# Bent Functions

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## Bent Functions

Author | : Natalia Tokareva |

Publsiher | : Academic Press |

Total Pages | : 220 |

Release | : 2015-08-24 |

ISBN 10 | : 0128025557 |

ISBN 13 | : 9780128025550 |

Language | : EN, FR, DE, ES & NL |

**Bent Functions Book Review:**

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 |

ISBN 10 | : 3319325957 |

ISBN 13 | : 9783319325958 |

Language | : EN, FR, DE, ES & NL |

**Bent Functions Book Review:**

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.

## Boolean Functions in Cryptology and Information Security

Author | : B. Preneel,O.A. Logachev |

Publsiher | : IOS Press |

Total Pages | : 364 |

Release | : 2008-07-16 |

ISBN 10 | : 1607503441 |

ISBN 13 | : 9781607503446 |

Language | : EN, FR, DE, ES & NL |

**Boolean Functions in Cryptology and Information Security Book Review:**

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.

## Discrete Geometry and Algebraic Combinatorics

Author | : Alexander Barg,Oleg R. Musin |

Publsiher | : American Mathematical Society |

Total Pages | : 190 |

Release | : 2014-08-28 |

ISBN 10 | : 1470409054 |

ISBN 13 | : 9781470409050 |

Language | : EN, FR, DE, ES & NL |

**Discrete Geometry and Algebraic Combinatorics Book Review:**

This volume contains the proceedings of the AMS Special Session on Discrete Geometry and Algebraic Combinatorics held on January 11, 2013, in San Diego, California. The collection of articles in this volume is devoted to packings of metric spaces and related questions, and contains new results as well as surveys of some areas of discrete geometry. This volume consists of papers on combinatorics of transportation polytopes, including results on the diameter of graphs of such polytopes; the generalized Steiner problem and related topics of the minimal fillings theory; a survey of distance graphs and graphs of diameters, and a group of papers on applications of algebraic combinatorics to packings of metric spaces including sphere packings and topics in coding theory. In particular, this volume presents a new approach to duality in sphere packing based on the Poisson summation formula, applications of semidefinite programming to spherical codes and equiangular lines, new results in list decoding of a family of algebraic codes, and constructions of bent and semi-bent functions.

## Discovery of Bent Functions Using the Fast Walsh Transform

Author | : Timothy R. O'Dowd |

Publsiher | : Unknown |

Total Pages | : 100 |

Release | : 2010 |

ISBN 10 | : |

ISBN 13 | : OCLC:697890327 |

Language | : EN, FR, DE, ES & NL |

**Discovery of Bent Functions Using the Fast Walsh Transform Book Review:**

Linear cryptanalysis attacks are a threat against cryptosystems. These attacks can be defended against by using combiner functions composed of highly nonlinear Boolean functions. Bent functions, which have the highest possible nonlinearity, are uncommon. As the number of variables in a Boolean function increases, bent functions become extremely rare. A method of computing the nonlinearity of Boolean functions using the Fast Walsh Transform (FWT) is presented. The SRC-6 reconfigurable computer allows testing of functions at a much faster rate than a PC. With a clock frequency of 100 MHz, throughput of the SRC-6 is 100,000,000 functions per second. An implementation of the FWT used to compute the nonlinearity of Boolean functions with up to five variables is presented. Since there are 22n Boolean functions of n variables, computation of the nonlinearity of every Boolean function with six or more variables takes thousands of years to complete. This makes discovery of bent functions difficult for large n. An algorithm is presented that uses information in the FWT of a function to produce similar functions with increasingly higher nonlinearity. This algorithm demonstrated the ability to enumerate every bent function for n = 4 without the necessity of exhaustively testing all fourvariable functions.

## Surveys in Combinatorics 2013

Author | : Simon R. Blackburn,Stefanie Gerke,Mark Wildon |

Publsiher | : Cambridge University Press |

Total Pages | : 384 |

Release | : 2013-06-27 |

ISBN 10 | : 1107651956 |

ISBN 13 | : 9781107651951 |

Language | : EN, FR, DE, ES & NL |

**Surveys in Combinatorics 2013 Book Review:**

Surveys of recent important developments in combinatorics covering a wide range of areas in the field.

