Boolean Functions
Boolean Functions

Author: Yves Crama

Publisher: Cambridge University Press

Published: 2011-05-16

Total Pages: 711

ISBN-13: 1139498630

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Written by prominent experts in the field, this monograph provides the first comprehensive, unified presentation of the structural, algorithmic and applied aspects of the theory of Boolean functions. The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations. This framework looks at the fundamental elements of the theory (Boolean equations and satisfiability problems, prime implicants and associated short representations, dualization), an in-depth study of special classes of Boolean functions (quadratic, Horn, shellable, regular, threshold, read-once functions and their characterization by functional equations) and two fruitful generalizations of the concept of Boolean functions (partially defined functions and pseudo-Boolean functions). Several topics are presented here in book form for the first time. Because of the depth and breadth and its emphasis on algorithms and applications, this monograph will have special appeal for researchers and graduate students in discrete mathematics, operations research, computer science, engineering and economics.

Analysis of Boolean Functions
Analysis of Boolean Functions

Author: Ryan O'Donnell

Publisher: Cambridge University Press

Published: 2014-06-05

Total Pages: 445

ISBN-13: 1107038324

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This graduate-level text gives a thorough overview of the analysis of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics.

Boolean Functions for Cryptography and Coding Theory
Boolean Functions for Cryptography and Coding Theory

Author: Claude Carlet

Publisher: Cambridge University Press

Published: 2021-01-07

Total Pages: 577

ISBN-13: 1108634664

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Boolean functions are essential to systems for secure and reliable communication. This comprehensive survey of Boolean functions for cryptography and coding covers the whole domain and all important results, building on the author's influential articles with additional topics and recent results. A useful resource for researchers and graduate students, the book balances detailed discussions of properties and parameters with examples of various types of cryptographic attacks that motivate the consideration of these parameters. It provides all the necessary background on mathematics, cryptography, and coding, and an overview on recent applications, such as side channel attacks on smart cards, cloud computing through fully homomorphic encryption, and local pseudo-random generators. The result is a complete and accessible text on the state of the art in single and multiple output Boolean functions that illustrates the interaction between mathematics, computer science, and telecommunications.

Boolean Reasoning
Boolean Reasoning

Author: Frank Markham Brown

Publisher: Courier Corporation

Published: 2012-02-10

Total Pages: 308

ISBN-13: 0486164594

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Concise text begins with overview of elementary mathematical concepts and outlines theory of Boolean algebras; defines operators for elimination, division, and expansion; covers syllogistic reasoning, solution of Boolean equations, functional deduction. 1990 edition.

Cryptographic Boolean Functions and Applications
Cryptographic Boolean Functions and Applications

Author: Thomas W. Cusick

Publisher: Academic Press

Published: 2009-03-04

Total Pages: 245

ISBN-13: 0080952224

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Boolean functions are the building blocks of symmetric cryptographic systems. Symmetrical cryptographic algorithms are fundamental tools in the design of all types of digital security systems (i.e. communications, financial and e-commerce).Cryptographic Boolean Functions and Applications is a concise reference that shows how Boolean functions are used in cryptography. Currently, practitioners who need to apply Boolean functions in the design of cryptographic algorithms and protocols need to patch together needed information from a variety of resources (books, journal articles and other sources). This book compiles the key essential information in one easy to use, step-by-step reference. Beginning with the basics of the necessary theory the book goes on to examine more technical topics, some of which are at the frontier of current research. Serves as a complete resource for the successful design or implementation of cryptographic algorithms or protocols using Boolean functions Provides engineers and scientists with a needed reference for the use of Boolean functions in cryptography Addresses the issues of cryptographic Boolean functions theory and applications in one concentrated resource Organized logically to help the reader easily understand the topic

Boolean Functions in Coding Theory and Cryptography
Boolean Functions in Coding Theory and Cryptography

Author: Oleg A. Logachev

Publisher: American Mathematical Soc.

Published: 2012-02-08

Total Pages: 352

ISBN-13: 0821846809

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This book offers a systematic presentation of cryptographic and code-theoretic aspects of the theory of Boolean functions. Both classical and recent results are thoroughly presented. Prerequisites for the book include basic knowledge of linear algebra, group theory, theory of finite fields, combinatorics, and probability. The book can be used by research mathematicians and graduate students interested in discrete mathematics, coding theory, and cryptography.

Logic and Boolean Algebra
Logic and Boolean Algebra

Author: Bradford Henry Arnold

Publisher: Courier Corporation

Published: 2011-01-01

Total Pages: 163

ISBN-13: 0486483851

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Orignally published: Englewood Cliffs, N.J.: Prentice-Hall, 1962.

Boolean Function Complexity
Boolean Function Complexity

Author: Stasys Jukna

Publisher: Springer Science & Business Media

Published: 2012-01-06

Total Pages: 618

ISBN-13: 3642245080

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Boolean circuit complexity is the combinatorics of computer science and involves many intriguing problems that are easy to state and explain, even for the layman. This book is a comprehensive description of basic lower bound arguments, covering many of the gems of this “complexity Waterloo” that have been discovered over the past several decades, right up to results from the last year or two. Many open problems, marked as Research Problems, are mentioned along the way. The problems are mainly of combinatorial flavor but their solutions could have great consequences in circuit complexity and computer science. The book will be of interest to graduate students and researchers in the fields of computer science and discrete mathematics.