  A model-theoretic approach can establish security theorems for cryptographic
protocols. Formulas expressing authentication and non-disclosure properties of
protocols have a special form. They are quantified implications for all xs .
(phi implies for some ys . psi). Models (interpretations) for these formulas
are *skeletons*, partially ordered structures consisting of a number of local
protocol behaviors. Realized skeletons contain enough local sessions to explain
all the behavior, when combined with some possible adversary behaviors. We show
two results. (1) If phi is the antecedent of a security goal, then there is a
skeleton A_phi such that, for every skeleton B, phi is satisfied in B iff there
is a homomorphism from A_phi to B. (2) A protocol enforces for all xs . (phi
implies for some ys . psi) iff every realized homomorphic image of A_phi
satisfies psi. Hence, to verify a security goal, one can use the Cryptographic
Protocol Shapes Analyzer CPSA (TACAS, 2007) to identify minimal realized
skeletons, or "shapes," that are homomorphic images of A_phi. If psi holds in
each of these shapes, then the goal holds.
