This book contains the proceedings of the NATO-Russia Advanced Study Institute (ASI) 'Boolean Functions in Cryptology and Information Security', which was held in Zvenigorod, Moscow region, Russia. 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. The book includes lectures and papers concern the following areas: cryptographic properties of Boolean functions and mappings; algebraic and combinatorial constructions of Boolean functions and mappings with prescribed cryptographic properties; Boolean functions and mappings in cryptosynthesis; classification of Boolean functions; cryptanalysis of ciphers; and, efficient computations in finite fields.
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Author(s): O.A. Logachev
Series: NATO Science for Peace and Security Series. Sub-Series D: In
Publisher: IOS Press
Year: 2008
Language: English
Pages: 365
Title page......Page 2
Preface......Page 6
Contents......Page 8
Invited Talks......Page 10
Bent Rectangles......Page 12
On Algebraic Algorithms Deciding Properties of Discrete Functions......Page 32
Non-Archimedean Theory of T-Functions......Page 42
Classification of the Cosets of RM(1, 7) in RM(3, 7) Revisited......Page 67
On Boolean Functions with Generalized Cryptographic Properties......Page 82
Conjectures on the Number of Balanced Boolean Functions of Bounded Degree......Page 106
Bit-Parallel Circuits for Arithmetic in Finite Fields......Page 113
On a Family of Perfect Nonlinear Binomials......Page 135
Classification of Boolean Quartic Forms in Eight Variables......Page 148
Local Affinity of Boolean Mappings......Page 157
Boolean Functions on Odd Number of Variables Having Nonlinearity Greater Than the Bent Concatenation Bound......Page 182
Decimation Based Algebraic and Correlation Attacks and Design of Boolean Functions......Page 192
Constructing Families of Latin Squares over Boolean Domains......Page 209
On Almost Perfect Nonlinear Boolean Functions......Page 217
On the Nonexistence of Homogeneous Rotation Symmetric Bent Boolean Functions of Degree Greater Than Two......Page 223
On Correlation Immune Boolean Functions......Page 228
A Cyclic Code Approach of Bent Functions over F2 and Z4......Page 241
On Balanced Nonlinear Boolean Functions......Page 252
Students' Talks......Page 290
On Properties of Correlation Immune Functions with High Nonlinearity......Page 292
Constructing Boolean Functions with Extremal Properties......Page 298
Tight Bounds Between Algebraic Immunity and Nonlinearities of High Orders......Page 305
On Implementation of One Type of Recursive Construction......Page 316
On Impossibility of Uniform Distribution of Codewords over Spheres......Page 324
On the Structure of the Spectrum Support of Boolean Functions......Page 340
Some Open Problems......Page 350
Open Problems in Boolean Function Theory. The Cryptographer's View......Page 352
Subject Index......Page 362
Author Index......Page 364
