Secondary constructions of highly nonlinear Boolean functions and disjoint spectra plateaued functions

摘要

In this paper, we modify a generalized indirect sum construction to construct functions with high nonlinearity. By utilizing the modified construction, highly nonlinear functions in (n + m) variables can be obtained from known bent functions in n variables and highly nonlinear functions in m variables. It is possible to obtain new (n + 15)-variable functions with nonlinearity 2~(n+15-1) - 2~(n+15-1)/2) + 20 × 2~(n/2) and new 12-variable 2-resilient functions with nonlinearity 2000 and algebraic degree 8, which achieve optimal algebraic immunity. Moreover, the modified construction can also be used as an iterative construction of a quadruple of disjoint spectra plateaued functions. In addition, we present sufficient conditions for a quadruple of disjoint spectra plateaued functions to have no nonzero linear structure.