Stream Ciphers and Number Theory

by Thomas W. Cusick, Cunsheng Ding, Ari R. Renvall

Overview

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.

Product Details

ISBN-13:	9780444516312
Publisher:	Elsevier Science
Publication date:	02/17/2004
Series:	North-Holland Mathematical Library , #66
Edition description:	Revised
Pages:	492
Product dimensions:	5.88(w) x 8.88(h) x (d)

About the Author

Thomas Cusick has 25 years of experience in cryptography, 60 published papers in that subject and 8 Ph. D. students whose thesis work was in that area. He is currently located at the State University of New York in Buffalo, New York.

Table of Contents

Contents Preface to the Revised EditionPreface 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.

What People are Saying About This

From the Publisher

It is a necessary reference book for cryptographers and number theorists.

Editorial Reviews

"...deals with many connections between stream ciphers and number theory covering topics like construction of generators, cryptographic properties of key streams such as linear complexity, pattern distribution, correlation properties and 2-adic complexity. The monograph gives a useful overview on the present stage of research, moreover it contains more than 30 open research problems." —Willfried Meidl, in ZENTRALBLATT MATH

From the Publisher

The authors--Cusick (State U. of New York-Buffalo), Cunsheng (National U. of Singapore), and Renvall (U. of Turku)--consider this the first book devoted to the cross-fertilization of stream ciphers and number theory. Stream ciphers are algorithms for encryption used in security-conscious business, military, and diplomatic settings. Presenting new results based on their recent research, the authors concentrate on a mathematical model which they call additive natural stream ciphers. Chapters cover topics such as: stream cipher systems, keystream generators, cyclotomy and cryptographic functions, special primes and sequences, generators based on permutations, prime ciphering algorithms, and cryptographic problems and philosophies. Interspersed research problems (summarized in an appendix) challenge readers. Annotation c. by Book News, Inc., Portland, Or.

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