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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 n

Combinatorial designs and configurations. --- Coding theory. --- Difference sets. --- Sets, Difference --- Combinatorial analysis --- Data compression (Telecommunication) --- Digital electronics --- Information theory --- Machine theory --- Signal theory (Telecommunication) --- Computer programming --- Configurations and designs, Combinatorial --- Designs and configurations, Combinatorial

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This is the unique book on cross-fertilisations between stream ciphers and number theory. It systematically and comprehensively covers known connections between the two areas that are available only in research papers. Some parts of this book consist of new research results that are not available elsewhere. In addition to exercises, over thirty research problems are presented in this book. In this revised edition almost every chapter was updated, and some chapters were completely rewritten. It is useful as a textbook for a graduate course on the subject, as well as a reference book for researc

Number theory --- Number theory. --- Ciphers. --- Stream ciphers. --- State ciphers --- Ciphers --- Codes --- Contractions --- Signs and symbols --- Symbolism --- Abbreviations --- Code names --- Cryptography --- Writing --- Number study --- Numbers, Theory of --- Algebra

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This book is almost entirely concerned with stream ciphers, concentrating on a particular mathematical model for such ciphers which are called additive natural stream ciphers. These ciphers use a natural sequence generator to produce a periodic keystream. Full definitions of these concepts are given in Chapter 2. This book focuses on keystream sequences which can be analysed using number theory. It turns out that a great deal of information can be deducted about the cryptographic properties of many classes of sequences by applying the terminology and theorems of number theory. These connections can be explicitly made by describing three kinds of bridges between stream ciphering problems and number theory problems. A detailed summary of these ideas is given in the introductory Chapter 1. Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

Number theory