Analysis of Boolean Functions

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.

Author: Ryan O'Donnell

Publisher: Cambridge University Press

ISBN: 9781107038325

Category: Computers

Page: 444

View: 573

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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.

Analysis of Boolean Functions

Notes The Fourier expansion for real-valued Boolean functions dates back to Walsh (Walsh, 1923) who introduced a complete orthonormal basis for L2([0 ... This proved to be a crucial tool for analysis of Boolean functions; see Chapter 9.

Author: Ryan O'Donnell

Publisher: Cambridge University Press

ISBN: 9781139952507

Category: Computers

Page:

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Boolean functions are perhaps the most basic objects of study in theoretical computer science. They also arise in other areas of mathematics, including combinatorics, statistical physics, and mathematical social choice. The field of analysis of Boolean functions seeks to understand them via their Fourier transform and other analytic methods. This text gives a thorough overview of the field, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry. Each chapter includes a 'highlight application' such as Arrow's theorem from economics, the Goldreich–Levin algorithm from cryptography/learning theory, Håstad's NP-hardness of approximation results, and 'sharp threshold' theorems for random graph properties. The book includes roughly 450 exercises and can be used as the basis of a one-semester graduate course. It should appeal to advanced undergraduates, graduate students and researchers in computer science theory and related mathematical fields.

Cryptographic Boolean Functions and Applications

[28] Bernasconi A, Codenotti B. Spectral analysis of Boolean functions as a graph eigenvalue problem. IEEE Trans Comput 1999;48:345–51. [29] Bernasconi A, Codenotti B. On Boolean functions associated to bipartite Cayley graphs.

Author: Thomas W. Cusick

Publisher: Academic Press

ISBN: 0080952224

Category: Mathematics

Page: 248

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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

Noise Sensitivity of Boolean Functions and Percolation

analysis. of. Boolean. functions. (first. facts). In this chapter, we introduce the key technical tool for our study, which is Fourier analysis on the hypercube; this allows us to define the spectrum of a Boolean function.

Author: Christophe Garban

Publisher: Cambridge University Press

ISBN: 9781107076433

Category: Computers

Page: 222

View: 760

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This is the first book to cover the theory of noise sensitivity of Boolean functions with particular emphasis on critical percolation.

Quantum Algorithms for Cryptographically Significant Boolean Functions

It is now evident that in certain cases we have more efficient quantum algorithms than the classical ones for the analysis of Boolean functions. Following the explanation of Deutsch-Jozsa in the second chapter ...

Author: Tharrmashastha SAPV

Publisher: Springer Nature

ISBN: 9789811630613

Category: Computers

Page: 118

View: 412

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This book is a timely report of the state-of-the-art analytical techniques in the domain of quantum algorithms related to Boolean functions. It bridges the gap between recent developments in the area and the hands-on analysis of the spectral properties of Boolean functions from a cryptologic viewpoint. Topics covered in the book include Qubit, Deutsch–Jozsa and Walsh spectrum, Grover’s algorithm, Simon’s algorithm and autocorrelation spectrum. The book aims at encouraging readers to design and implement practical algorithms related to Boolean functions. Apart from combinatorial techniques, this book considers implementing related programs in a quantum computer. Researchers, practitioners and educators will find this book valuable.

Boolean Functions

[716] R. O'Donnell, Some topics in analysis of Boolean functions, in: Proceedings of the 40th ACM Annual Symposium on Theory of Computing (STOC), 2008, pp. 569–578. [717] R. O'Donnell and R.A. Servedio, The Chow parameters problem, ...

Author: Yves Crama

Publisher: Cambridge University Press

ISBN: 9781139498630

Category: Mathematics

Page:

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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.

Boolean Functions for Cryptography and Coding Theory

Symmetric Boolean functions depending on an odd number of variables with maximum algebraic immunity. IEEE Transactions on Information Theory 52 (5), pp. 2271–2273, 2006. See page 357. [766] N. Li and W.-F. Qi. Construction and analysis ...

Author: Claude Carlet

Publisher: Cambridge University Press

ISBN: 9781108634663

Category: Computers

Page:

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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.