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## Details

Genre/Form: | Electronic books |
---|---|

Additional Physical Format: | Print version: Cusick, Thomas W. Stream Ciphers and Number Theory. Burlington : Elsevier Science, ©2004 |

Material Type: | Document, Internet resource |

Document Type: | Internet Resource, Computer File |

All Authors / Contributors: |
Thomas W Cusick; Cunsheng Ding; Ari R Renvall |

ISBN: | 9780080541839 0080541836 |

OCLC Number: | 861559599 |

Notes: | 8.3 Two-Prime Generator of Order 4. |

Description: | 1 online resource (857 pages). |

Contents: | Cover image; Title page; Table of Contents; North-Holland Mathematical Library; Copyright page; Dedication; Preface to the Revised Edition; Preface to the First Edition; Chapter 1: Introduction; 1.1 Applications of Number Theory; 1.2 An Outline of this Book; Chapter 2: Stream Ciphers; 2.1 Stream Cipher Systems; 2.2 Some Keystream Generators; 2.3 Cryptographic Aspects of Sequences; 2.4 Harmony of Binary NSGs; 2.5 Security and Attacks; Chapter 3: Primes, Primitive Roots and Sequences; 3.1 Cyclotomic Polynomials; 3.2 Two Basic Problems from Stream Ciphers; 3.3 A Basic Theorem and Main Bridge. 3.4 Primes, Primitive Roots and Binary Sequences3.5 Primes, Primitive Roots and Ternary Sequences; 3.6 Primes, Negord and Sequences; 3.7 Prime Powers, Primitive Roots and Sequences; 3.8 Prime Products and Sequences; 3.9 On Cryptographic Primitive Roots; 3.10 Linear Complexity of Sequences over Zm; 3.11 Period and its Cryptographic Importance; 3.12 Recent Advances on the Sphere Complexity; Chapter 4: Cyclotomy and Cryptographic Functions; 4.1 Cyclotomic Numbers; 4.2 Cyclotomy and Cryptography; 4.3 Cryptographic Functions from to; 4.4 Cryptographic Functions from to. 4.5 Cryptographic Functions from Zp2 to Z24.6 Cryptographic Functions Defined on GF(pm); 4.7 The Origin of Cyclotomic Numbers; Chapter 5: Special Primes and Sequences; 5.1 Sophie Germain Primes and Sequences; 5.2 Tchebychef Primes and Sequences; 5.3 Other Primes of Form k × 2n + 1 and Sequences; 5.4 Primes of Form (an -- 1)/(a -- 1) and Sequences; 5.5 n! ± 1 and p# ± 1 Primes and Sequences; 5.6 Twin Primes and Sequences over GF(2); 5.7 Twin Primes and Sequences over GF(3); 5.8 Other Special Primes and Sequences; 5.9 Prime Distributions and their Significance. 5.10 Primes for Stream Ciphers and for RSAChapter 6: Highly Nonlinear Functions; 6.1 Preliminaries; 6.2 Functions with perfect nonlinearity; 6.2.1 Stability of the set of perfect nonlinear functions under actions of general affine groups; 6.2.2 Perfect nonlinear functions and difference partitions; 6.2.3 Functions with perfect nonlinearity and difference matrices; 6.2.4 A characterization of perfect nonlinearity by means of Fourier transform; 6.2.5 Obtaining functions with perfect nonlinearity from known ones; 6.2.6 Bent functions and perfect nonlinearity. 6.3 Binary functions with optimum nonlinearity6.3.3 The case n a"2 (mod 4); 6.3.4 The case n a"1 (mod 4) and n> 1; 6.3.5 Minimum distance from affine functions; 6.4 Nonbinary functions with optimum nonlinearity; 6.5 Constructions of functions with optimum nonlinearity; Chapter 7: Difference Sets and Sequences; 7.1 The NSG Realization of Sequences; 7.2 Differential Analysis of Sequences; 7.3 Linear Complexity of DSC (ADSC) Sequences; 7.4 Barker Sequences; Chapter 8: Binary Cyclotomic Generators; 8.1 Cyclotomic Generator of Order 2k; 8.2 Two-Prime Generator of Order 2. |

Series Title: | North-Holland mathematical library. |

More information: |

### Abstract:

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 researc.

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