ABSTRACT
The functions f1(1), f2(1), f1(2), and f2(2) define a pair of BFs in three variables, which describe some CEs as a whole. If v = 0, then CE implements the S1 box substitution. If v = 1, then CE implements the S2 box substitution. In other words the controlling bit defines selection of the current elementary substitution operation (F.(0)2/1 or F.(1)2/1 modification of the F2/1 operation). The formulas shown in Figure 3.1d describe the selection of the current modification in some evident form. The formulas can be rewritten as follows:
Using some given topology of the Pn/m box and replacing the P2/1 units by F2/1 elements of different types, we can get different variants of the controlled operational boxes Fn/m performing transformations of different types, i.e., those that in a general case do not conserve the weight of the transformed binary vectors. A heterogeneous box Fn/m can be composed using elementary boxes F2/1 of several different types, for example, each active layer can be unique. Usually we consider the Fn/m boxes with uniform structure, which are built up using elementary boxes F2/1 of the single type, and nonuniform boxes constructed using two types of the CEs that represent mutual inverses F2/1 and F−12/1. The Fn/m boxes represent different types of the CSPNs built up using minimum size CEs.
