Soundness of Symbolic Equivalence for Modular Exponentiation

Yassine Lakhnech (1) , Laurent Mazare (1) , Bogdan Warinschi (2)

1 VERIMAG - IMAG - VERIMAG
2 CASSIS - Combination of approaches to the security of infinite states systems

In this paper, we study the Dynamic Decisional Diffie-Hellman (3DH) problem, a powerful generalization of the Decisional Diffie-Hellman (DDH) problem. Our main result is that DDH implies 3DH. This result leads to significantly simpler proofs for protocols by relying directly on the more general problem. Our second contribution is a computationally sound symbolic technique for reasoning about protocols that use symmetric encryption and modular exponentiation. We show how to apply our results in the case of the Burmester & Desmedt protocol.

Mots clés: Diffie-Hellman assumptions; soundness of formal encryption; provable security

Domaines: Cryptographie et sécurité [cs.CR]

Yassine Lakhnech, Laurent Mazare, Bogdan Warinschi. Soundness of Symbolic Equivalence for Modular Exponentiation. Workshop on Formal and Computational Cryptography - FCC 2006, Véronique Cortier et Steve Kremer, Jul 2006, Venice/Italy. ⟨inria-00080673⟩