Stream Ciphers and Number Theory

Thomas W. Cusick, Cunsheng Ding, Ari R. Renvall044451631X, 9780444516312

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. · Unique book on interactions of stream ciphers and number theory. · Research monograph with many results not available elsewhere. · A revised edition with the most recent advances in this subject. · Over thirty research problems for stimulating interactions between the two areas. · Written by leading researchers in stream ciphers and number theory.

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Table of contents :
Cover……Page 1
Preface to the Revised Edition……Page 2
Preface to the First Edition……Page 3
1 Introduction……Page 5
2 Stream Ciphers……Page 15
3 Primes, Primitive Roots and Sequences……Page 48
4 Cyclotomy and Cryptographic Functions ……Page 85
5 Special Primes and Sequences……Page 122
6 Highly Nonlinear Functions……Page 148
7 Difference Sets and Sequences……Page 185
8 Binary Cyclotomic Generators……Page 194
9 Analysis of Cyclotomic Generators of Order 2……Page 226
10 Nonbinary Cyclotomic Generators……Page 250
11 Generators Based on Permutations ……Page 258
12 Quadratic Partitions and Cryptography……Page 294
13 Group Characters and Cryptography……Page 316
14 P-Adic Numbers, Class Numbers and Sequences……Page 336
15 Prime Ciphering Algorithms……Page 378
16 Cryptographic Problems and Philosophies……Page 390
A More About Cyclotomic Numbers……Page 406
B Cyclotomic Formulae of Orders 6, 8 and 10……Page 413
C Finding Practical Primes……Page 420
D List of Research Problems……Page 422
E Exercises……Page 425
F List of Mathematical Symbols……Page 430
Bibliography……Page 432
Index……Page 467
Back Cover……Page 470