Boolean Functions

The book focuses on algebraic representations of Boolean functions, especially disjunctive and conjunctive normal form representations.

Boolean Functions

Author: Yves Crama

Publisher: Cambridge University Press

ISBN: 1139498630

Page:

View: 713

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 and Their Applications in Cryptography

This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties.

Boolean Functions and Their Applications in Cryptography

Author: Chuan-Kun Wu

Publisher: Springer

ISBN: 3662488655

Page: 256

View: 317

This book focuses on the different representations and cryptographic properties of Booleans functions, presents constructions of Boolean functions with some good cryptographic properties. More specifically, Walsh spectrum description of the traditional cryptographic properties of Boolean functions, including linear structure, propagation criterion, nonlinearity, and correlation immunity are presented. Constructions of symmetric Boolean functions and of Boolean permutations with good cryptographic properties are specifically studied. This book is not meant to be comprehensive, but with its own focus on some original research of the authors in the past. To be self content, some basic concepts and properties are introduced. This book can serve as a reference for cryptographic algorithm designers, particularly the designers of stream ciphers and of block ciphers, and for academics with interest in the cryptographic properties of Boolean functions.

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.

Analysis of Boolean Functions

Author: Ryan O'Donnell

Publisher: Cambridge University Press

ISBN: 1107038324

Page: 444

View: 525

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 Cryptography and Applications

En mars 2006 s'est tenu à Rouen BFCA'06, le second atelier sur le thème des Fonctions Booléennes. Pendant trois jours, de nombreux chercheurs internationaux s'y sont rencontrés et y ont parlé de leurs travaux.

Boolean Functions  Cryptography and Applications

Author: Jean-Francis Michon

Publisher: Publication Univ Rouen Havre

ISBN: 9782877754224

Page: 201

View: 685

En mars 2006 s'est tenu à Rouen BFCA'06, le second atelier sur le thème des Fonctions Booléennes. Pendant trois jours, de nombreux chercheurs internationaux s'y sont rencontrés et y ont parlé de leurs travaux. Cet ouvrage est composé des articles associés aux différentes conférences qui s'y sont tenues.

Boolean Functions

This book: Presents up-to-date research in the field of Boolean networks, Includes the information needed to understand the construction of an asynchronous Boolean systems theory and contains proofs, Employs use of the language of algebraic ...

Boolean Functions

Author: Serban E. Vlad

Publisher: John Wiley & Sons

ISBN: 1119517516

Page: 208

View: 768

The essential guide showing how the unbounded delay model of computation of the Boolean functions may be used in the analysis of the Boolean networks Boolean Functions: Topics in Asynchronicity contains the most current research in several issues of asynchronous Boolean systems. In this framework, asynchronicity means that the functions which model the digital circuits from electronics iterate their coordinates independently on each other and the author—a noted expert in the field—includes a formal mathematical description of these systems. Filled with helpful definitions and illustrative examples, the book covers a range of topics such as morphisms, antimorphisms, invariant sets, path connected sets, attractors. Further, it studies race freedom, called here the technical condition of proper operation, together with some of its generalized and strengthened versions, and also time reversal, borrowed from physics and also from dynamical systems, together with the symmetry that it generates. This book: Presents up-to-date research in the field of Boolean networks, Includes the information needed to understand the construction of an asynchronous Boolean systems theory and contains proofs, Employs use of the language of algebraic topology and homological algebra. Written formathematicians and computer scientists interested in the theory and applications of Boolean functions, dynamical systems, and circuits, Boolean Functions: Topics in Asynchronicity is an authoritative guide indicating a way of using the unbounded delay model of computation of the Boolean functions in the analysis of the Boolean networks.

Cryptographic Boolean Functions and Applications

This book follows the previous edition in sifting through this compendium and gathering the most significant information in one concise reference book.

Cryptographic Boolean Functions and Applications

Author: Thomas W. Cusick

Publisher: Academic Press

ISBN: 0128111305

Page: 288

View: 921

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

Boolean Functions in Cryptology and Information Security

Here we briefly survey the state of the art nonlinearity results for Boolean
functions on odd number of input variables having very high nonlinearity. We
outline some results on even variable Boolean functions too. Keywords. Boolean
function ...

