LEADER 00000cam a2200769 i 4500 001 919201561 003 OCoLC 005 20240129213017.0 006 m o d 007 cr cnu|||unuuu 008 150826t20152015enka ob 001 0 eng d 019 919297114|a923546855|a929142768|a1066653364|a1088983040 |a1228531868|a1391163327 020 9780128025550|q(electronic bk.) 020 0128025557|q(electronic bk.) 029 1 AU@|b000055409571 029 1 CHNEW|b001013081 029 1 DEBBG|bBV043216503 029 1 DEBBG|bBV043622929 029 1 DEBSZ|b451528697 029 1 DEBSZ|b48237621X 029 1 GBVCP|b856732303 029 1 NLGGC|b400914093 035 (OCoLC)919201561|z(OCoLC)919297114|z(OCoLC)923546855 |z(OCoLC)929142768|z(OCoLC)1066653364|z(OCoLC)1088983040 |z(OCoLC)1228531868|z(OCoLC)1391163327 037 825603|bMIL 040 N$T|beng|erda|epn|cN$T|dN$T|dYDXCP|dCDX|dOPELS|dIDEBK |dOCLCF|dEBLCP|dB24X7|dCOO|dD6H|dDEBSZ|dMCW|dOCLCA|dLIV |dOCLCQ|dMERUC|dOCLCQ|dWRM|dU3W|dCEF|dAU@|dOCLCQ|dWYU|dCUY |dLOA|dZCU|dICG|dK6U|dCOCUF|dVT2|dDKC|dOCLCQ|dBRF|dOCLCO |dOCLCQ|dINARC|dOCLCO|dOCLCL 049 INap 082 04 511.3/3 082 04 511.3/3|223 099 eBook O'Reilly for Public Libraries 100 1 Tokareva, Natalia,|eauthor. 245 10 Bent functions :|bresults and applications to cryptography /|cby Natalia Tokareva.|h[O'Reilly electronic resource] 264 1 London :|bAcademic Press,|c[2015] 264 4 |c©2015 300 1 online resource :|billustrations (some color) 336 text|btxt|2rdacontent 337 computer|bc|2rdamedia 338 online resource|bcr|2rdacarrier 504 Includes bibliographical references and index. 505 0 Front Cover -- Bent Functions: Results and Applications to Cryptography -- Copyright -- Contents -- Foreword -- Preface -- Notation -- Chapter 1: Boolean Functions -- Introduction -- 1.1 Definitions -- 1.2 Algebraic Normal Form -- 1.3 Boolean Cube and Hamming Distance -- 1.4 Extended Affinely Equivalent Functions -- 1.5 Walsh- Hadamard Transform -- 1.6 Finite Field and Boolean Functions -- 1.7 Trace Function -- 1.8 Polynomial Representation of a Boolean Function -- 1.9 Trace Representation of a Boolean Function -- 1.10 Monomial Boolean Functions 505 8 Chapter 2: Bent Functions: An IntroductionIntroduction -- 2.1 Definition of a Nonlinearity -- 2.2 Nonlinearity of a Random Boolean Function -- 2.3 Definition of a Bent Function -- 2.4 If n Is Odd? -- 2.5 Open Problems -- 2.6 Surveys -- Chapter 3: History of Bent Functions -- Introduction -- 3.1 Oscar Rothaus -- 3.2 V.A. Eliseev and O.P. Stepchenkov -- 3.3 From the 1970s to the Present -- Chapter 4: Applications of Bent Functions -- Introduction -- 4.1 Cryptography: Linear Cryptanalysis and Boolean Functions -- 4.2 Cryptography: One Historical Example 505 8 4.3 Cryptography: Bent Functions in CAST4.4 Cryptography: Bent Functions in Grain -- 4.5 Cryptography: Bent Functions in HAVAL -- 4.6 Hadamard Matrices and Graphs -- 4.7 Links to Coding Theory -- 4.8 Bent Sequences -- 4.9 Mobile Networks, CDMA -- 4.10 Remarks -- Chapter 5: Properties of Bent Functions -- Introduction -- 5.1 Degree of a Bent Function -- 5.2 Affine Transformations of Bent Functions -- 5.3 Rank of a Bent Function -- 5.4 Dual Bent Functions -- 5.5 Other Properties -- Chapter 6: Equivalent Representations of Bent Functions -- Introduction 505 8 6.1 Hadamard Matrices6.2 Difference Sets -- 6.3 Designs -- 6.4 Linear Spreads -- 6.5 Sets of Subspaces -- 6.6 Strongly Regular Graphs -- 6.7 Bent Rectangles -- Chapter 7: Bent Functions with a Small Number of Variables -- Introduction -- 7.1 Two and Four Variables -- 7.2 Six Variables -- 7.3 Eight Variables -- 7.4 Ten and More Variables -- 7.5 Algorithms for Generation of Bent Functions -- 7.6 Concluding Remarks -- Chapter 8: Combinatorial Constructions of Bent Functions -- Introduction -- 8.1 Rothaus's Iterative Construction 505 8 8.2 Maiorana-McFarland Class8.3 Partial Spreads: PS+, PS- -- 8.4 Dillon's Bent Functions: PSap -- 8.5 Dobbertin's Construction -- 8.6 More Iterative Constructions -- 8.7 Minterm Iterative Constructions -- 8.8 Bent Iterative Functions: BI -- 8.9 Other Constructions -- Chapter 9: Algebraic Constructions of Bent Functions -- Introduction -- 9.1 An Algebraic Approach -- 9.2 Bent Exponents: General Properties -- 9.3 Gold Bent Functions -- 9.4 Dillon Exponent -- 9.5 Kasami Bent Functions -- 9.6 Canteaut-Leander Bent Functions (MF-1) 520 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. 588 0 Online resource; title from PDF title page (Ebsco, viewed August 27 2015). 590 O'Reilly|bO'Reilly Online Learning: Academic/Public Library Edition 650 0 Algebraic functions. 650 0 Algebra, Boolean. 650 0 Cryptography|xMathematics. 650 6 Fonctions algébriques. 650 6 Algèbre de Boole. 650 6 Cryptographie|xMathématiques. 650 7 MATHEMATICS|xGeneral.|2bisacsh 650 7 Algebra, Boolean|2fast 650 7 Algebraic functions|2fast 650 7 Cryptography|xMathematics|2fast 776 08 |iPrint version:|aTokareva, Natalia.|tBent Functions : Results and Applications to Cryptography.|d: Elsevier Science, ©2015|z9780128023181 856 40 |uhttps://ezproxy.naperville-lib.org/login?url=https:// learning.oreilly.com/library/view/~/9780128025550/?ar |zAvailable on O'Reilly for Public Libraries 938 Books 24x7|bB247|nbks00091953 938 Coutts Information Services|bCOUT|n32406134 938 EBL - Ebook Library|bEBLB|nEBL2192079 938 EBSCOhost|bEBSC|n1056353 938 ProQuest MyiLibrary Digital eBook Collection|bIDEB |ncis32406134 938 YBP Library Services|bYANK|n12587161 938 Internet Archive|bINAR|nbentfunctionsres0000toka 994 92|bJFN