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001 ocn919201561
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005 20190328114812.0
006 m o d
007 cr cnu|||unuuu
008 150826t20152015enka ob 001 0 eng d
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019 _a919297114
_a923546855
_a929142768
_a1066653364
_a1088983040
020 _a9780128025550
_q(electronic bk.)
020 _a0128025557
_q(electronic bk.)
020 _z9780128023181
020 _z012802318X
035 _a(OCoLC)919201561
_z(OCoLC)919297114
_z(OCoLC)923546855
_z(OCoLC)929142768
_z(OCoLC)1066653364
_z(OCoLC)1088983040
050 4 _aQA341
072 7 _aMAT
_x000000
_2bisacsh
082 0 4 _a511.3/3
_223
100 1 _aTokareva, Natalia,
_eauthor.
245 1 0 _aBent functions : results and applications to cryptography /
_h[electronic resource]
_cby Natalia Tokareva.
264 1 _aLondon :
_bAcademic Press,
_c2015
264 4 _c�2015
300 _a1 online resource :
_billustrations (some color)
336 _atext
_btxt
_2rdacontent
337 _acomputer
_bc
_2rdamedia
338 _aonline resource
_bcr
_2rdacarrier
588 0 _aOnline resource; title from PDF title page (Ebsco, viewed August 27 2015).
504 _aIncludes bibliographical references and index.
520 _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 researchers, discussing proofs of several results, including the automorphism group of bent functions, the lower bound for the number of bent functions, and more.
505 0 _a""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 _a""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""
505 8 _a""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""
505 8 _a""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""
505 8 _a""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)""
650 0 _aAlgebraic functions.
650 0 _aAlgebra, Boolean.
650 0 _aCryptography
_xMathematics.
650 7 _aMATHEMATICS
_xGeneral.
_2bisacsh
650 7 _aAlgebra, Boolean.
_2fast
_0(OCoLC)fst00804924
650 7 _aAlgebraic functions.
_2fast
_0(OCoLC)fst00804933
650 7 _aCryptography
_xMathematics.
_2fast
_0(OCoLC)fst00884558
655 0 _aElectronic book.
655 4 _aElectronic books.
655 7 _aElectronic books.
_2lcgft
776 0 8 _iPrint version:
_aTokareva, Natalia.
_tBent Functions : Results and Applications to Cryptography.
_d: Elsevier Science, �2015
_z9780128023181
856 4 0 _3ScienceDirect
_uhttp://www.sciencedirect.com/science/book/9780128023181
999 _c247144
_d247144