Quaternary cryptographic bent functions and their binary projection
Résumé
The nonlinearity of sequences is one of the important security measures for stream cipher systems. Recently, in the study of vectorized stream cipher systems, bent functions have been generalized to the alphabet Zq=Z/qZ and also studied by several authors. This generalization maps the classical definition of binary bent functions to generalized bent functions. This paper propose a new approach for generalized bent functions over Z4 and their associated derived boolean functions. We present in this paper a new construction of a family of m-variable quaternary (Z4=Z/4Z={0,1,2,3}-valued) bent functions over Galois ring and cyclotomic classes using an intern function defined on a particular partition of the Teichmüller set. Using a particular binary projection map we obtain a family of (2m)-variable boolean bent functions and a family of (2m+1)-variable boolean plateaued functions of amplitude 2^(m+1) with nonlinearity equal to 4^m-2^m.