Chapter 4

Applications of Bent Functions

Abstract

Distinct applications of bent functions are discussed. First, we consider the use of bent functions in cryptography for constructing the ciphers CAST, Grain, and hash function HAVAL. Further we review connections between bent functions and distinct objects of discrete mathematics and coding theory (Hadamard matrices, strongly regular graphs, and Reed-Muller and Kerdock codes). Some applications to mobile networks are considered (constant-amplitude codes for code division multiple access, CDMA).

Keywords

Cryptography

Cryptanalysis

Block cipher

Stream cipher

Nonlinearity

Linear cryptanalysis

Differential cryptanalysis

S-box

DES

CAST

Grain

HAVAL

Hadamard matrix

Strongly regular graph

Reed-Muller ...

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