Cryptographic Boolean functions and applications /
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| Author / Creator: | Cusick, Thomas W., 1943- |
|---|---|
| Edition: | 1st ed. |
| Imprint: | Amsterdam ; Boston : Academic Press/Elsevier, 2009. |
| Description: | xii, 232 p. : ill. ; 25 cm. |
| Language: | English |
| Subject: | |
| Format: | Print Book |
| URL for this record: | http://pi.lib.uchicago.edu/1001/cat/bib/7785129 |
Table of Contents:
- Preface
- Chapter 1. A bit of history
- 1.1. George Boole (1815-1864)
- 1.2. Claude Elwood Shannon (1916-2001)
- Chapter 2. Fourier analysis of Boolean functions
- 2.1. Basic Definitions on Boolean Functions
- 2.2. Walsh Transform
- 2.3. Autocorrelation Function
- 2.4. Walsh Transform on Subspaces
- 2.5. Linear Transformations and the Sign Function
- 2.6. Parseval Equation
- 2.7. Asymptotic Results on Walsh Coeffcients
- 2.8. Probability Distributions
- 2.9. Hadamard Matrices and Nonlinearity Bounds
- 2.10. Fast Walsh Transform
- 2.11. LFSRs and Linear Complexity
- 2.12. The Berlekamp-Massey Algorithm
- 2.13. De Bruijn Sequence
- Chapter 3. Avalanche and propagation criteria
- 3.1. Introduction
- 3.2. Counting SAC Functions
- 3.3. Counting Balanced SAC Functions
- 3.4. Higher Order SAC
- 3.5. Propagation Criteria
- 3.6. Higher Order PC(k)
- 3.7. Construction of SAC(k) and PC(k) Functions
- Chapter 4. Correlation immune and resilient Boolean functions
- 4.1. Introduction
- 4.2. Basic Properties of Correlation Immunity
- 4.3. LFSRs and Correlation Immunity
- 4.4. Counting Correlation Immune Functions
- 4.5. Resilient Functions
- 4.6. Tradeoff Between Correlation Immunity and Degree
- 4.7. Connections with Orthogonal Arrays
- 4.8. Constructing Correlation Immune Functions
- 4.9. Tradeoff Between Correlation Immunity and Nonlinearity
- Chapter 5. Bent Bollean functions
- 5.1. Introduction
- 5.2. Definitions and Background
- 5.3. Characterizations of the Bent Property
- 5.4. Meier and Staffelbach's Approach
- 5.5. Degree of a Bent Function
- 5.6. New From Old Bent Functions
- 5.7. Rothaus's Construction
- 5.8. Maiorana and McFarland's Construction
- 5.9. Dillon's Construction
- 5.10. Dobbertin's Construction
- 5.11. Carlet's Construction
- 5.12. Extended Maiorana-McFarland Class
- 5.13. Normal and Nonnormal Bent Functions
- 5.14. Counting Bent Functions
- 5.15. Highly Nonlinear Balanced Functions
- 5.16. Partially Bent Functions
- 5.17. Semi-bent Functions
- 5.18. Symmetric Bent Functions
- 5.19. Rotation Symmetric Functions
- 5.20. Enumeration of Rotation Symmetric Functions
- Chapter 6. Stream cipher design
- 6.1. Introduction
- 6.2. Boolean Functions in Pseudorandom Bit Generators
- 6.3. Nonlinear Combination Generators
- 6.4. Nonlinear Filter Generators
- 6.5. Multiplexer Generator
- 6.6. Irregularly Clocked LFSRs in Generators
- 6.7. Algebraic and Linearization Attacks
- 6.8. The eStream Project
- Chapter 7. Block ciphers
- 7.1. Some History
- 7.2. Introduction
- 7.3. Block Ciphers' Modes of Operation
- 7.3.1. Confidentiality modes
- 7.3.2. Authentication modes
- 7.4. Design Approaches
- 7.4.1. Feistel ciphers
- 7.4.2. Substitution permutation networks
- 7.5. Notable Symmetric Ciphers
- 7.5.1. Data Encryption Standard
- 7.5.2. Advanced Encryption Standard
- 7.6. Periods of Rijndael Transformations
- 7.7. Algebraic Representations of Rijndael/AES
- 7.8. Embedding AES in BES
- 7.9. Further Embeddings of AES
- Chapter 8. Boolean Cayley graphs
- 8.1. Introduction
- 8.2. Spectra of Boolean Cayley Graphs
- 8.3. Few Spectral Coefficients of Boolean Functions
- 8.4. Bent Boolean Cayley Graphs
- 8.5. Coloring the Boolean Cayley Graph
- 8.6. Avalanche Features of the Cayley Graphs
- 8.7. Sensitivity of Hamming Weight of f to Spec (Tf)
- 8.8. Boolean Cayley Graphs Under Affine Transformations
- References
- Index
