Intruder Deductions, Constraint Solving and Insecurity Decision in Presence of Exclusive or

We present decidability results for the verification ofcryptographic protocols in the presence of equational theoriescorresponding to xorand Abelian groups. Since theperfect cryptography assumption is unrealistic for cryptographicprimitives with visible algebraic properties such asxor, we extend the conventional Dolev-Yao model by permittingthe intruder to exploit these properties. We showthat the ground reachability problem in NP for the extendedintruder theories in the cases of xor and Abelian groups.This result follows from a normal proof theorem. Then, weshow how to lift this result in the xorcase: we consider asymbolic constraint system expressing the reachability (e.g.,secrecy) problem for a finite number of sessions. We provethat such constraint system is decidable, relying in particularon an extension of combination algorithms for unificationprocedures. As a corollary, this enables automaticsymbolic verification of cryptographic protocols employingxorfor a fixed number of sessions.