Correlation immune functions with respect to the q-transform

Abstract

Correlation immunity is a measure of resistance to Siegenthaler’s divide and conquer attack on nonlinear combiners. In this work, we study functions with regard to the q-transform, a generalization of the Walsh-Hadamard transform, that measures the proximity of a function to the set of functions obtained from a function q(x) by linear base change. We propose two notions of q-correlation immune functions and study their relationship between them. We also analyze certain properties of these functions and present some techniques to design these functions.