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__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 Complexity -- 2.12 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 Degree -- 4.7 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 Construction

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.

• Presents a foundational approach, beginning with the basics of the necessary theory, then progressing to more complex content
• Includes major concepts that are presented with complete proofs, with an emphasis on how they can be applied
• Includes an extensive list of references, including 100 new to this edition that were chosen to highlight relevant topics
• Contains a section on special functions and all-new numerical examples

Content: Front Matter,Copyright,Dedication,PrefaceEntitled to full textChapter 1 - A Bit of History, Pages 1-5 Chapter 2 - Fourier Analysis of Boolean Functions, Pages 7-29 Chapter 3 - Avalanche and Propagation Criteria, Pages 31-54 Chapter 4 - Correlation Immune and Resilient Boolean Functions, Pages 55-82 Chapter 5 - Bent Boolean Functions, Pages 83-108 Chapter 6 - Special Types of Boolean Functions, Pages 109-142 Chapter 7 - Stream Cipher Design, Pages 143-185 Chapter 8 - Block Ciphers, Pages 187-221 Chapter 9 - Boolean Cayley Graphs, Pages 223-238 Bibliography, Pages 239-270 Index, Pages 271-275