is safe, error-free, efficient, and fast Includes a pseudo-code that readers may implement in theirpreferential programming language Features descriptive diagrams and illustrations, and almost 150exercises, with corrections, of varying complexity to enhancecomprehension Foundations of Coding: Compression, Encryption,Error-Correction is an invaluable resource for understandingthe various ways information is structured for its secure andreliable transmission in the 21st-century world.

Coding and Cryptology

Second International Workshop, IWCC 2009


Author: Yeow Meng Chee,Chao Li,San Ling,Huaxiong Wang,Chaoping Xing

Publisher: Springer Science & Business Media

ISBN: 3642018130

Category: Computers

Page: 273

View: 4476

The biennial International Workshop on Coding and Cryptology (IWCC) aims to bring together many of the world's greatest minds in coding and crypt- ogy to share ideas and exchange knowledge related to advancements in c- ing and cryptology, amidst an informal setting conducive for interaction and collaboration. It is well known that fascinating connections exist between coding and cr- tology. Therefore this workshop series was organized to facilitate a fruitful - teraction and stimulating discourse among experts from these two areas. The inaugural IWCC was held at Wuyi Mountain, Fujian Province, China, during June 11-15, 2007 and attracted over 80 participants. Following this s- cess, the second IWCC was held June 1-5, 2009 at Zhangjiajie, Hunan Province, China. Zhangjiajie is one of the most scenic areas in China. The proceedings of this workshop consist of 21 technical papers, covering a wide range of topics in coding and cryptology, as well as related ?elds such as combinatorics. All papers, except one, are contributed by the invited speakers of the workshop and each paper has been carefully reviewed. We are grateful to the external reviewers for their help, which has greatly strengthened the quality of the proceedings. IWCC 2009 was co-organizedby the National University of Defense Techn- ogy (NUDT), China and Nanyang Technological University (NTU), Singapore. We acknowledge with gratitude the ?nancial support from NUDT. We wouldliketo expressourthanks to Springer formaking it possible forthe proceedings to be published in the Lecture Notes in Computer Science series.

A Commonsense Approach to the Theory of Error Correcting Codes


Author: Benjamin Arazi

Publisher: MIT Press

ISBN: 9780262010986

Category: Computers

Page: 208

View: 9079

Teaching the theory of error correcting codes on an introductory level is a difficulttask. The theory, which has immediate hardware applications, also concerns highly abstractmathematical concepts. This text explains the basic circuits in a refreshingly practical way thatwill appeal to undergraduate electrical engineering students as well as to engineers and techniciansworking in industry.Arazi's truly commonsense approach provides a solid grounding in the subject,explaining principles intuitively from a hardware perspective. He fully covers error correctiontechniques, from basic parity check and single error correction cyclic codes to burst errorcorrecting codes and convolutional codes. All this he presents before introducing Galois fieldtheory - the basic algebraic treatment and theoretical basis of the subject, which usually appearsin the opening chapters of standard textbooks. One entire chapter is devoted to specific practicalissues, such as Reed-Solomon codes (used in compact disc equipment), and maximum length sequences(used in various fields of communications). The basic circuits explained throughout the book areredrawn and analyzed from a theoretical point of view for readers who are interested in tackling themathematics at a more advanced level.Benjamin Arazi is an Associate Professor in the Department ofElectrical and Computer Engineering at the Ben-Gurion University of the Negev. His book is includedin the Computer Systems Series, edited by Herb Schwetman.

Codes and Rings

Theory and Practice


Author: Minjia Shi,Adel Alahmadi,Patrick Solé

Publisher: Academic Press

ISBN: 0128133910

Category: Business & Economics

Page: 318

View: 5615

Codes and Rings: Theory and Practice is a systematic review of literature that focuses on codes over rings and rings acting on codes. Since the breakthrough works on quaternary codes in the 1990s, two decades of research have moved the field far beyond its original periphery. This book fills this gap by consolidating results scattered in the literature, addressing classical as well as applied aspects of rings and coding theory. New research covered by the book encompasses skew cyclic codes, decomposition theory of quasi-cyclic codes and related codes and duality over Frobenius rings. Primarily suitable for ring theorists at PhD level engaged in application research and coding theorists interested in algebraic foundations, the work is also valuable to computational scientists and working cryptologists in the area. Consolidates 20+ years of research in one volume, helping researchers save time in the evaluation of disparate literature Discusses duality formulas in the context of Frobenius rings Reviews decomposition of quasi-cyclic codes under ring action Evaluates the ideal and modular structure of skew-cyclic codes Supports applications in data compression, distributed storage, network coding, cryptography and across error-correction

