International Association for Cryptologic Research (IACR)
Abstract
Kumar et al.(1985) have extended the
notion of classical bent Boolean functions in the generalized setup
on \BBZ_q^n. They have provided an analogue of classical
Maiorana-McFarland type bent functions. In this paper, we study the
crosscorrelation of a subclass of such generalized
Maiorana-McFarland (\mbox{GMMF}) type bent functions. We provide a
construction of quaternary (q=4) bent functions on n+1
variables in terms of their subfunctions on n-variables. Analogues
of sum-of-squares indicator and absolute indicator of
crosscorrelation of Boolean functions are defined in the generalized
setup. Further, q-ary functions are studied in terms of these
indictors and some upper bounds of these indicators are obtained.
Finally, we provide some constructions of balanced quaternary
functions with high nonlinearity under Lee metric