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Boolean Functions and Their Applications in Cryptography 1st ed. 2016 [Kõva köide]

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  • Formaat: Hardback, 256 pages, kõrgus x laius: 235x155 mm, kaal: 5325 g, 9 Illustrations, color; XV, 256 p. 9 illus. in color., 1 Hardback
  • Sari: Advances in Computer Science and Technology
  • Ilmumisaeg: 02-Mar-2016
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662488639
  • ISBN-13: 9783662488638
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Boolean Functions and Their Applications in Cryptography 1st ed. 2016Suurem pilt
  • Formaat: Hardback, 256 pages, kõrgus x laius: 235x155 mm, kaal: 5325 g, 9 Illustrations, color; XV, 256 p. 9 illus. in color., 1 Hardback
  • Sari: Advances in Computer Science and Technology
  • Ilmumisaeg: 02-Mar-2016
  • Kirjastus: Springer-Verlag Berlin and Heidelberg GmbH & Co. K
  • ISBN-10: 3662488639
  • ISBN-13: 9783662488638
Teised raamatud teemal:
Püsilink: https://www.kriso.ee/db/9783662488638.html
Märksõnad:
This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties. More specifically, Walsh spectrum description of the traditional cryptographic properties of Boolean functions, including linear structure, propagation criterion, nonlinearity, and correlation immunity are presented. Constructions of symmetric Boolean functions and of Boolean permutations with good cryptographic properties are specifically studied. This book is not meant to be comprehensive, but with its own focus on some original research of the authors in the past. To be self content, some basic concepts and properties are introduced. This book can serve as a reference for cryptographic algorithm designers, particularly the designers of stream ciphers and of block ciphers, and for academics with interest in the cryptographic properties of Boolean functions.

1. Boolean Functions and Their Walsh Transforms.- 2. Independence of Boolean Functions of Their Variables.- 3. Nonlinearity and Linear Structures of Boolean Functions.- 4. Correlation Immunity of Boolean Functions.- 5. Algebraic Immunity of Boolean Functions.- 6. The Symmetric Property of Boolean Functions.- 7.Boolean Function Representation of S-boxes and Boolean Permutations.- 8. Cryptographic Applications of Boolean Functions.

Arvustused

The authors present an enjoyable book for young researchers and students working in the area of cryptography and coding. The book turns out to be an easy read. I would like to use it as a textbook for a course on BF and their applications. I recommend it to people working in the area of coding and cryptography. (Computing Reviews, August, 2017) 

The book gives a very detailed overview of various cryptographic properties of Boolean functions and their applications in cryptography. This book can serve as a reference for academics interested in the cryptographic properties of Boolean functions. It is also a valuable tool for the design and security analysis of stream and block ciphers if they employ Boolean functions in their construction. (Vladimír Lacko, zbMATH 1364.94010, 2017)

