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Stream Ciphers and Number Theory, Volume 55 [Kietas viršelis]

(The National University of Singapore, Singapore), (University of Turku, Finland), (State University of New York, Buffalo, NY, USA)
  • Formatas: Hardback, 430 pages, aukštis: 230 mm, bibliography, index
  • Serija: North-Holland Mathematical Library v.55
  • Išleidimo metai: 20-Apr-1998
  • Leidėjas: North-Holland
  • ISBN-10: 0444828737
  • ISBN-13: 9780444828736
Kitos knygos pagal šią temą:
Stream Ciphers and Number Theory, Volume 55Didesnis paveikslėlis
  • Formatas: Hardback, 430 pages, aukštis: 230 mm, bibliography, index
  • Serija: North-Holland Mathematical Library v.55
  • Išleidimo metai: 20-Apr-1998
  • Leidėjas: North-Holland
  • ISBN-10: 0444828737
  • ISBN-13: 9780444828736
Kitos knygos pagal šią temą:
Pastovi nuoroda: https://www.kriso.lt/db/9780444828736.html
Raktažodžiai:
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.

Recenzijos

...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.Cyptologia, Vol. XXIII...This is a cryptography book which focuses on methods for producing keystream sequences fpr stream ciphers.Mathematical ReviewsT. HellesethThis book is a readable and important contribution for stimulating the interaction between stream ciphers and number theory.Zentralblatt fur Mathematik, Vol. 916

Preface VII
1 Introduction
1(10)
1.1 Applications of Number Theory
1(4)
1.2 An Outline of this Book
5(6)
2 Stream Ciphers
11(32)
2.1 Stream Cipher Systems
11(10)
2.1.1 Additive Synchronous Stream Ciphers
13(1)
2.1.2 Additive Self-Synchronous Stream Ciphers
14(1)
2.1.3 Nonadditive Synchronous Stream Ciphers
14(2)
2.1.4 Stream Ciphering with Block Ciphers
16(2)
2.1.5 Cooperatively Distributed Ciphering
18(3)
2.2 Some Keystream Generators
21(4)
2.2.1 Generators Based on Counters
22(1)
2.2.2 Some Number-Theoretic Generators
23(2)
2.3 Cryptographic Aspects of Sequences
25(11)
2.3.1 Minimal Polynomial and Linear Complexity
25(4)
2.3.2 Pattern Distribution of Key Streams
29(2)
2.3.3 Correlation Functions
31(1)
2.3.4 Sphere Complexity and Linear Cryptanalysis
32(3)
2.3.5 Higher Order Complexities
35(1)
2.4 Harmony of Binary NSGs
36(4)
2.5 Security and Attacks
40(3)
3 Primes, Primitive Roots and Sequences
43(34)
3.1 Cyclotomic Polynomials
43(1)
3.2 Two Basic Problems from Stream Ciphers
44(3)
3.3 A Basic Theorem and Main Bridge
47(3)
3.4 Primes, Primitive Roots and Binary Sequences
50(5)
3.5 Primes, Primitive Roots and Ternary Sequences
55(3)
3.6 Primes, Negord and Sequences
58(2)
3.7 Prime Powers, Primitive Roots and Sequences
60(2)
3.8 Prime Products and Sequences
62(3)
3.8.1 Binary Sequences and Primes
63(1)
3.8.2 Ternary Sequences and Primes
64(1)
3.9 On Cryptographic Primitive Roots
65(2)
3.10 Linear Complexity of Sequences over Z(m)
67(8)
3.11 Period and its Cryptographic Importance
75(2)
4 Cyclotomy and Cryptographic Functions
77(36)
4.1 Cyclotomic Numbers
77(2)
4.2 Cyclotomy and Cryptography
79(3)
4.2.1 Cyclotomy and Difference Parameters
79(2)
4.2.2 Cyclotomy and the Differential Cryptanalysis
81(1)
4.2.3 Cryptographic Cyclotomic Numbers
82(1)
4.3 Cryptographic Functions from Z(p) to Z(d)
82(11)
4.3.1 The Case d = 2
84(1)
4.3.2 The Case d = 3
85(1)
4.3.3 The Case d = 4
86(1)
4.3.4 The Case d = 5
87(2)
4.3.5 The Case d = 6
89(1)
4.3.6 The Case d = 8
