Cryptographic Boolean Functions and Applications

Author: Thomas W. Cusick
Publisher: Academic Press
ISBN: 0128111305
Format: PDF, ePub, Mobi
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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 and Their Applications in Cryptography

Author: Chuan-Kun Wu
Publisher: Springer
ISBN: 3662488655
Format: PDF, ePub, Mobi
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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.

Boolean Functions

Author: Jean-Francis Michon
Publisher: Publication Univ Rouen Havre
ISBN: 9782877754224
Format: PDF, Mobi
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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.

Progress in Applications of Boolean Functions

Author: Tsutomu Sasao
Publisher: Morgan & Claypool Publishers
ISBN: 160845181X
Format: PDF, ePub, Mobi
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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

Bent Functions

Author: Natalia Tokareva
Publisher: Academic Press
ISBN: 0128025557
Format: PDF
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Bent Functions: Results and Applications to Cryptography offers a unique survey of the objects of discrete mathematics known as Boolean bent functions. As these maximal, nonlinear Boolean functions and their generalizations have many theoretical and practical applications in combinatorics, coding theory, and cryptography, the text provides a detailed survey of their main results, presenting a systematic overview of their generalizations and applications, and considering open problems in classification and systematization of bent functions. The text is appropriate for novices and advanced researchers, discussing proofs of several results, including the automorphism group of bent functions, the lower bound for the number of bent functions, and more. Provides a detailed survey of bent functions and their main results, presenting a systematic overview of their generalizations and applications Presents a systematic and detailed survey of hundreds of results in the area of highly nonlinear Boolean functions in cryptography Appropriate coverage for students from advanced specialists in cryptography, mathematics, and creators of ciphers

Cryptographic Applications of Analytic Number Theory

Author: Igor Shparlinski
Publisher: Birkhäuser
ISBN: 3034880375
Format: PDF
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The book introduces new techniques that imply rigorous lower bounds on the com plexity of some number-theoretic and cryptographic problems. It also establishes certain attractive pseudorandom properties of various cryptographic primitives. These methods and techniques are based on bounds of character sums and num bers of solutions of some polynomial equations over finite fields and residue rings. Other number theoretic techniques such as sieve methods and lattice reduction algorithms are used as well. The book also contains a number of open problems and proposals for further research. The emphasis is on obtaining unconditional rigorously proved statements. The bright side of this approach is that the results do not depend on any assumptions or conjectures. On the downside, the results are much weaker than those which are widely believed to be true. We obtain several lower bounds, exponential in terms of logp, on the degrees and orders of o polynomials; o algebraic functions; o Boolean functions; o linear recurrence sequences; coinciding with values of the discrete logarithm modulo a prime p at sufficiently many points (the number of points can be as small as pI/2+O:). These functions are considered over the residue ring modulo p and over the residue ring modulo an arbitrary divisor d of p - 1. The case of d = 2 is of special interest since it corresponds to the representation of the rightmost bit of the discrete logarithm and defines whether the argument is a quadratic residue.

Kryptografie verst ndlich

Author: Christof Paar
Publisher: Springer-Verlag
ISBN: 3662492970
Format: PDF
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Das Buch gibt eine umfassende Einführung in moderne angewandte Kryptografie. Es behandelt nahezu alle kryptografischen Verfahren mit praktischer Relevanz. Es werden symmetrische Verfahren (DES, AES, PRESENT, Stromchiffren), asymmetrische Verfahren (RSA, Diffie-Hellmann, elliptische Kurven) sowie digitale Signaturen, Hash-Funktionen, Message Authentication Codes sowie Schlüsselaustauschprotokolle vorgestellt. Für alle Krypto-Verfahren werden aktuelle Sicherheitseinschätzungen und Implementierungseigenschaften beschrieben.

Finite Fields with Applications to Coding Theory Cryptography and Related Areas

Author: Gary L. Mullen
Publisher: Springer Science & Business Media
ISBN: 3642594352
Format: PDF, ePub
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The Sixth International Conference on Finite Fields and Applications, Fq6, held in the city of Oaxaca, Mexico, from May 21-25, 2001, continued a series of biennial international conferences on finite fields. This volume documents the steadily increasing interest in this topic. Finite fields are an important tool in discrete mathematics and its applications cover algebraic geometry, coding theory, cryptology, design theory, finite geometries, and scientific computation, among others. An important feature is the interplay between theory and applications which has led to many new perspectives in research on finite fields and other areas. This interplay has been emphasized in this series of conferences and certainly was reflected in Fq6. This volume offers up-to-date original research papers by leading experts in the area.

Bent Functions

Author: Sihem Mesnager
Publisher: Springer
ISBN: 3319325957
Format: PDF, ePub, Docs
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This book gives a detailed survey of the main results on bent functions over finite fields, presents a systematic overview of their generalizations, variations and applications, considers open problems in classification and systematization of bent functions, and discusses proofs of several results. This book uniquely provides a necessary comprehensive coverage of bent functions.It serves as a useful reference for researchers in discrete mathematics, coding and cryptography. Students and professors in mathematics and computer science will also find the content valuable, especially those interested in mathematical foundations of cryptography. It can be used as a supplementary text for university courses on discrete mathematics, Boolean functions, or cryptography, and is appropriate for both basic classes for under-graduate students and advanced courses for specialists in cryptography and mathematics.