Bent Functions

Generalities on Boolean functions and p-ary functions.- Mathematical Foundations.- Boolean Functions and Cryptography.- Bent Functions-Generalities.- Bent Functions: Primary Constructions (Part I).- Bent Functions: Secondary Constructions.- Bent Functions: Primary Constructions (Part II).- Class H, Niho Bent Functions and O-Polynomials.- Subclasses of Bent Functions: Hyper-Bent Functions.- Hyper-Bent Functions: Primary Constructions with Multiple Trace Terms.- (Hyper)-Bent Functions, Exponential Sums and (Hyper-)elliptic Curves.- Bent Vectorial Functions.- Bent Functions in Arbitrary Characteristic.- Bent Functions and (Partial-)spreads.- Various Cryptographic and Algebraic Generalizations of Bent Functions.- Plateaued Functions: Generalities and Characterizations.- Plateaued Boolean Functions: Constructions of Semi-Bent Functions.- Linear Codes from Bent, Semi-Bent, and Almost Bent Functions.

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• Teoria da codificação e criptologia
• A matemática discreta
• Teoria da informação
• Cálculo diferencial e equações

Bent functions;Boolean functions;Vectorial functions;S-boxes;Non-linearity;Walsh-Hadamard transform;Symmetric cryptography;Coding theory;Combinatorics;Plateaued functions;Hyper-bent functions;Semi-bent functions;Near-bent functions;Generalized bent functions;Difference Sets;Finite fields;Exponential sums;Kloosterman sums;Dillon exponents;Niho exponents