89(2)
4.3.7 The Case d = 10
91(2)
4.3.8 The Case d = 12
93(1)
4.4 Cryptographic Functions from Z(pq) to Z(d)
93(11)
4.4.1 Whiteman's Generalized Cyclotomy and Cryptography
94(5)
4.4.2 Cryptographic Functions from Z(pq) to Z(2)
99(3)
4.4.3 Cryptographic Functions from Z(pq) to Z(4)
102(2)
4.5 Cryptographic Functions from Z(p^2) to Z(2)
104(3)
4.6 Cryptographic Functions Defined on GF(p^m)
107(1)
4.7 The Origin of Cyclotomic Numbers
107(6)
5 Special Primes and Sequences
113(26)
5.1 Sophie Germain Primes and Sequences
113(4)
5.1.1 Their Importance in Stream Ciphers
114(1)
5.1.2 Their Relations with Other Number-theoretic Problems
115(1)
5.1.3 The Existence Problem
116(1)
5.1.4 A Search for Cryptographic Sophie Germain Primes
116(1)
5.2 Tchebychef Primes and Sequences
117(2)
5.2.1 Their Cryptographic Significance
117(1)
5.2.2 Existence and Search Problem
118(1)
5.3 Other Primes of Form k x 2^n + 1 and Sequences
119(4)
5.4 Primes of Form (a^n - 1)/(a - 1) and Sequences
123(4)
5.4.1 Mersenne Primes and Sequences
123(3)
5.4.2 Cryptographic Primes of Form ((4u)^n - 1)/(4u - 1)
126(1)
5.4.3 Prime Repunits and their Cryptographic Values
127(1)
5.5 n! (+)(-) 1 and p# (+)(-) 1 Primes and Sequences
127(2)
5.6 Twin Primes and Sequences over GF(2)
129(4)
5.6.1 The Significance of Twins and their Sexes
130(1)
5.6.2 Cryptographic Twins and the Sex Distribution
131(2)
5.7 Twin Primes and Sequences over GF(3)
133(1)
5.8 Other Special Primes and Sequences
134(1)
5.9 Prime Distributions and their Significance
134(1)
5.10 Primes for Stream Ciphers and for RSA
135(4)
6 Difference Sets and Cryptographic Functions
139(18)
6.1 Rudiments of Difference Sets
139(3)
6.2 Difference Sets and Autocorrelation Functions
142(1)
6.3 Difference Sets and Nonlinearity
143(2)
6.4 Difference Sets and Information Stability
145(2)
6.5 Difference Sets and Linear Approximation
147(2)
6.6 Almost Difference Sets
149(4)
6.7 Almost Difference Sets and Autocorrelation Functions
153(1)
6.8 Almost Difference Sets, Nonlinearity and Approximation
154(1)
6.9 Summary
154(3)
7 Difference Sets and Sequences
157(10)
7.1 The NSG Realization of Sequences
157(2)
7.2 Differential Analysis of Sequences
159(2)
7.3 Linear Complexity of DSC (ADSC) Sequences
161(3)
7.4 Barker Sequences
164(3)
8 Binary Cyclotomic Generators
167(32)
8.1 Cyclotomic Generator of Order 2k
167(3)
8.2 Two-Prime Generator of Order 2
170(12)
8.3 Two-Prime Generator of Order 4
182(1)
8.4 Prime-Square Generator
183(12)
8.5 Implementation and Performance
195(1)
8.6 A Summary of Binary Cyclotomic Generators
196(3)
9 Analysis of Cyclotomic Generators of Order 2
199(24)
9.1 Crosscorrelation Property
200(1)
9.2 Decimation Property
201(1)
9.3 Linear Complexity
201(4)
9.4 Security against a Decision Tree Attack
205(14)
9.5 Sums of DSC Sequences
219(4)
9.5.1 Linear Complexity Analysis
219(1)
9.5.2 Balance Analysis
220(1)
9.5.3 Correlation Analysis
220(1)
9.5.4 Differential Analysis
220(3)
10 Nonbinary Cyclotomic Generators
223(8)
10.1 The rth-Order Cyclotomic Generator
223(1)
10.2 Linear Complexity
224(2)
10.3 Autocorrelation Property
226(2)
10.4 Decimation Property
228(1)
10.5 Ideas Behind the Cyclotomic Generators
228(3)
11 Generators Based on Permutations
231(34)
11.1 The Cryptographic Idea
231(2)
11.2 Permutations on Finite Fields
233(1)
11.3 A Generator Based on Inverse Permutations
234(2)
