CED2: Communication Efficient Disjointness Decision

Enforcing security often requires the two legitimate parties of a communication to determine whether they share a secret, without disclosing information (e.g. the shared secret itself, or just the existence of such a secret) to third parties—or even to the other party, if it is not the legitimate party but an adversary pretending to impersonate the legitimate one. In this paper, we propose CED2 (Communication Efficient Disjointness Decision), a probabilistic and distributed protocol that allows two parties—each one having a finite set of elements—to decide about the disjointness of their sets. CED2 is particularly suitable for devices having constraints on energy, communication, storage, and bandwidth. Examples of these devices are satellite phones, or nodes of wireless sensor networks. We show that CED2 significantly improves the communication cost compared to the state of the art, while providing the same degree of privacy and security. Analysis and simulations support the findings.