Optimal Proximity Proofs Revisited

Distance bounding protocols become important since wireless technologies become more and more common. Therefore, the security of the distance bounding protocol should be carefully analyzed. However, most of the protocols are not secure or their security is proven informally. Recently, Boureanu and Vaudenay defined the common structure which is commonly followed by most of the distance bounding protocols: answers to challenges are accepted if they are correct and on time. They further analyzed the optimal security that we can achieve in this structure and proposed DBopt which reaches the optimal security bounds. In this paper, we define three new structures: when the prover registers the time of a challenge, when the verifier randomizes the sending time of the challenge, and the combined structure. Then, we show the optimal security bounds against distance fraud and mafia fraud which are lower than the bounds showed by Boureanu and Vaudenay for the common structure. Finally, we adapt the DBopt protocol according to our new structures and we get three new distance bounding protocols. All of them are proven formally. In the end, we compare the performance of the new protocols with DBopt and we see that we have a better efficiency. For instance, we can reduce the number of rounds in DB2 (one of the instances of DBopt) from $123$ to $5$ with the same security.