This book is devoted to such objects of discrete mathematics as Boolean bent functions. These functions have a remarkable property distinguishes bent functions as a special mysterious class and leads to numerous applications of bent functions in combinatorics, coding theory, and cryptography. In this book a detailed overview of results in bent functions is given. We discuss historical aspects of the invention of bent functions and describe their applications in cryptography and discrete mathematics. Basic properties and ...
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This book is devoted to such objects of discrete mathematics as Boolean bent functions. These functions have a remarkable property distinguishes bent functions as a special mysterious class and leads to numerous applications of bent functions in combinatorics, coding theory, and cryptography. In this book a detailed overview of results in bent functions is given. We discuss historical aspects of the invention of bent functions and describe their applications in cryptography and discrete mathematics. Basic properties and equivalent representations of bent functions are studied. Detailed classifications of bent functions in a small number of variables, and combinatorial and algebraic constructions of bent functions are considered. Connections between bent functions and other cryptographic functions are studied. Hamming distances between bent functions and the group of automorphisms of the set of all bent functions are considered. Upper and lower bounds for the number of bent functions and hypotheses on the asymptotic value of this number are discussed. A detailed systematic survey on generalizations of bent functions with respect to their algebraic, combinatorial, and cryptographic properties is given: we consider at least 25 distinct generalizations. Open problems in bent functions are also discussed. There are about 125 theorems in bent functions. Some results were presented before only in Russian and are still not widely known. The book is oriented at specialists in Boolean functions and cryptography, academic staff, and students. --
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