Extensions to Athena: Constraint Satisfiability Problem and New Pruning Theorems Based on Type System Extensions for Messages

This is a writeup of some extensions to the strand space algorithm Athena [2]. In particular, I formulate an open problem within the Athena algorithm of whether the splitting step is decidable in full generality. 1 The Terms and the Type System We assume the reader’s familiarity with the concepts in our original Athena paper [2], and we skip most of the introductions and motivations, except for those that directly concern the subject of this writeup. First, the reason for the type extension is to generalize the two pruning theorems from our paper and replace them with only one rule. As a bonus, we hope that this more general rule will be sound for arbitrary penetrator model. Since the SyMP implementation of Athena [1] allows user-defined penetrators, this is our primary motivation for the extension. Without it, protocols with user-defined penetrators will only be able to use the three basic rules (init, nal, and split), and most likely end up in an infinite expansion of obviously contradictory states. The type system is a collection of types with the subtyping relation forming a lattice with the largest element Message. The types listed in Figure 1 as sub-items of another type are its immediate subtypes, but incomparable with each other. Some types have parameter types, for instance En rypted takes another type as a parameter. The subtyping relation for such types with different parameters is determined according to the subtyping relation of their parameters. The precise subtyping relation is given in Figure 2.