UID:
almahu_9949698061702882
Format:
1 online resource (446 p.)
ISBN:
1-281-05853-X
,
9786611058531
,
0-08-054184-4
Series Statement:
North-Holland mathematical library ; v. 55
Content:
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.
Note:
Description based upon print version of record.
,
Front Cover; Stream Ciphers and Number Theory; Copyright Page; Contents; Preface; 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 Sequences
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3.5 Primes. Primitive Roots and Ternary Sequences3.6 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; Chapter 4. Cyclotomy and Cryptographic Functions; 4.1 Cyclotomic Numbers; 4.2 Cyclotomy and Cryptography; 4.3 Cryptographic Functions from Zp, to Zd; 4.4 Cryptographic Functions from Zpq to Zd; 4.5 Cryptographic Functions from Zp2 to Z2; 4.6 Cryptographic Functions Defined on GF(pm)
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4.7 The Origin of Cyclotomic NumbersChapter 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 x 2n + 1 and Sequences; 5.4 Primes of Form (an - l)/(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 RSA; Chapter 6. Difference Sets and Cryptographic Functions
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6.1 Rudiments of Difference Sets6.2 Difference Sets and Autocorrelation Functions; 6.3 Difference Sets and Nonlinearity; 6.4 Difference Sets and Information Stability; 6.5 Difference Sets and Linear Approximation; 6.6 Almost Difference Sets; 6.7 Almost Difference Sets and Autocorrelation Functions; 6.8 Almost Difference Sets, Nonlinearity and Approximation; 6.9 Summary; 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
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Chapter 8. Binary Cyclotomic Generators8.1 Cyclotomic Generator of Order 2k; 8.2 Two-Prime Generator of Order 2; 8.3 Two-Prime Generator of Order 4; 8.4 Prime-Square Generator; 8.5 Implementation and Performance; 8.6 A Summary of Binary Cyclotomic Generators; Chapter 9. Analysis of Cyclotomic Generators of Order 2; 9.1 Crosscorrelation Property; 9.2 Decimation Property; 9.3 Linear Complexity; 9.4 Security against a Decision Tree Attack; 9.5 Sums of DSC Sequences; chapter 10. Nonbinary Cyclotomic Generators; 10.1 The rth-Order Cyclotomic Generator; 10.2 Linear Complexity
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10.3 Autocorrelation Property
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English
Additional Edition:
ISBN 0-444-82873-7
Language:
English
