View article

Since their introduction by Rothaus in 1976 [4], bent functions played an important role in the security of cryptographic systems. As functions which have a maximum Hamming distance from the set of affine functions, they are extensively used to achieve nonlinearity of S-boxes for block and stream ciphers. While the theory behind bent functions is substantially developed [3],[5], their enumeration is difficult even for a small number of variables (listed for n≤ 6). Bent functions are rare and they are found by sieving on a large number of prospective Boolean functions or constructed by various methods, such as the iterative Maiorana-McFarland method. This work observes the use of the novel sieving technique based on the Binary Decision Diagram (BDD) representation of Boolean functions. The BDD structure was introduced by Akers [1], and gained true popularity with Bryant’s work [2]. It is distinguished for compact representation of Boolean functions and for efficient manipulation with them. The BDD stands as a variant of the directed acyclic graph with two terminal vertices and efficiently represents a truth table of Boolean functions by encoding their values as paths from the top vertex to terminal vertices. Many variations of BDDs are developed for different purposes, for example, the Zero Decision Diagram (ZDD) to represent combinatorial sets. Herein we use the Reduced Ordered BDD (ROBDD) structure which is a canonical representation of Boolean functions, ie under certain conditions the Boolean function has only one representation with the ROBDD graph. It is an established fact that the total number of Boolean functions with n-variables is …