Cryptographic Boolean Functions and Applications - 2nd Edition - ISBN: 9780128111291, 9780128111307

Cryptographic Boolean Functions and Applications

2nd Edition

Authors: Thomas Cusick Pantelimon Stanica
eBook ISBN: 9780128111307
Paperback ISBN: 9780128111291
Imprint: Academic Press
Published Date: 30th March 2017
Page Count: 288
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Description

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.

Key Features

  • 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

Readership

Researchers in cryptography, engineers and scientists who are involved in designing or implementing cryptographic algorithms or protocols, engineers and scientists who want to have a reference for the use of Boolean functions in cryptography. Graduate students (mainly math and computer science) who are doing research in the area of cryptographic Boolean functions. An advanced undergraduate course in an applied math department. Those interested in cryptography with a view to applying it in areas such as business, financial services and computer security

Table of Contents

Chapter 1: A Bit of History

  • Abstract
  • 1.1. George Boole (1815–1864)
  • 1.2. Claude Elwood Shannon (1916–2001)
  • References

Chapter 2: Fourier Analysis of Boolean Functions

  • Abstract
  • 2.1. Basic Definitions 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 Coefficients
  • 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
  • References

Chapter 3: Avalanche and Propagation Criteria

  • Abstract
  • 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
  • References

Chapter 4: Correlation Immune and Resilient Boolean Functions

  • Abstract
  • 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
  • References

Chapter 5: Bent Boolean Functions

  • Abstract
  • 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. Normal and Nonnormal Bent Functions
  • 5.13. Counting Bent Functions
  • 5.14. Partially Bent Functions
  • 5.15. Semi-bent Functions
  • References

Chapter 6: Special Types of Boolean Functions

  • Abstract
  • 6.1. Symmetric Functions
  • 6.2. Rotation Symmetric Functions
  • 6.3. k-Rotation Symmetric Functions
  • 6.4. Balanced Functions
  • 6.5. Cryptographic Boolean Functions with Biased Inputs
  • References

Chapter 7: Stream Cipher Design

  • Abstract
  • 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
  • References

Chapter 8: Block Ciphers

  • Abstract
  • 8.1. Some History
  • 8.2. Introduction
  • 8.3. Block Ciphers' Modes of Operation
  • 8.4. Design Approaches
  • 8.5. Notable Symmetric Ciphers
  • 8.6. Periods of Rijndael Transformations
  • 8.7. Algebraic Representations of Rijndael/AES
  • 8.8. Embedding AES in BES
  • 8.9. Further Embeddings of AES
  • References

Chapter 9: Boolean Cayley Graphs

  • Abstract
  • 9.1. Introduction
  • 9.2. Spectra of Boolean Cayley Graphs
  • 9.3. Few Spectral Coefficients of Boolean Functions
  • 9.4. Bent Boolean Cayley Graphs
  • 9.5. Coloring the Boolean Cayley Graph
  • 9.6. Avalanche Features of the Cayley Graphs
  • 9.7. Sensitivity of Hamming Weight of f to Spec(Γf)
  • 9.8. Boolean Cayley Graphs Under Affine Transformations
  • References

Details

No. of pages:
288
Language:
English
Copyright:
© Academic Press 2017
Published:
Imprint:
Academic Press
eBook ISBN:
9780128111307
Paperback ISBN:
9780128111291

About the Author

Thomas Cusick

Thomas Cusick has 25 years of experience in cryptography, 60 published papers in that subject and 8 Ph. D. students whose thesis work was in that area. He is currently located at the State University of New York in Buffalo, New York.

Affiliations and Expertise

State University of New York, Buffalo, USA

Pantelimon Stanica

Pantelimon Stanica has more than 15 years of experience in the area of cryptography and Boolean functions, more than 35 papers in this subject and 3 Ph.D. students working in the area. He is currently located at the Naval Postgraduate School in Monterey, California.

Affiliations and Expertise

Naval Postgraduate School, Monterey, CA USA