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# Volume 55. Stream Ciphers and Number Theory

## 1st Edition

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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.

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

Many results in the book are new, and over seventy percent of these results described in this book are based on recent research results.

- No. of pages:
- 430

- Language:
- English

- Copyright:
- © 1998

- Published:
- 20th April 1998

- Imprint:
- North Holland

- Print ISBN:
- 9780444828736

- Electronic ISBN:
- 9780080541846

State University of New York, Buffalo, NY, USA

The National University of Singapore, Singapore

University of Turku, Finland

@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