Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography, the text provides a detailed survey of their main results, presenting a systematic overview of their generalizations and applications, and considering open problems in classification and systematization of bent functions. The text is appropriate for novices and advanced researchers, discussing proofs of several results, including the automorphism group of bent functions, the lower bound for the number of bent functions, and more. - Provides a detailed survey of bent functions and their main results, presenting a systematic overview of their generalizations and applications - Presents a systematic and detailed survey of hundreds of results in the area of highly nonlinear Boolean functions in cryptography - Appropriate coverage for students from advanced specialists in cryptography, mathematics, and creators of ciphers

This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results. This book uniquely provides a necessary comprehensive coverage of bent functions.It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.

This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes. This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.

This book constitutes the refereed proceedings of the 2nd International Castle Meeting, ISMCTA 2008, Castillo de la Mota, Medina del Campo, Spain, September 2008. The 14 full papers and 5 invited papers presented were carefully reviewed and selected from 34 submissions for inclusion in the book. The papers cover network coding, quantum codes, group codes, codes and combinatorial structures, agebraic-geometry codes, as well as codes and applications.

This reference work looks at modern concepts of computer security. It introduces the basic mathematical background necessary to follow computer security concepts before moving on to modern developments in cryptography. The concepts are presented clearly and illustrated by numerous examples. Subjects covered include: private-key and public-key encryption, hashing, digital signatures, authentication, secret sharing, group-oriented cryptography, and many others. The section on intrusion detection and access control provide examples of security systems implemented as a part of operating system. Database and network security is also discussed. The final chapters introduce modern e- business systems based on digital cash.

This proceeding covers topics such as universal sourcing code, estimation, cyclic codes, multi-user channels, synchronization, CDMA sequences, pattern recognition and estimation, and signal processing techniques. Applications to communications channels and recovery from faults are described.