11.4 Binary Generators and Permutations of GF(2^n)
236(15)
11.4.1 APN Permutations and their Properties
237(4)
11.4.2 Quadratic Permutations with Controllable Nonlinearity
241(1)
11.4.3 Permutations of Order 3
242(2)
11.4.4 APN Permutations of Order n - 1
244(1)
11.4.5 Permutations of Order n - 2
245(1)
11.4.6 Permutations X^d with d = 2^m - 1
246(1)
11.4.7 APN Permutations via Crosscorrelation Function
246(5)
11.4.8 Other Power Functions with Good Nonlinearity
251(1)
11.4.9 Choosing the Linear Functions
251(1)
11.5 Cyclic-Key Generators and their Problems
251(5)
11.5.1 Cyclic-Key Generators
251(3)
11.5.2 Several Specific Forms: An Overview
254(2)
11.6 A Generator Based on Permutations of Z(m)
256(9)
12 Quadratic Partitions and Cryptography
265(22)
12.1 Quadratic Partition and Cryptography
266(1)
12.2 p = x^2 + y^2 and p = x^2 + 4y^2
267(7)
12.3 p = x^2 + 2y^2 and p = x^2 + 3y^2
274(1)
12.4 p = x^2 + ny^2 and Quadratic Reciprocity
275(1)
12.5 p = x^2 + 7y^2 and Quadratic Forms
275(4)
12.6 p = x^2 + 15y^2 and Genus Theory
279(2)
12.7 p = x^2 + ny^2 and Class Field Theory
281(2)
12.8 Other Cryptographic Quadratic Partitions
283(4)
13 Group Characters and Cryptography
287(20)
13.1 Group Characters
287(2)
13.2 Field Characters and Cryptography
289(10)
13.2.1 Field Multiplicative Characters: Most Used Ones
291(2)
13.2.2 Field Additive Characters: Most Used Ones
293(6)
13.3 The Nonlinearity of Characters
299(2)
13.3.1 The Nonlinearity of Multiplicative Characters
299(1)
13.3.2 The Nonlinearity of Additive Characters
300(1)
13.4 Ring Characters and Cryptography
301(1)
13.5 Group Characters and Cyclotomic Numbers
302(5)
14 P-Adic Numbers, Class Numbers and Sequences
307(40)
14.1 The 2-Adic Value and 2-Adic Expansion
307(6)
14.2 A Fast Algorithm for the 2-Adic Expansion
313(1)
14.3 The Arithmetic of Q[ 2] and Z[ 2]
313(5)
14.4 Feedback Shift Registers with Carry
318(2)
14.5 Analysis and Synthesis of FCSRs
320(6)
14.6 The 2-Adic Span and 2-RA Algorithm
326(9)
14.7 Some Properties of FCSR Sequences
335(4)
14.8 Blum-Blum-Shub Sequences & Class Numbers
339(8)
15 Prime Ciphering Algorithms
347(12)
15.1 Prime-32: A Description
347(5)
15.2 Theoretical Results about Prime-32
352(2)
15.3 Security Arguments
354(3)
15.4 Performance of Prime-32
357(1)
15.5 Prime-32 with a 192-Bit Key
357(1)
15.6 Prime-64
357(2)
16 Cryptographic Problems and Philosophies
359(16)
16.1 Nonlinearity and Linearity
359(3)
16.2 Stability and Instability
362(5)
16.2.1 Stability and Diffusion
363(2)
16.2.2 Stability of Local Nonlinearities and Differences
365(1)
16.2.3 Correlation Stability and Pattern Stability
365(1)
16.2.4 Mutual Information Stability
366(1)
16.3 Localness and Globalness
367(2)
16.4 Goodness and Badness
369(1)
16.5 About Good plus Good
370(1)
16.6 About Good plus Bad
371(1)
16.7 About Bad plus Good
372(1)
16.8 Hardware and Software Model Complexity
373(2)
Appendices 375(26)
A More About Cyclotomic Numbers 375(8)
A.1 Cyclotomic Numbers of Order 7 375(2)
A.2 Cyclotomic Numbers of Orders 9, 18 377(1)
A.3 Cyclotomic Numbers of Order Eleven 378(1)
A.4 On Other Cyclotomic Numbers 378(1)
A.5 Behind Cyclotomic Numbers 379(4)
B Cyclotomic Formulae of Orders 6, 8 and 10 383(6)
C Finding Practical Primes 389(2)
D List of Research Problems 391(2)
E Exercises 393(6)
F List of Mathematical Symbols 399(2)
Bibliography 401(28)
Index 429