1 Boolean Functions and Their Walsh Transforms
1(30)
1.1 Logic Gates and Boolean Variables
1(1)
1.2 Boolean Functions and Their Representations
2(7)
1.2.1 Algebraic Normal Form
4(1)
1.2.2 Truth Table Representation
5(1)
1.2.3 Support Representation
5(1)
1.2.4 Minterm Representation
6(1)
1.2.5 Representation Conversions
7(2)
1.2.6 Enumeration of Boolean Functions
9(1)
1.3 Walsh Transforms and Walsh Spectrum of Boolean Functions
9(11)
1.3.1 Walsh Functions and Walsh Transforms
10(2)
1.3.2 Properties of Walsh Transforms
12(6)
1.3.3 Hadamard Matrices
18(2)
1.4 Basic Models of Stream Ciphers That Use Boolean Functions
20(5)
1.4.1 Linear Feedback Shift Registers
22(2)
1.4.2 Nonlinear Filtering Generators and Nonlinear Combiners
24(1)
1.5 Cryptographic Properties of Boolean Functions
25(6)
1.5.1 Algebraic Degree
25(1)
1.5.2 Balance
26(1)
1.5.3 Nonlinearity
27(1)
1.5.4 Linear Structure
27(1)
1.5.5 Propagation Criterion
27(1)
1.5.6 Correlation Immunity
28(1)
1.5.7 Algebraic Immunity
28(1)
1.5.8 Remarks
29(1)
References
29(2)
2 Independence of Boolean Functions of Their Variables
31(42)
2.1 Introduction
31(1)
2.2 The Algebraic Independence of Boolean Functions of Their Variables
31(6)
2.3 The Degeneracy of Boolean Functions
37(5)
2.4 Images of Boolean Functions on a Hyperplane
42(2)
2.5 Derivatives of Boolean Functions
44(4)
2.6 The Statistical Independence of Boolean Functions of Their Variables
48(5)
2.7 The Statistical Independence of Two Individual Boolean Functions
53(20)
2.7.1 Properties of the Statistical Independence of Boolean Functions
54(2)
2.7.2 How to Judge When Two Boolean Functions Are Statistically Independent
56(3)
2.7.3 Construction of Statistically Independent Boolean Functions
59(4)
2.7.4 Enumeration of Statistically Independent Boolean Functions
63(2)
2.7.5 On the Statistical Independence of a Group of Boolean Functions
65(6)
References
71(2)
3 Nonlinearity Measures of Boolean Functions
73(24)
3.1 Introduction
73(1)
3.2 Algebraic Degree and Nonlinearity of Boolean Functions
74(1)
3.3 Walsh Spectrum Description of Nonlinearity
75(2)
3.4 Nonlinearity of Some Basic Operations of Boolean Functions
77(7)
3.5 Upper and Lower Bounds of Nonlinearity of Boolean Functions
84(2)
3.6 Nonlinearity of Balanced Boolean Functions
86(1)
3.7 Higher-Order Nonlinearity of Boolean Functions
87(2)
3.8 Linear Structures of Boolean Functions
89(5)
3.9 Remarks
94(3)
References
95(2)
4 Correlation Immunity of Boolean Functions
97(50)
4.1 The Correlation Attack of Nonlinear Combiners
97(4)
4.2 The Correlation Immunity and Correlation Attacks
101(2)
4.3 Correlation Immunity of Boolean Functions
103(1)
4.4 Correlation Immune Functions and Error-Correcting Codes
104(2)
4.5 Construction of Correlation Immune Boolean Functions
106(7)
4.5.1 Known Constructions of Correlation Immune Boolean Functions
107(1)
4.5.2 Construction of Correlation Immune Boolean Functions Based on A Single Code
108(2)
4.5.3 Preliminary Enumeration of Correlation Immune Boolean Functions
110(1)
4.5.4 Construction of Correlation Immune Boolean Functions Using a Family of Error-Correcting Codes
110(3)
4.6 Lower Bounds on Enumeration of the Correlation Immune Functions Constructible from the Error-Correcting Code Construction
113(1)
4.7 Examples
114(3)
4.8 Exhaustive Construction of Correlation Immune Boolean Functions
117(2)
4.9 An Example of Exhaustive Construction of Correlation Immune Functions
119(3)
4.10 Construction of High-Order Correlation Immune Boolean Functions
122(2)
4.11 Construction of Correlation Immune Boolean Functions with Other Cryptographic Properties
124(9)
4.11.1 Correlation Immune Functions with Good Balance
125(1)
4.11.2 Correlation Immune Functions with High Algebraic Degree
126(1)
4.11.3 Correlation Immune Functions with High Nonlinearity
127(3)
4.11.4 Correlation Immune Functions with Propagation Criterion
130(1)
4.11.5 Linear Structure Characteristics of Correlation Immune Functions
131(2)
4.12 Construction of Algebraically Nondegenerate Correlation Immune Functions
133(6)
4.12.1 On the Algebraic Degeneration of Correlation Immune Functions
134(1)
4.12.2 Construction of Algebraically Nondegenerate Correlation Immune Functions
135(4)
