### Cryptographic Boolean Functions and Applications

 Author : Thomas W. Cusick,Pantelimon Stanica Publsiher : Academic Press Total Pages : 248 Release : 2009-03-04 Genre : Mathematics ISBN : 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 and Their Applications in Cryptography

 Author : Chuan-Kun Wu,Dengguo Feng Publsiher : Springer Total Pages : 256 Release : 2016-02-23 Genre : Computers ISBN : 9783662488652

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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.

### Cryptographic Boolean Functions and Applications

 Author : Thomas W. Cusick,Pantelimon Stanica Publsiher : Academic Press Total Pages : 288 Release : 2017-03-31 Genre : Mathematics ISBN : 9780128111307

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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 for Cryptography and Coding Theory

 Author : Claude Carlet Publsiher : Cambridge University Press Total Pages : 574 Release : 2021-01-07 Genre : Computers ISBN : 9781108473804

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

### Bent Functions

 Author : Natalia Tokareva Publsiher : Academic Press Total Pages : 220 Release : 2015-08-24 Genre : Mathematics ISBN : 9780128025550

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

### Bent Functions

 Author : Sihem Mesnager Publsiher : Springer Total Pages : 544 Release : 2016-08-09 Genre : Computers ISBN : 9783319325958

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.

### Discrete Mathematics With Cryptographic Applications

 Author : Alexander I. Kheyfits Publsiher : Mercury Learning and Information Total Pages : 375 Release : 2021-09-20 Genre : Computers ISBN : 9781683927617

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This book covers discrete mathematics both as it has been established after its emergence since the middle of the last century and as its elementary applications to cryptography. It can be used by any individual studying discrete mathematics, finite mathematics, and similar subjects. Any necessary prerequisites are explained and illustrated in the book. As a background of cryptography, the textbook gives an introduction into number theory, coding theory, information theory, that obviously have discrete nature. Designed in a “self-teaching” format, the book includes about 600 problems (with and without solutions) and numerous, practical examples of cryptography. FEATURES: Designed in a “self-teaching” format, the book includes about 600 problems (with and without solutions) and numerous examples of cryptography Provides an introduction into number theory, game theory, coding theory, and information theory as background for the coverage of cryptography Covers cryptography topics such as CRT, affine ciphers, hashing functions, substitution ciphers, unbreakable ciphers, Discrete Logarithm Problem (DLP), and more.

### Boolean Functions

 Author : Yves Crama,Peter L. Hammer Publsiher : Cambridge University Press Total Pages : 135 Release : 2011-05-16 Genre : Mathematics ISBN : 9781139498630

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 Models and Methods in Mathematics Computer Science and Engineering

 Author : Yves Crama,Peter L. Hammer Publsiher : Cambridge University Press Total Pages : 759 Release : 2010-06-28 Genre : Computers ISBN : 9780521847520

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A collection of papers written by prominent experts that examine a variety of advanced topics related to Boolean functions and expressions.

### Cryptographic Applications of Analytic Number Theory

 Author : Igor Shparlinski Publsiher : Springer Science & Business Media Total Pages : 411 Release : 2003-02-12 Genre : Computers ISBN : 3764366540

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The book introduces new ways of using analytic number theory in cryptography and related areas, such as complexity theory and pseudorandom number generation. Cryptographers and number theorists will find this book useful. The former can learn about new number theoretic techniques which have proved to be invaluable cryptographic tools, the latter about new challenging areas of applications of their skills.

### Analysis and Design of Boolean Functions for Cryptographic Applications

 Author : William L. Millan Publsiher : Unknown Total Pages : 142 Release : 1997 Genre : Boolean functions ISBN : OCLC:222297301

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### Analysis of Boolean Functions

 Author : Ryan O'Donnell Publsiher : Cambridge University Press Total Pages : 444 Release : 2014-06-05 Genre : Computers ISBN : 9781107038325

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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.

### Construction and Analysis of Cryptographic Functions

 Author : Lilya Budaghyan Publsiher : Springer Total Pages : 168 Release : 2015-01-06 Genre : Computers ISBN : 9783319129914

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This book covers novel research on construction and analysis of optimal cryptographic functions such as almost perfect nonlinear (APN), almost bent (AB), planar and bent functions. These functions have optimal resistance to linear and/or differential attacks, which are the two most powerful attacks on symmetric cryptosystems. Besides cryptographic applications, these functions are significant in many branches of mathematics and information theory including coding theory, combinatorics, commutative algebra, finite geometry, sequence design and quantum information theory. The author analyzes equivalence relations for these functions and develops several new methods for construction of their infinite families. In addition, the book offers solutions to two longstanding open problems, including the problem on characterization of APN and AB functions via Boolean, and the problem on the relation between two classes of bent functions.

### Boolean Functions

 Author : Serban E. Vlad Publsiher : Wiley Total Pages : 208 Release : 2019-02-20 Genre : Mathematics ISBN : 9781119517474