A Maiorana–McFarland type construction for resilient Boolean functions on n variables (n even) with nonlinearity >2n-1-2n/2+2n/2-2

AbstractIn 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 2n-1-2n/2+2n/2-2. Here, we show that given any m, one can construct n-variable, m-resilient functions with nonlinearity 2n-1-11·2n/2-4 for all n⩾8m+6 which is strictly greater than 2n-1-2n/2+2n/2-2. We also demonstrate that in some specific cases one may get such nonlinearity even for some values of n, where n