Construction of cryptographically important Boolean functions

Abstract

Boolean functions are used as nonlinear combining functions in certain stream ciphers. 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. Maitra and Pasalic [3] have constructed 8-variable 1-resilient Boolean functions with nonlinearity 116. Their technique interlinks mathematical results with classical computer search. In this paper we describe a new technique to construct 8-variable 1-resilient Boolean functions with the same nonlinearity. Using a similar technique, we directly construct 10-variable (resp. 12-variable), 1-resilient functions with nonlinearity 488 (resp. 1996). Finally, we describe some results on the construction of n-variable t-resilient functions with maximum nonlinearity.