ENUMERATING BOOLEAN FUNCTIONS Page 1 ENUMERATING BOOLEAN FUNCTIONS OF CRYPTOGRAPHIC SIGNIFICANCE

In this paper we describe applications of functions from GF(2) m onto GF(2) n in the design of encryption algorithms. If such a function is to be useful it must satisfy a set of criteria, the actual definition of which depends on the type of encryption technique involved. This in turn means that it is important to ensure that the selected criteria do not restrict the choice of function too severely, i.e. the set of functions must be enumerated. We discuss some of the possible sets of criteria and then give partial results on the corresponding enumeration problems. Many open problems remain, some of them corresponding to well known hard enumeration questions.