Mathematical Structures for Computer Science


Author: Judith L. Gersting

Publisher: N.A

ISBN: 9780716713050

Category: Computer science

Page: 452

View: 3904

Computing Curricula 2001 (CC2001), a joint undertaking of the Institute for Electrical and Electronic Engineers/Computer Society (IEEE/CS) and the Association for Computing Machinery (ACM), identifies the essential material for an undergraduate degree in computer science. This Sixth Edition of "Mathematical Structures for Computer Science" covers all the topics in the CC2001 suggested curriculum for a one-semester intensive discrete structures course, and virtually everything suggested for a two-semester version of a discrete structures course. Gersting's text binds together what otherwise appears to be a collection of disjointed topics by emphasizing the following themes: - Importance of logical thinking- Power of mathematical notation- Usefulness of abstractions

Fundamentals of Convolutional Coding


Author: Rolf Johannesson,Kamil Sh. Zigangirov

Publisher: John Wiley & Sons

ISBN: 0470276835

Category: Technology & Engineering

Page: 688

View: 9031

Convolutional codes, among the main error control codes, are routinely used in applications for mobile telephony, satellite communications, and voice-band modems. Written by two leading authorities in coding and information theory, this book brings you a clear and comprehensive discussion of the basic principles underlying convolutional coding. FUNDAMENTALS OF CONVOLUTIONAL CODING is unmatched in the field for its accessible analysis of the structural properties of convolutional encoders. The new edition, updated and revised throughout, includes two new chapters, "Low-Density Parity-Check Convolutional Codes", "Iterative Decoding." Other essentials covered in FUNDAMENTALS OF CONVOLUTIONAL CODING include: Distance properties of convolutional codes Viterbi, list, sequential, and iterative decoding Modulation codes Tables of good convolutional encoders An extensive set of homework problems. The authors draw on their own research and more than twenty years of teaching experience to present the fundamentals needed to understand the types of codes used in a variety of applications today. This book can be used as a textbook for graduate-level electrical engineering students. It will be of key interest to researchers and engineers of wireless and mobile communications, satellite communication, and data communication."

Algebraic Curves and Finite Fields

Cryptography and Other Applications


Author: Harald Niederreiter,Alina Ostafe,Daniel Panario,Arne Winterhof

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3110317915

Category: Mathematics

Page: 251

View: 3938

This book collects the results of the workshops on Applications of Algebraic Curves and Applications of Finite Fields at the RICAM in 2013. These workshops brought together the most prominet researchers in the area of finite fields and their applications around the world, addressing old and new problems on curves and other aspects of finite fields, with emphasis on their diverse applications to many areas of pure and applied mathematics.

Elements of Computer Algebra With Applications


Author: Alkiviadis G. Akritas

Publisher: Wiley-Interscience


Category: Mathematics

Page: 448

View: 8114

Numerical Modeling in Science and Engineering Myron B. Allen, George F. Pinder, and Ismael Herrera Emphasizing applications, this treatment combines three traditionally distinct disciplines—continuum mechanics, differential equations, and numerical analysis—to provide a unified treatment of numerical modeling of physical systems. Covers basic equations of macroscopic systems, numerical methods, steady state systems, dissipative systems, nondissipative systems, and high order, nonlinear, and coupled systems. 1988 (0 471-80635-8) 418 pp. Mathematical Modeling and Digital Simulation for Engineers and Scientists Second Edition Jon M. Smith Totally updated, this Second Edition reflects the many developments in simulation and computer modeling theory and practice that have occurred over the past decade. It includes a new section on the use of modern numerical methods for generating chaos and simulating random processes, a section on simulator verification, and provides applications of these methods for personal computers. Readers will find a wealth of practical fault detection and isolation techniques for simulator verification, fast functions evaluation techniques, and nested parenthetical forms and Chebyshev economization techniques. 1987 (0 471-08599-5) 430 pp. Numerical Analysis 1987 David F. Griffiths and George Alistair Watson An invaluable guide to the direction of current research in many areas of numerical analysis, this volume will be of great interest to anyone involved in software design, curve and surface fitting, the numerical solution of ordinary, partial, and integro-differential equations, and the real-world application of numerical techniques. 1988 (0 470-21012-5) 300 pp.

Quantum Cryptography and Computing--theory and Implementation


Author: Ryszard Horodecki,Sergei Ya Kilin,Janusz S. Kowalik

Publisher: IOS Press

ISBN: 1607505460

Category: Political Science

Page: 261

View: 5986

Theory and Implementation. This volume contains papers presented at the NATO Advanced Research Workshop September 9-12, 2009, Quantum Cryptography and Computing Theory and Implementation, that was held in Sopot, Poland and organized by the National Quantum Information Centre of