Progress in Applications of Boolean Functions PDF Download

Author: Tsutomu Sasao
Publisher: Springer Nature
ISBN: 3031798120
Category : Technology & Engineering
Languages : en
Pages : 139

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Book Description
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 plaintext 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

Author: Tsutomu Sasao
Publisher: Morgan & Claypool Publishers
ISBN: 160845181X
Category : Algebra, Boolean
Languages : en
Pages : 153

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Book Description
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

Author: Thomas W. Cusick
Publisher: Academic Press
ISBN: 0128111305
Category : Mathematics
Languages : en
Pages : 288

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Book 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. 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

Author: Bernd Steinbach
Publisher: Cambridge Scholars Publishing
ISBN: 1527588734
Category : Computers
Languages : en
Pages : 254

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Book Description
This book gathers together the results of research on the Boolean domain related to important real-life applications that will support the reader in solving their scientific and practical tasks. It highlights that ongoing digitalization leads to increasing amounts of complex applications, the digits of which are usually encoded by Boolean variables due to their simplicity as only two values are used. However, as shown here, an exponentially growing number of vectors of Boolean variables can negate this simplicity, which leads to challenges in advancing progress in the Boolean domain and supporting a wide range of applications.

Author: Winfrid G. Schneeweiss
Publisher: Springer
ISBN:
Category : Mathematics
Languages : en
Pages : 284

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Book Description
Modern systems engineering (e. g. switching circuits design) and operations research (e. g. reliability systems theory) use Boolean functions with increasing regularity. For practitioners and students in these fields books written for mathe maticians are in several respects not the best source of easy to use information, and standard books, such as, on switching circuits theory and reliability theory, are mostly somewhat narrow as far as Boolean analysis is concerned. Further more, in books on switching circuits theory the relevant stochastic theory is not covered. Aspects of the probabilistic theory of Boolean functions are treated in some works on reliability theory, but the results deserve a much broader interpre tation. Just as the applied theory (e. g. of the Laplace transform) is useful in control theory, renewal theory, queueing theory, etc. , the applied theory of Boolean functions (of indicator variables) can be useful in reliability theory, switching circuits theory, digital diagnostics and communications theory. This book is aimed at providing a sufficiently deep understanding of useful results both in practical work and in applied research. Boolean variables are restricted here to indicator or O/l variables, i. e. variables whose values, namely 0 and 1, are not free for a wide range of interpretations, e. g. in digital electronics 0 for L ==low voltage and 1 for H == high voltage.

Author: Stasys Jukna
Publisher: Springer Science & Business Media
ISBN: 3642245080
Category : Mathematics
Languages : en
Pages : 620

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Book Description
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.

Author: C. Pandu Rangan
Publisher: Springer Science & Business Media
ISBN: 3540430105
Category : Computers
Languages : en
Pages : 363

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Book Description
This book constitutes the refereed proceedings of the Second International Conference in Cryptology in India, INDOCRYPT 2001, held in Chennai, India in December 2001. The 31 revised full papers presented together with an invited survey were carefully reviewed and selected from 77 submissions. The papers are organized in topical sections on hashing, algebraic schemes, elliptic curves, coding theory, applications, cryptanalysis, distributed cryptography, Boolean functions, digitial signatures, and shift registers.

Author: Bernd Steinbach
Publisher: Springer Nature
ISBN: 3031798929
Category : Technology & Engineering
Languages : en
Pages : 203

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Book Description
The Boolean Differential Calculus (BDC) is a very powerful theory that extends the basic concepts of Boolean Algebras significantly. Its applications are based on Boolean spaces and n, Boolean operations, and basic structures such as Boolean Algebras and Boolean Rings, Boolean functions, Boolean equations, Boolean inequalities, incompletely specified Boolean functions, and Boolean lattices of Boolean functions. These basics, sometimes also called switching theory, are widely used in many modern information processing applications. The BDC extends the known concepts and allows the consideration of changes of function values. Such changes can be explored for pairs of function values as well as for whole subspaces. The BDC defines a small number of derivative and differential operations. Many existing theorems are very welcome and allow new insights due to possible transformations of problems. The available operations of the BDC have been efficiently implemented in several software packages. The common use of the basic concepts and the BDC opens a very wide field of applications. The roots of the BDC go back to the practical problem of testing digital circuits. The BDC deals with changes of signals which are very important in applications of the analysis and the synthesis of digital circuits. The comprehensive evaluation and utilization of properties of Boolean functions allow, for instance, to decompose Boolean functions very efficiently; this can be applied not only in circuit design, but also in data mining. Other examples for the use of the BDC are the detection of hazards or cryptography. The knowledge of the BDC gives the scientists and engineers an extended insight into Boolean problems leading to new applications, e.g., the use of Boolean lattices of Boolean functions.

Author: Ryan O'Donnell
Publisher: Cambridge University Press
ISBN: 1107038324
Category : Computers
Languages : en
Pages : 445

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Book Description
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: Anne Canteaut
Publisher: Springer
ISBN: 3540305564
Category : Computers
Languages : en
Pages : 431

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Book Description
The INDOCRYPT series of conferences started in 2000. INDOCRYPT 2004 was the ?fth one in this series. The popularity of this series is increasing every year. The number of papers submitted to INDOCRYPT 2004 was 181, out of which 147 papers conformed to the speci?cations in the call for papers and, therefore, were accepted to the review process. Those 147 submissions were spread over 22 countries. Only 30 papers were accepted to this proceedings. We should note that many of the papers that were not accepted were of good quality but only the top 30 papers were accepted. Each submission received at least three independent - views. The selection process also included a Web-based discussion phase. We made e?orts to compare the submissions with other ongoing conferences around the world in order to ensure detection of double-submissions, which were not - lowed by the call for papers. We wish to acknowledge the use of the Web-based review software developed by Bart Preneel, Wim Moreau, and Joris Claessens in conducting the review process electronically. The software greatly facilitated the Program Committee in completing the review process on time. We would like to thank C ́ edric Lauradoux and the team at INRIA for their total support in c- ?guring and managing the Web-based submission and review softwares. We are unable to imagine the outcome of the review process without their participation. This year the invited talks were presented by Prof. Colin Boyd and Prof.