A Maiorana–McFarland type construction for resilient Boolean functions on n variables (n even) with nonlinearity image Original Research Article

In this paper, we present a construction method of m-resilient Boolean functions with very high nonlinearity for low values of m. The construction only considers functions in even number of variables n. So far the maximum nonlinearity attainable by resilient functions was image. Here, we show that given any m, one can construct n-variable, m-resilient functions with nonlinearity image for all image which is strictly greater than image. We also demonstrate that in some specific cases one may get such nonlinearity even for some values of n, where image. Further, we show that for sufficiently large n, it is possible to get such functions with nonlinearity reaching almost image. This is the upper bound on nonlinearity when one uses our basic construction recursively. Lastly, we discuss the autocorrelation property of the functions and show that the maximum absolute value in the autocorrelation spectra is image.