4.13 The ε-Correlation Immunity of Boolean Functions
139(4)
4.14 Remarks
143(4)
References
143(4)
5 Algebraic Immunity of Boolean Functions
147(30)
5.1 Algebraic Attacks on Stream Ciphers
147(2)
5.2 A Small Example of Algebraic Attack
149(2)
5.3 Annihilators and Algebraic Immunity of Boolean Functions
151(3)
5.4 Construction of Annihilators of Boolean Functions
154(7)
5.5 On the Upper and Lower Bounds of Algebraic Immunity of Boolean Functions
161(1)
5.6 Computing the Annihilators of Boolean Funetions
162(15)
5.6.1 Computing the Annihilators of Boolean Functions: Approach I
163(3)
5.6.2 Computing the Annihilators of Boolean Functions: Approach II
166(9)
References
175(2)
6 The Symmetric Property of Boolean Functions
177(40)
6.1 Basic Properties of Symmetric Boolean Functions
177(3)
6.2 Computing the Walsh Transform of Symmetric Boolean Functions
180(7)
6.2.1 Walsh Transforms on Symmetric Boolean Functions
180(4)
6.2.2 Computational Complexity
184(3)
6.3 Correlation Immunity of Symmetric Functions
187(5)
6.3.1 When n Is Odd
189(1)
6.3.2 When n Is Even
190(1)
6.3.3 Higher-Order Correlation Immunity
191(1)
6.4 On Symmetric Resilient Functions
192(6)
6.4.1 Constructions of Symmetric Resilient Boolean Functions
193(1)
6.4.2 Searching for More Solutions
194(2)
6.4.3 The Exact Resiliency of Constructed Resilient Functions
196(2)
6.5 Basic Properties of Majority Functions
198(5)
6.6 The Walsh Spectrum of Majority Functions
203(3)
6.6.1 When n Is Odd
203(1)
6.6.2 When n Is Even
204(2)
6.7 The Correlation Immunity of Majority Functions
206(3)
6.8 The ε-Correlation Immunity of Majority Functions
209(4)
6.8.1 When n Is Odd
209(2)
6.8.2 When n Is Even
211(2)
6.9 Remarks
213(4)
References
214(3)
7 Boolean Function Representation of S-Boxes and Boolean Permutations
217(26)
7.1 Vectorial Boolean Function Representation of S-Boxes
217(1)
7.2 Boolean Function Representation of S-Boxes
218(5)
7.2.1 On the Properties of (n, n)-Boolean Permutations
220(3)
7.3 Properties of Boolean Permutations
223(2)
7.4 Inverses of Boolean Permutations
225(4)
7.5 Intractability Assumption and One-Way Trapdoor Boolean Permutations
229(1)
7.6 Construction of Boolean Permutations
230(8)
7.6.1 Some Primary Constructions
232(4)
7.6.2 On the Flexibility of the New Construction Method for Boolean Permutations
236(1)
7.6.3 Construction of Trapdoor Boolean Permutations with Limited Number of Terms
237(1)
7.7 A Small Example of Boolean Permutations
238(5)
7.7.1 Linearity and Nonlinearity of Boolean Permutations
239(1)
References
240(3)
8 Cryptographic Applications of Boolean Functions
243
8.1 Applications of Degenerate Boolean Functions to Logic Circuit Representation
243(2)
8.2 An Application of Boolean Permutations to Public Key Cryptosystem Design
245(3)
8.2.1 Public Key Cryptosystem 1 (PKC1)
245(1)
8.2.2 Public Key Cryptosystem 2 (PKC2)
246(1)
8.2.3 Public Key Cryptosystem 3 (PKC3)
247(1)
8.3 Application of Boolean Permutations to Digital Signatures
248(1)
8.4 Application of Boolean Permutations to Shared Signatures
249(1)
8.5 An Application of Boolean Permutations to Key Escrow Scheme
250(3)
8.5.1 Setup
250(1)
8.5.2 Escrowing Verification
251(1)
8.5.3 Key Recovery
252(1)
8.5.4 Properties
252(1)
8.6 A Small Example of Key Escrow Scheme Based on Boolean Permutations
253(3)
8.6.1 Selecting a Boolean Permutation of Order 6
253(1)
8.6.2 Preparation
254(1)
8.6.3 Verification
255(1)
8.6.4 Key Recovery
255(1)
8.7 Remarks
256
References
256
Chuan-Kun Wu, a research professor at the Institute of Information Engineering, Chinese Academy of Sciences, majoring in information security and related fundamental mathematics. He has published over 100 refereed research papers, and has co-authored a few books. Dengguo Feng, a research professor at the Institute of Software, Chinese Academy of Sciences, majoring in information security and cryptology. He has published over 200 refereed research papers, including those published in journals such as "Theoretical Computer Science", "IEEE Trans. on Information Theory", and conference papers presented at Crypto and Eurocrypt. He has published over 20 books and has leaded drafting over 20 international and national standards.