05982cam a2200577Ii 4500 ocn919201561 OCoLC 20190328114812.0 m o d cr cnu|||unuuu 150826t20152015enka ob 001 0 eng d 2015935721 N$T eng rda pn N$T N$T YDXCP CDX OPELS IDEBK OCLCF EBLCP B24X7 COO D6H DEBSZ MCW OCLCA LIV OCLCQ MERUC OCLCQ WRM U3W CEF AU@ OCLCQ WYU CUY LOA ZCU ICG K6U COCUF VT2 DKC 919297114 923546855 929142768 1066653364 1088983040 9780128025550 (electronic bk.) 0128025557 (electronic bk.) 9780128023181 012802318X (OCoLC)919201561 (OCoLC)919297114 (OCoLC)923546855 (OCoLC)929142768 (OCoLC)1066653364 (OCoLC)1088983040 QA341 MAT 000000 bisacsh 511.3/3 23 Tokareva, Natalia, author. Bent functions : results and applications to cryptography / [electronic resource] by Natalia Tokareva. London : Academic Press, 2015 �2015 1 online resource : illustrations (some color) text txt rdacontent computer c rdamedia online resource cr rdacarrier Online resource; title from PDF title page (Ebsco, viewed August 27 2015). Includes bibliographical references and index. 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. ""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"" ""Chapter 2: Bent Functions: An Introduction""""Introduction""; ""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"" ""4.3 Cryptography: Bent Functions in CAST""""4.4 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"" ""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""; ""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"" ""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""; ""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)"" Algebraic functions. Algebra, Boolean. Cryptography Mathematics. MATHEMATICS General. bisacsh Algebra, Boolean. fast (OCoLC)fst00804924 Algebraic functions. fast (OCoLC)fst00804933 Cryptography Mathematics. fast (OCoLC)fst00884558 Electronic book. Electronic books. Electronic books. lcgft Print version: Tokareva, Natalia. Bent Functions : Results and Applications to Cryptography. : Elsevier Science, �2015 9780128023181 ScienceDirect http://www.sciencedirect.com/science/book/9780128023181 247144 247144