Boolean Functions in Cryptology and Information Security

Author: Bart Preneel

Publisher: IOS Press

ISBN: 1586038788

Page: 355

View: 555

This book contains the proceedings of the NATO-Russia Advanced Study Institute (ASI) 'Boolean Functions in Cryptology and Information Security', which was held in Zvenigorod, Moscow region, Russia. These proceedings consist of three parts. The first part contains survey lectures on various areas of Boolean function theory that are of primary importance for cryptology. These lectures were delivered by leading researchers from many countries and contain both classic and recent results. The second part contains research papers written by graduate and postgraduate students of Lomonosov University, Moscow.The third part contains a list of open problems in Boolean function theory. The book includes lectures and papers concern the following areas: cryptographic properties of Boolean functions and mappings; algebraic and combinatorial constructions of Boolean functions and mappings with prescribed cryptographic properties; Boolean functions and mappings in cryptosynthesis; classification of Boolean functions; cryptanalysis of ciphers; and, efficient computations in finite fields.

Boolean Functions and Computation Models

There is one function of type ( 1 ) , 2 ( 22 * - ? – 1 ) functions of type ( 2 ) and 22 "
– 2 ( 22 " -- - 1 ) - 1 functions of type ( 3 ) . We compose a universal circuit for n -
ary boolean functions by using the circuit implied by the identity f = ( - n ^ fo ) V (
In ...

Boolean Functions and Computation Models

Author: Peter Clote

Publisher: Springer Science & Business Media

ISBN: 9783540594369

Page: 602

View: 346

The two internationally renowned authors elucidate the structure of "fast" parallel computation. Its complexity is emphasised through a variety of techniques ranging from finite combinatorics, probability theory and finite group theory to finite model theory and proof theory. Non-uniform computation models are studied in the form of Boolean circuits; uniform ones in a variety of forms. Steps in the investigation of non-deterministic polynomial time are surveyed as is the complexity of various proof systems. Providing a survey of research in the field, the book will benefit advanced undergraduates and graduate students as well as researchers.

Progress in Applications of Boolean Functions

Leander,“Crytographer'stoolkitforconstructionof8-bitbentfunctions,” preprint: http://
eprint.iacr.org/2005/089.pdf 2.7 [4] R. Forré, “The strict avalanche criterion:
Spectral properties of Boolean functions and an extended definition,” Advances
in ...

Progress in Applications of Boolean Functions

Author: Tsutomu Sasao

Publisher: Morgan & Claypool Publishers

ISBN: 160845181X

Page: 139

View: 872

This book brings together five topics on the application of Boolean functions. They are 1. Equivalence classes of Boolean functions: The number of n-variable functions is large, even for values as small as n = 6, and there has been much research on classifying functions. There are many classifications, each with their own distinct merit. 2. Boolean functions for cryptography: The process of encrypting/decrypting plain text messages often depends on Boolean functions with specific properties. For example, highly nonlinear functions are valued because they are less susceptible to linear attacks. 3. Boolean differential calculus: An operation analogous to taking the derivative of a real-valued function offers important insight into the properties of Boolean functions. One can determine tests or susceptibility to hazards. 4. Reversible logic: Most logic functions are irreversible; it is impossible to reconstruct the input, given the output. However, Boolean functions that are reversible are necessary for quantum computing, and hold significant promise for low-power computing. 5. Data mining: The process of extracting subtle patterns from enormous amounts of data has benefited from the use of a graph-based representation of Boolean functions. This has use in surveillance, fraud detection, scientific discovery including bio-informatics, genetics, medicine, and education. Written by experts, these chapters present a tutorial view of new and emerging technologies in Boolean functions. Table of Contents: Equivalence Classes of Boolean Functions / Boolean Functions for Cryptography / Boolean Differential Calculus / Synthesis of Boolean Functions in Reversible Logic / Data Mining Using Binary Decision Diagrams

Boolean Functions in Coding Theory and Cryptography

The notion of nonlinearity for Boolean functions, which was introduced in §2.2, is
basic for cryptography. In this chapter we will describe this notion by using
examples of well-known classes of Boolean functions having extremal (or close
to ...

Boolean Functions in Coding Theory and Cryptography

Author: Oleg A. Logachev

Publisher: American Mathematical Soc.

ISBN: 0821846809

Page: 334

View: 417

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.

Timed Boolean Functions

This book presents a methodology for timing research which facilitates analy sis and design of circuits and systems in a unified temporal and logical domain.

