Construction of Cryptographically Significant Boolean Functions

摘要

Boolean functions have many applications in computer security practices including the construction of key stream generators based on a set of shift registers. A Boolean function is said to be correlation immune if its output leaks no information about its input values. Balanced correlation immune functions are called resilient functions. Finding methods for easy construction of resilient functions with additional properties is an active research area. In this paper we present a strategy to construct 1-resilient Boolean functions with very good nonlinearity and autocorrelation. Our strategy to construct an 1-resilient function is based on modifying a bent function, by toggling some of its output bits. In particular, the technique is applied to 8 and 10-variable functions and we show that the construction provides 1-resilient functions reaching currently best known nonlinearity and achieving very low autocorrelation values which were not known earlier.