New characterizations for the multi-output correlation-immune Boolean functions

Abstract

Correlation-immune (CI) multi-output Boolean functions have the property of keeping the same output distributions when some input variables are fixed. Recently, a new application of CI functions has appeared in the system of resisting side-channel attacks (SCA). In this paper, three new methods are proposed to characterize the tth-order CI multi-output (n-input and m-output) Boolean functions. The first characterization is to regard the multi-output Boolean functions as the corresponding generalized Boolean functions. It is shown that a generalized Boolean function fg is a tth-order CI function if and only if the Walsh transform of fg defined here vanishes at all points with Hamming weights between 1 and t. The last two methods are generalized from Fourier spectral characterizations. Especially, Fourier spectral characterizations are efficient to characterize the symmetric multi-output CI Boolean functions.