Stream Ciphers and Number Theory, Volume 55

1st Edition

Authors: T.W. Cusick C. Ding Ari Renvall
Hardcover ISBN: 9780444828736
eBook ISBN: 9780080541846
Imprint: North Holland
Published Date: 20th April 1998
Page Count: 430
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Table of Contents

Preface. Introduction. Applications of number theory. An outline of this book. Stream Ciphers. Stream cipher systems. Additive synchronous stream ciphers. Nonadditive synchronous stream ciphers. Stream ciphering with block ciphers. Cooperative distributed ciphering. Some keystream generators. Generators based on counters. Some number-theoretic generators. Cryptographic aspects of sequences. Minimal polynominal and linear complexity. Pattern distribution of key streams. Correlation functions. Sphere complexity and linear cryptanalysis. Higher order complexities. Harmony on binary NSGs. Security attacks. Primes, Primitive Roots and Sequences. Cyclotomic polynominals. Two basic problems from stream ciphers. A basic theorem and main bridge. Primes, primitive roots and binary sequences. Primes, primitive roots and ternary sequences. Primes, negord and sequences. Prime powers, primitive roots and sequences. Prime products and sequences. Binary sequences and primes. Ternary sequences and primes. On cryptographic primitive roots. Linear complexity of sequences over Zm. Period and its cryptographic importance. Cyclotomy and Cryptographic Functions. Cyclotomic numbers. Cyclotomy and cryptography. Cyclotomy and difference parameters. Cyclotomy and the differential cryptanalysis. Cryptographic cyclotomic numbers. Cryptographic functions from Zp to Zd. The case d = 2. The case d = 3. The case d = 4. The case d = 5. The case d = 6. The case d = 8. The case d = 10. The case d = 12. Cryptographic functions from Zpq to Zd. Whiteman's generalized cyclotomy and cryptography. Cryptographic functions from Zpq to Z2. Cryptographic functions from Zpq to Z4. Cryptographic fu


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.


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© North Holland 1998
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@qu:...This is the first book devoted to the study of the extensive cross-fertilization between stream ciphers and number theory. Many results in the book are new, and over seventy percent of the results described are based on recent research by the authors. @source:Cyptologia, Vol. XXIII @qu:...This is a cryptography book which focuses on methods for producing keystream sequences fpr stream ciphers. @source:Mathematical Reviews @from:T. Helleseth @qu:This book is a readable and important contribution for stimulating the interaction between stream ciphers and number theory. @source:Zentralblatt fur Mathematik, Vol. 916

About the Authors

T.W. Cusick Author

Affiliations and Expertise

State University of New York, Buffalo, NY, USA

C. Ding Author

Affiliations and Expertise

The National University of Singapore, Singapore

Ari Renvall Author

Affiliations and Expertise

University of Turku, Finland