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Cryptographic Boolean functions and applications
Cryptographic Boolean Functions and Applications, Second Edition is designed to be a comprehensive reference for the use of Boolean functions in modern cryptography. While the vast majority of research on cryptographic Boolean functions has been achieved since the 1970s, when cryptography began to be widely used in everyday transactions, in particular banking, relevant material is scattered over hundreds of journal articles, conference proceedings, books, reports and notes, some of them only available online. This book follows the previous edition in sifting through this compendium and gathering the most significant information in one concise reference book. The work therefore encompasses over 600 citations, covering every aspect of the applications of cryptographic Boolean functions. Since 2008, the subject has seen a very large number of new results, and in response, the authors have prepared a new chapter on special functions. The new edition brings 100 completely new references and an expansion of 50 new pages, along with heavy revision throughout the text.
Front Cover; Cryptographic Boolean Functions and Applications; Copyright; Contents; Preface; 1 A Bit of History; 1.1 George Boole (1815-1864); 1.2 Claude Elwood Shannon (1916-2001); 2 Fourier Analysis of Boolean Functions; 2.1 Basic De nitions for 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 Coef cients; 2.8 Probability Distributions; 2.9 Hadamard Matrices and Nonlinearity Bounds; 2.10 Fast Walsh Transform.
2.11 LFSRs and Linear Complexity2.12 The Berlekamp-Massey Algorithm; 2.13 De Bruijn Sequences; 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; 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 Degree4.7 Connections with Orthogonal Arrays; 4.8 Constructing Correlation Immune Functions; 4.9 Tradeoff Between Correlation Immunity and Nonlinearity; 4.10 Some Computational Data; 5 Bent Boolean Functions; 5.1 Introduction; 5.2 De nitions 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 Construction5.12 Normal and Nonnormal Bent Functions; 5.13 Counting Bent Functions; 5.14 Partially Bent Functions; 5.15 Semi-bent Functions; 6 Special Types of Boolean Functions; 6.1 Symmetric Functions; 6.1.1 Introduction; 6.1.2 Balanced symmetric functions; 6.1.3 A conjecture for balanced elementary symmetric functions; 6.1.4 Resilient symmetric functions; 6.2 Rotation Symmetric Functions; 6.2.1 Early results; 6.2.2 Weight and nonlinearity; 6.2.3 Enumeration of rotation symmetric functions; 6.2.4 Af ne equivalence of rotation symmetric functions.
6.3 k-Rotation Symmetric Functions6.4 Balanced Functions; 6.5 Cryptographic Boolean Functions with Biased Inputs; 7 Stream Cipher Design; 7.1 Introduction; 7.2 Boolean Functions in Pseudorandom Bit Generators; 7.3 Nonlinear Combination Generators; 7.4 Nonlinear Filter Generators; 7.5 Multiplexer Generator; 7.6 Irregularly Clocked LFSRs in Generators; 7.7 Algebraic and Linearization Attacks; 7.8 The eStream Project; 7.9 AIDA and Cube Attacks on Tweakable Symmetric Ciphers; 8 Block Ciphers; 8.1 Some History; 8.2 Introduction; 8.3 Block Ciphers' Modes of Operation; 8.3.1 Con dentiality Modes.
Includes bibliographical references and index.