Autocorrelation properties of correlation immune Boolean functions

Abstract

In this paper we study the autocorrelation values of correlation immune and resilient Boolean functions. We provide new lower bounds and related results on absolute indicator and sum of square indicator of auto correlation values for low orders of correlation immunity. Recently it has been identified that the nonlinearity and algebraic degree of the correlation immune and resilient functions are optimized simultaneously. Our analysis shows that in such a scenario the sum of square indicator attains its minimum value too. We also point out the weakness of two recursive construction techniques for resilient functions in terms of auto correlation values.