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.
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.
A series of research papers on various aspects of coding theory, cryptography, and other areas, including new and unpublished results on the subjects. The book will be useful to students, researchers, professionals, and tutors interested in this area of research.
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.
Although devoted to constructions of good codes for error control, secrecy or data compression, the emphasis is on the first direction. Introduces a number of important classes of error-detecting and error-correcting codes as well as their decoding methods. Background material on modern algebra is presented where required. The role of error-correcting codes in modern cryptography is treated as are data compression and other topics related to information theory. The definition-theorem proof style used in mathematics texts is employed through the book but formalism is avoided wherever possible.
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.
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