## Combinatorics and Finite Fields

Author | : Kai-Uwe Schmidt,Arne Winterhof |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 354 |

Release | : 2019-07-08 |

ISBN 10 | : 3110641968 |

ISBN 13 | : 9783110641967 |

Language | : EN, FR, DE, ES & NL |

**Combinatorics and Finite Fields Book Review:**

Combinatorics and finite fields are of great importance in modern applications such as in the analysis of algorithms, in information and communication theory, and in signal processing and coding theory. This book contains survey articles on topics such as difference sets, polynomials, and pseudorandomness.

## Partial Spreads and Hyperbent Functions in Odd Characteristic

Author | : Hui Yi Lu |

Publsiher | : Unknown |

Total Pages | : 118 |

Release | : 2011 |

ISBN 10 | : |

ISBN 13 | : OCLC:902823008 |

Language | : EN, FR, DE, ES & NL |

**Partial Spreads and Hyperbent Functions in Odd Characteristic Book Review:**

We study bent functions which are as different as possible from linear functions. Functions that remain bent under all bijective monomial substitutions are called hyperbent. In Chapter 2 we introduce partial spreads to construct a family of bent functions on vector spaces of even dimension over a finite field. This generalizes the construction given by Dillon for fields of characteristic 2. In Chapter 3 we use finite fields to introduce an explicit family of functions in the trace form whose hyperbentness can be tested using results of Chapter 2. This test is more efficient than using the definition of a bent function. It is an analogue of a result by Charpin and Gong for characteristic 2. The motivation for studying bent functions is their important role in cryptography and coding theory. For example, the CAST cipher constructed using bent functions is approved for use by the Canadian government.

## Lecture Notes in Real Time Intelligent Systems

Author | : Jolanta Mizera-Pietraszko,Pit Pichappan |

Publsiher | : Springer |

Total Pages | : 508 |

Release | : 2017-08-07 |

ISBN 10 | : 3319607448 |

ISBN 13 | : 9783319607443 |

Language | : EN, FR, DE, ES & NL |

**Lecture Notes in Real Time Intelligent Systems Book Review:**

Intelligent computing refers greatly to artificial intelligence with the aim at making computer to act as a human. This newly developed area of real-time intelligent computing integrates the aspect of dynamic environments with the human intelligence. This book presents a comprehensive practical and easy to read account which describes current state-of-the art in designing and implementing real-time intelligent computing to robotics, alert systems, IoT, remote access control, multi-agent systems, networking, mobile smart systems, crowd sourcing, broadband systems, cloud computing, streaming data and many other applications areas. The solutions discussed in this book will encourage the researchers and IT professional to put the methods into their practice.

## Selected Areas in Cryptography

Author | : Serge Vaudenay,Amr M. Youssef |

Publsiher | : Springer |

Total Pages | : 364 |

Release | : 2003-06-30 |

ISBN 10 | : 354045537X |

ISBN 13 | : 9783540455370 |

Language | : EN, FR, DE, ES & NL |

**Selected Areas in Cryptography Book Review:**

This book constitutes the thoroughly refereed post-proceedings of the 8th International Workshop on Selected Areas in Cryptology, SAC 2001, held in Toronto, Ontario, Canada in August 2001. The 25 revised full papers presented together with the abstracts of two invited talks were carefully reviewed and selected during two rounds of refereeing and revision. The papers are organized in topical sections on cryptanalysis, Boolean functions, Rijndael, elliptic curves and efficient implementation, public key systems, and protocols and MAC.

