Cap Unification: Application to Protocol Security modulo Homomorphic Encryption
Résumé
We address the insecurity problem for cryptographic protocols, for an active intruder and a bounded number of sessions. The protocol steps are modeled as rigid Horn clauses, and the intruder abilities as an equational theory. The problem of active intrusion -- such as whether a secret term can be derived, possibly via interaction with the honest participants of the protocol -- is then formulated as a Cap Unification problem. Cap Unification is an extension of Equational Unification: look for a cap to be placed on a given set of terms, so as to unify it with a given term modulo the equational theory. We give a decision procedure for Cap Unification, when the intruder capabilities are modeled as homomorphic encryption theory. Our procedure can be employed in a simple manner to detect attacks exploiting some properties of block ciphers.