Establishing and preserving protocol security goals

We take a model-theoretic viewpoint on security goals and how to establish them. The models are (possibly fragmentary) executions. Security goals such as authentication and confidentiality are implications over the geometric fragment of predicate logic, i.e. implications Φ −→ Ψ where Φ and Ψ are built from atomic formulas without negations, implications, or universal quantifiers. Security goals are then essentially statements about homomorphisms where the source is a minimal (fragmentary) model of the antecedent Φ. If every homomorphism to a model representing a non-fragmentary, complete execution factors through a model in which Ψ is satisfied, then the goal is achieved. This idea suggests validating security goals via a process of information enrichment. This idea also clarifies protocol transformation. A protocol transformation preserves security goals when it preserves the form of the information enrichment process. We formalize this idea using simulation relations between labeled transition systems.