LEADER 05431nam 2200661 450 001 9910797415103321 005 20200520144314.0 010 $a0-12-802555-7 010 $a0-12-802318-X 035 $a(CKB)3710000000467007 035 $a(EBL)2192079 035 $a(SSID)ssj0001598418 035 $a(PQKBManifestationID)16299119 035 $a(PQKBTitleCode)TC0001598418 035 $a(PQKBWorkID)14887011 035 $a(PQKB)10986034 035 $a(Au-PeEL)EBL2192079 035 $a(CaPaEBR)ebr11093402 035 $a(CaONFJC)MIL825603 035 $a(OCoLC)919201561 035 $a(CaSebORM)9780128025550 035 $a(MiAaPQ)EBC2192079 035 $a(PPN)198684126 035 $a(EXLCZ)993710000000467007 100 $a20150901h20152015 uy| 0 101 0 $aeng 135 $aur|n|---||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aBent functions $eresults and applications to cryptography /$fby Natalia Tokareva, Sobolev Institute of Mathematics, Novosibirsk State University, Novosibirsk, Russia 210 1$aLondon, UK :$cElsevier Science,$d[2015] 210 4$dİ2015 215 $a1 online resource (221 p.) 300 $aDescription based upon print version of record 320 $aIncludes bibliographical references and index. 327 $aFront 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; Chapter 2: Bent Functions: An Introduction; Introduction 327 $a2.1 Definition of a Nonlinearity2.2 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; 4.3 Cryptography: Bent Functions in CAST; 4.4 Cryptography: Bent Functions in Grain; 4.5 Cryptography: Bent Functions in HAVAL 327 $a4.6 Hadamard Matrices and Graphs4.7 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; 6.1 Hadamard Matrices; 6.2 Difference Sets; 6.3 Designs; 6.4 Linear Spreads; 6.5 Sets of Subspaces; 6.6 Strongly Regular Graphs; 6.7 Bent Rectangles 327 $aChapter 7: Bent Functions with a Small Number of VariablesIntroduction; 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; 8.2 Maiorana-McFarland Class; 8.3 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 327 $a8.9 Other ConstructionsChapter 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); 9.7 Canteaut-Charpin-Kuyreghyan Bent Functions (MF-2); 9.8 Niho Exponents; 9.9 General Algebraic Approach; 9.10 Other Constructions; Chapter 10: Bent Functions and Other Cryptographic Properties; Introduction; 10.1 Cryptographic Criteria; 10.2 High Degree and Balancedness; 10.3 Correlation Immunity and Resiliency 327 $a10.4 Algebraic Immunity 330 $aBent 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 606 $aComputer security 606 $aData encryption (Computer science) 606 $aAlgebra, Boolean 615 0$aComputer security. 615 0$aData encryption (Computer science) 615 0$aAlgebra, Boolean. 676 $a511.324 700 $aTokareva$b Natalia$0959655 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910797415103321 996 $aBent functions$92174829 997 $aUNINA