Helmut Seidl and Kumar Neeraj Verma. Flat and one-variable clauses: Complexity of verifying cryptographic protocols with single blind copying. ACM Trans. Comput. Log., 9(4), 2008.
Cryptographic protocols with single blind copying were defined and modeled by Comon and Cortier using the new class of first-order clauses. They showed its satisfiability problem to be in 3-DEXPTIME. We improve this result by showing that satisfiability for this class is NEXPTIME-complete, using new resolution techniques. We show satisfiability to be DEXPTIME-complete if clauses are Horn, which is what is required for modeling cryptographic protocols. While translation to Horn clauses only gives a DEXPTIME upper bound for the secrecy problem for these protocols, we further show that this secrecy problem is actually DEXPTIME-complete.
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