Timed Boolean Functions

Author: William K.C. Lam

Publisher: Springer Science & Business Media

ISBN: 1461526884

Page: 273

View: 211

Timing research in high performance VLSI systems has advanced at a steady pace over the last few years, while tools, especially theoretical mechanisms, lag behind. Much present timing research relies heavily on timing diagrams, which, although intuitive, are inadequate for analysis of large designs with many parameters. Further, timing diagrams offer only approximations, not exact solutions, to many timing problems and provide little insight in the cases where temporal properties of a design interact intricately with the design's logical functionalities. This book presents a methodology for timing research which facilitates analy sis and design of circuits and systems in a unified temporal and logical domain. In the first part, we introduce an algebraic representation formalism, Timed Boolean Functions (TBF's), which integrates both logical and timing informa tion of digital circuits and systems into a single formalism. We also give a canonical form, TBF BDD's, for them, which can be used for efficient ma nipulation. In the second part, we apply Timed Boolean Functions to three problems in timing research, for which exact solutions are obtained for the first time: 1. computing the exact delays of combinational circuits and the minimum cycle times of finite state machines, 2. analysis and synthesis of wavepipelining circuits, a high speed architecture for which precise timing relations between signals are essential for correct operations, 3. verification of circuit and system performance and coverage of delay faults by testing.

Noise Sensitivity of Boolean Functions and Percolation

In a nutshell, the authors showed that (1) if a monotone function is very
uncorrelated with all majority functions, then it is ... 8.2 The revealment theorem
An algorithm for a Boolean function f is an algorithm A that queries (asks the
values of) the ...

Noise Sensitivity of Boolean Functions and Percolation

Author: Christophe Garban

Publisher: Cambridge University Press

ISBN: 1107076439

Page: 222

View: 238

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

The Complexity of Boolean Functions

Presents a large number of recent research results previously unavailable in book form.

The Complexity of Boolean Functions

Author: Ingo Wegener

Publisher: Wiley

ISBN: 9780471915553

Page: 470

View: 291

Presents a large number of recent research results previously unavailable in book form. Initially deals with the wee-known computation models, and goes on to special types of circuits, parallel computers, and branching programs. Includes basic theory as well recent research findings. Each chapter includes exercises.

Application of Consensus Theory to the Minimization of Boolean Functions

Given two implicants of a boolean function, we can by performing their consensus, find a third implicant. This operation has been used for finding the prime implicants of a boolean function.

Application of Consensus Theory to the Minimization of Boolean Functions

Author: Pierre Tison

Publisher:

ISBN:

Page: 43

View: 976

Given two implicants of a boolean function, we can by performing their consensus, find a third implicant. This operation has been used for finding the prime implicants of a boolean function. In this paper, the consensus is extended from two to any number of terms. A property of these generalized consensus relations leads to a systematic way of finding them. It is shown that any prime implicant of a boolean function is a generalized consensus, therefore the algorithm for the determination of the consensus relations can be used for finding the prime implicants. This new method is simpler than the usual process of iterative consensus. It is also shown in this paper that consensus theory can be used for finding the minimal sums of a boolean function. The methods applicable for any boolean function, with or without don't care conditions, with a single or a multiple output. (Author).

Boolean Functions for Cryptography and Coding Theory

A complete, accessible book on single and multiple output Boolean functions in cryptography and coding, with recent applications and problems.

Boolean Functions for Cryptography and Coding Theory

Author: Claude Carlet

Publisher: Cambridge University Press

ISBN: 1108473806

Page: 620

View: 650

A complete, accessible book on single and multiple output Boolean functions in cryptography and coding, with recent applications and problems.

Boolean Function Complexity

Introduction In recent years several methods have been developed for obtaining
superpolynomial lower bounds on the monotone formula and circuit size of
explicitly given Boolean functions. Among these are the method of
approximations [3, ...

Boolean Function Complexity

Author: Mike S. Paterson

Publisher: Cambridge University Press

ISBN: 9780521408264

Page: 201

View: 244

Here Professor Paterson brings together papers from the 1990 Durham symposium on Boolean function complexity. The participants include many well known figures in the field.

Boolean Function Complexity

Some of the results are asymptotic, and we use the standard asymptotic notation:
for two functions f and g, we write f D O.g/ if f Ä c1g C c2 for all possible values of
the two functions, where c1 ;c2 are constants. We write f D ̋.g/ if g D O.f/, and f ...

Boolean Function Complexity

Author: Stasys Jukna

Publisher: Springer Science & Business Media

ISBN: 3642245080

Page: 620

View: 794

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.