Enumerative encoding of correlation-immune Boolean functions

Le Bars and Viola have recently proposed an innovative recursive decomposition of the first-order correlation-immune Boolean functions. Based on their work this paper presents the design of an enumerative encoding of these Boolean functions. This is the first enumerative encoding of a class of Boolean functions defined by a cryptographic property. In this paper we study three major milestones to do this encoding: the conceptual computational tree, the use of normal classes and signed permutations, and a dynamic selection of the decomposition. Our enumerative encoding algorithm is practicable up to 8 variables which is the best result we may expect due to the combinatorial explosion of the numbers of classes.