## Hadamard Matrices and Their Applications

Author | : K. J. Horadam |

Publsiher | : Princeton University Press |

Total Pages | : 263 |

Release | : 2007 |

ISBN 10 | : 069111921X |

ISBN 13 | : 9780691119212 |

Language | : EN, FR, DE, ES & NL |

**Hadamard Matrices and Their Applications Book Review:**

In Hadamard Matrices and Their Applications, K. J. Horadam provides the first unified account of cocyclic Hadamard matrices and their applications in signal and data processing. This original work is based on the development of an algebraic link between Hadamard matrices and the cohomology of finite groups that was discovered fifteen years ago. The book translates physical applications into terms a pure mathematician will appreciate, and theoretical structures into ones an applied mathematician, computer scientist, or communications engineer can adapt and use. The first half of the book explains the state of our knowledge of Hadamard matrices and two important generalizations: matrices with group entries and multidimensional Hadamard arrays. It focuses on their applications in engineering and computer science, as signal transforms, spreading sequences, error-correcting codes, and cryptographic primitives. The book's second half presents the new results in cocyclic Hadamard matrices and their applications. Full expression of this theory has been realized only recently, in the Five-fold Constellation. This identifies cocyclic generalized Hadamard matrices with particular "stars" in four other areas of mathematics and engineering: group cohomology, incidence structures, combinatorics, and signal correlation. Pointing the way to possible new developments in a field ripe for further research, this book formulates and discusses ninety open questions.

## Probabilistic Methods in Discrete Mathematics

Author | : Anonim |

Publsiher | : Walter de Gruyter GmbH & Co KG |

Total Pages | : 399 |

Release | : 2020-05-28 |

ISBN 10 | : 3112314107 |

ISBN 13 | : 9783112314104 |

Language | : EN, FR, DE, ES & NL |

**Probabilistic Methods in Discrete Mathematics Book Review:**

## Information and Communication Security

Author | : Vijay Varadharajan,Yi Mu |

Publsiher | : Springer |

Total Pages | : 328 |

Release | : 2004-06-01 |

ISBN 10 | : 3540479422 |

ISBN 13 | : 9783540479420 |

Language | : EN, FR, DE, ES & NL |

**Information and Communication Security Book Review:**

ICICSâ€™99, the Second International Conference on Information and C- munication Security, was held in Sydney, Australia, 9-11 November 1999. The conference was sponsored by the Distributed System and Network Security - search Unit, University of Western Sydney, Nepean, the Australian Computer Society, IEEE Computer Chapter (NSW), and Harvey World Travel. I am g- teful to all these organizations for their support of the conference. The conference brought together researchers, designers, implementors and users of information security systems and technologies. A range of aspects was addressed from security theory and modeling to system and protocol designs and implementations to applications and management. The conference con- sted of a series of refereed technical papers and invited technical presentations. The program committee invited two distinguished key note speakers. The ?rst keynote speech by Doug McGowan, a Senior Manager from Hewlett-Packard, USA, discussed cryptography in an international setting. Doug described the current status of international cryptography and explored possible future trends and new technologies. The second keynote speech was delivered by Sushil Ja- dia of George Mason University, USA. Sushilâ€™s talk addressed the protection of critical information systems. He discussed issues and methods for survivability of systems under malicious attacks and proposed a fault-tolerance based - proach. The conference also hosted a panel on the currently much debated topic of Internet censorship. The panel addressed the issue of censorship from various viewpoints namely legal, industrial, governmental and technical.

## Cryptographic Boolean Functions and Applications

Author | : Thomas W. Cusick,Pantelimon Stanica |

Publsiher | : Academic Press |

Total Pages | : 248 |

Release | : 2009-03-04 |

ISBN 10 | : 9780080952222 |

ISBN 13 | : 0080952224 |

Language | : EN, FR, DE, ES & NL |

**Cryptographic Boolean Functions and Applications Book Review:**

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

## Applied Algebra Algebraic Algorithms and Error Correcting Codes

Author | : Serdar Boztas,Hsiao-feng Lu |

Publsiher | : Springer |

Total Pages | : 368 |

Release | : 2007-11-29 |

ISBN 10 | : 3540772243 |

ISBN 13 | : 9783540772248 |

Language | : EN, FR, DE, ES & NL |

**Applied Algebra Algebraic Algorithms and Error Correcting Codes Book Review:**

This book constitutes the refereed proceedings of the 17th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Correcting Codes, AAECC-17, held in Bangalore, India, in December 2007. Among the subjects addressed are block codes, including list-decoding algorithms; algebra and codes: rings, fields, algebraic geometry codes; algebra: rings and fields, polynomials, permutations, lattices; cryptography: cryptanalysis and complexity; computational algebra.

