Stream ciphers and number theory
著者
書誌事項
Stream ciphers and number theory
（North-Holland mathematical library, v. 55）
Elsevier, 1998
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注記
Includes bibliographical references (p. 401-428) and index
内容説明・目次
内容説明
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.
目次
Section Headings only. Preface. Introduction. Stream Ciphers. Primes, Primitive Roots and Sequences. Cyclotomy and Cryptographic Functions. Special Primes and Sequences. Difference Sets and Cryptographic Functions. Difference Sets and Sequences. Binary Cyclotomic Generators. Analysis of Cyclotomic Generators of Order 2. Nonbinary Cyclotomic Generators. Generators Based on Permutations. Quadratic Partitions and Cryptography. Group Characters and Cryptography. P-Adic Numbers, Class Number and Sequences. Prime Ciphering Algorithms. Cryptographic Problems and Philosophies. A. More About Cyclotomic Numbers. B. Cyclotomic Formulae of Orders 6,8 and 10, C. Finding Practical Primes. D. List of Research Problems. E. Exercises. F. List of Mathematical Symbols. Bibliography. Index.
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