Intruder Deduction for the Equational Theory of Exclusive-or with Commutative and Distributive Encryption

Pascal Lafourcade (1)

1 Institute of Information Security [ETH Zürich]

The first step in the verification of cryptographic protocols is to decide the intruder deduction problem, that is the vulnerability to a so-called passive attacker. We extend the Dolev-Yao model in order to model this problem in presence of the equational theory of a commutative encryption operator which distributes over the exclusive-or operator. The interaction between the commutative distributive law of the encryption and exclusive-or offers more possibilities to decrypt an encrypted message than in the non-commutative case, which imply a more careful analysis of the proof system. We prove decidability of the intruder deduction problem for a commutative encryption which distributes over exclusive-or with a DOUBLE-EXP-TIME procedure. And we obtain that this problem is EXPSPACE-hard in the binary case.

Domaines: Cryptographie et sécurité [cs.CR]

Pascal Lafourcade. Intruder Deduction for the Equational Theory of Exclusive-or with Commutative and Distributive Encryption. Electronic Notes in Theoretical Computer Science, 2007, 171 (4), pp.37 - 57. ⟨10.1016/j.entcs.2007.02.054⟩. ⟨hal-01759944⟩