| Preface | p. xi |
| A bit of history | p. 1 |
| George Boole (1815-1864) | p. 1 |
| Claude Elwood Shannon (1916-2001) | p. 3 |
| Fourier analysis of Boolean functions | p. 5 |
| Basic Definitions on Boolean Functions | p. 5 |
| Walsh Transform | p. 7 |
| Autocorrelation Function | p. 8 |
| Walsh Transform on Subspaces | p. 9 |
| Linear Transformations and the Sign Function | p. 10 |
| Parseval Equation | p. 12 |
| Asymptotic Results on Walsh Coeffcients | p. 13 |
| Probability Distributions | p. 14 |
| Hadamard Matrices and Nonlinearity Bounds | p. 16 |
| Fast Walsh Transform | p. 18 |
| LFSRs and Linear Complexity | p. 19 |
| The Berlekamp-Massey Algorithm | p. 21 |
| De Bruijn Sequence | p. 22 |
| Avalanche and propagation criteria | p. 25 |
| Introduction | p. 25 |
| Counting SAC Functions | p. 26 |
| Counting Balanced SAC Functions | p. 28 |
| Higher Order SAC | p. 29 |
| Propagation Criteria | p. 38 |
| Higher Order PC(k) | p. 39 |
| Construction of SAC(k) and PC(k) Functions | p. 41 |
| Correlation immune and resilient Boolean functions | p. 49 |
| Introduction | p. 49 |
| Basic Properties of Correlation Immunity | p. 50 |
| LFSRs and Correlation Immunity | p. 52 |
| Counting Correlation Immune Functions | p. 59 |
| Resilient Functions | p. 60 |
| Tradeoff Between Correlation Immunity and Degree | p. 61 |
| Connections with Orthogonal Arrays | p. 63 |
| Constructing Correlation Immune Functions | p. 65 |
| Tradeoff Between Correlation Immunity and Nonlinearity | p. 68 |
| Bent Bollean functions | p. 73 |
| Introduction | p. 73 |
| Definitions and Background | p. 74 |
| Characterizations of the Bent Property | p. 76 |
| Meier and Staffelbach's Approach | p. 79 |
| Degree of a Bent Function | p. 80 |
| New From Old Bent Functions | p. 81 |
| Rothaus's Construction | p. 84 |
| Maiorana and McFarland's Construction | p. 85 |
| Dillon's Construction | p. 86 |
| Dobbertin's Construction | p. 89 |
| Carlet's Construction | p. 90 |
| Extended Maiorana-McFarland Class | p. 90 |
| Normal and Nonnormal Bent Functions | p. 96 |
| Counting Bent Functions | p. 97 |
| Highly Nonlinear Balanced Functions | p. 100 |
| Partially Bent Functions | p. 104 |
| Semi-bent Functions | p. 106 |
| Symmetric Bent Functions | p. 107 |
| Rotation Symmetric Functions | p. 108 |
| Enumeration of Rotation Symmetric Functions | p. 113 |
| Stream cipher design | p. 119 |
| Introduction | p. 119 |
| Boolean Functions in Pseudorandom Bit Generators | p. 120 |
| Nonlinear Combination Generators | p. 124 |
| Nonlinear Filter Generators | p. 128 |
| Multiplexer Generator | p. 132 |
| Irregularly Clocked LFSRs in Generators | p. 140 |
| Algebraic and Linearization Attacks | p. 147 |
| The eStream Project | p. 155 |
| Block ciphers | p. 157 |
| Some History | p. 157 |
| Introduction | p. 158 |
| Block Ciphers' Modes of Operation | p. 159 |
| Confidentiality modes | p. 159 |
| Authentication modes | p. 162 |
| Design Approaches | p. 163 |
| Feistel ciphers | p. 163 |
| Substitution permutation networks | p. 164 |
| Notable Symmetric Ciphers | p. 165 |
| Data Encryption Standard | p. 166 |
| Advanced Encryption Standard | p. 173 |
| Periods of Rijndael Transformations | p. 180 |
| Algebraic Representations of Rijndael/AES | p. 181 |
| Embedding AES in BES | p. 185 |
| Further Embeddings of AES | p. 190 |
| Boolean Cayley graphs | p. 193 |
| Introduction | p. 193 |
| Spectra of Boolean Cayley Graphs | p. 195 |
| Few Spectral Coefficients of Boolean Functions | p. 196 |
| Bent Boolean Cayley Graphs | p. 197 |
| Coloring the Boolean Cayley Graph | p. 200 |
| Avalanche Features of the Cayley Graphs | p. 201 |
| Sensitivity of Hamming Weight of f to Spec (Tf) | p. 204 |
| Boolean Cayley Graphs Under Affine Transformations | p. 205 |
| References | p. 209 |
| Index | p. 229 |
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