We address the insecurity problem for cryptographic protocols, for an
active intruder and a bounded number of sessions. By modeling the
intruder abilities as an equational theory, the problem of active
intrusion is formulated as a Cap Unification problem. Cap Unification
is an extension of Equational Unification: we look for a cap to be
placed on a given set of terms, so that it unifies with a given term
modulo the equational theory. We give a decision procedure for Cap
Unification when the equational theory represents the traditional
Dolev Yao abilities, with some additional assumptions satisfied by usual
protocols. In addition, we try to extend our result to the case of
Homomorphic Encryption. We give an algorithm solving the
E-unification problem for the theory of Homomorphic Encryption, and we
discuss how this could be extended to Cap Unification.