Stream Ciphers and Number Theory

Stream Ciphers and Number Theory, 1st Edition

Stream Ciphers and Number Theory, 1st Edition,Thomas Cusick,Cunsheng Ding,Ari Renvall,ISBN9780444516312

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Elsevier Science




225 X 150

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

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Key Features

· 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.


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.


Cryptographers and mathematicians.

Thomas Cusick

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.

Affiliations and Expertise

State University of New York, Buffalo, USA

View additional works by Thomas W. Cusick

Cunsheng Ding

Affiliations and Expertise

Hong Kong University of Science and Technology, Hong Kong.

Ari Renvall

Affiliations and Expertise

University of Turku, Finland

Stream Ciphers and Number Theory, 1st Edition

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.

Quotes and 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
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