Undecidability of bounded security protocols

Using a multiset rewriting formalism with existen-tial quantiication, it is shown that protocol security remains undecidable even when rather severe restrictions are placed on protocols. In particular, even if data constructors, message depth, message width, number of distinct roles, role length, and depth of encryp-tion are bounded by constants, secrecy is an undecidable property. If protocols are further restricted to have no new data (nonces), then secrecy is dexptime-complete. Both lower bounds are obtained by encoding decision problems from existential Horn theories without function symbols into our protocol framework. The way that encryption and adversary behavior are used in the reduction sheds some light on protocol analysis.