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# STREAM CIPHERS AND NUMBER THEORY

**Thomas Cusick, Cunsheng Ding, Ari Renvall**

ISBN **044451631X**

Pages **492**

Description

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 researchers in related fields.

Contents

Contents Preface to the Revised Edition Preface to the First Edition. 1 Introduction. 2 Stream Ciphers. 3 Primes, Primitive Roots and Sequences. 4 Cyclotomy and Cryptographic Functions. 5 Special Primes and Sequences. 6 Highly Nonlinear Functions. 7 Difference Sets and Sequences. 8 Binary Cyclotomic Generators. 9 Analysis of Cyclotomic Generators of Order 2. 10 Nonbinary Cyclotomic Generators. 11 Generators Based on Permutations. 12 Quadratic Partitions and Cryptography. 13 Group Characters and Cryptography. 14 P-Adic Numbers, Class Numbers and Sequences. 15 Prime Ciphering Algorithms. 16 Cryptographic Problems and Philosophies. Appendix A: More About Cyclotomic Numbers. Appendix B: Cyclotomic Formulae of Orders 6, 8 and 10. Appendix C: Finding Practical Primes. Appendix D: List of Research Problems. Appendix E: Exercises. Appendix F: List of Mathematical Symbols. Bibliography. Index.