## An Analysis of Bent Function Properties Using the Transeunt Triangle and the SRC 6 Reconfigurable Computer

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 121 |

Release | : 2009 |

ISBN 10 | : |

ISBN 13 | : OCLC:463629446 |

Language | : EN, FR, DE, ES & NL |

**An Analysis of Bent Function Properties Using the Transeunt Triangle and the SRC 6 Reconfigurable Computer Book Review:**

Linear attacks against cryptosystems can be defeated when combiner functions are composed of highly nonlinear Boolean functions. The highest nonlinearity Boolean functions, or bent functions, are not common- especially when they have many variables-bent functions are difficult to find. Understanding what properties are common to bent functions will help ease the search for them. Using the SRC-6 reconfigurable computer, functions can be generated or tested at a rate much higher than a PC. This thesis uses the SRC-6 to characterize data for functions with 4, 5 and 6 variables. The data compiled showed trends based on the order, homogeneity, balance, and symmetry of Boolean functions. The transeunt triangle is used to convert a Boolean function into Algebraic Normal Form, so that the properties are easily determined. The first known proof that the transeunt triangle correctly converts between the two Boolean functions' representations is included. The SRC-6, while capable of pipelining code so that it runs up to six thousand times faster than a PC, is limited by the speed of the FPGA, 100 MHz. Functions with up to six variables were tested. Predictions on this data, as well as ways to improve the computing capability of the SRC-6, are included.

## Codes From Difference Sets

Author | : Ding Cunsheng |

Publsiher | : World Scientific |

Total Pages | : 356 |

Release | : 2014-08-08 |

ISBN 10 | : 981461937X |

ISBN 13 | : 9789814619370 |

Language | : EN, FR, DE, ES & NL |

**Codes From Difference Sets Book Review:**

This is the first monograph on codebooks and linear codes from difference sets and almost difference sets. It aims at providing a survey of constructions of difference sets and almost difference sets as well as an in-depth treatment of codebooks and linear codes from difference sets and almost difference sets. To be self-contained, this monograph covers necessary mathematical foundations and the basics of coding theory. It also contains tables of best BCH codes and best cyclic codes over GF(2) and GF(3) up to length 125 and 79, respectively. This repository of tables can be used to benchmark newly constructed cyclic codes. This monograph is intended to be a reference for postgraduates and researchers who work on combinatorics, or coding theory, or digital communications.

## CONSTRUCTIONS OF BENT FUNCTIONS

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2001 |

ISBN 10 | : |

ISBN 13 | : OCLC:611691268 |

Language | : EN, FR, DE, ES & NL |

**CONSTRUCTIONS OF BENT FUNCTIONS Book Review:**

In cryptography especially in block cipher design, Boolean functions are the basic elements. A cryptographic function should have high nonlinearity as it can be attacked by linear attack. In this thesis the highest possible nonlinear boolean functions in the even dimension, that is bent functions, basic properties and construction methods of bent functions are studied. Also normal bent functions and generalized bent functions are presented.

## Bulletin of the Institute of Combinatorics and Its Applications

Author | : Anonim |

Publsiher | : Unknown |

Total Pages | : 329 |

Release | : 2001 |

ISBN 10 | : |

ISBN 13 | : UOM:39015053942408 |

Language | : EN, FR, DE, ES & NL |

**Bulletin of the Institute of Combinatorics and Its Applications Book Review:**

## Fast Software Encryption

Author | : Lars Knudsen |

Publsiher | : Springer Science & Business Media |

Total Pages | : 316 |

Release | : 1999-06-29 |

ISBN 10 | : 354066226X |

ISBN 13 | : 9783540662266 |

Language | : EN, FR, DE, ES & NL |

**Fast Software Encryption Book Review:**

This book constitutes the thoroughly refereed post-workshop proceedings of the 6th International Workshop on Fast Software Encryption, FSE'99, held in Rome, Italy, in March 1999. The 22 revised full papers presented were carefully selected from a total of 51 submissions during two rounds of reviewing and revision. The volume is divided into sections on advanced encryption standard (AES), remotely keyed encryptions, analysis of block ciphers, miscellaneous, modes of operation, and stream ciphers.