Optimal Proximity Proofs

Abstract

Abstract. Provably secure distance-bounding is a rising subject, yet an unsettled one; indeed, very few distance-bounding protocols, with formal security proofs, have been proposed. In fact, so far only two protocols, namely SKI (by Boureanu et al.) and FO (by Fischlin and Onete), offer all-encompassing security guaranties, i.e., resistance to distance-fraud, mafia-fraud, and terrorist-fraud. Matters like security, alongside with soundness, or added tolerance to noise do not always coexist in the (new) distance-bounding designs. Moreover, as we will show in this paper, efficiency and simultaneous protection against all frauds seem to be rather conflicting matters, leading to proposed solutions which were/are sub-optimal. In fact, in this recent quest for provable security, efficiency has been left in the shadow. Notably, the tradeoffs between the security and efficiency have not been studied. In this paper, we will address these limitations, setting the "security vs. efficiency" record straight. Concretely, by combining ideas from SKI and FO, we propose symmetric protocols that are efficient, noise-tolerant and-at the same time-provably secure against all known frauds. Indeed, our new distancebounding solutions outperform the two aforementioned provably secure distance-bounding protocols. For instance, with a noise level of 5%, we obtain the same level of security as those of the pre-existent protocols, but we reduce the number of rounds needed from 181 to 54.

Sound Proof of Proximity of Knowledge

“…To compare with the literature, we could see that terrorist frauds in our model make the secret leak instead of only making man-in-the-middle attack feasible as in the notion of collusion fraud proposed in [6,8,9], and on which the SKI protocol is based, or only making impersonation attack feasible as in [10]. Our soundness is thus stronger.…”

“…We adopt the multiparty setting from [10] and only adapt it to accommodate public-key distance bounding. We consider a setting with participants which are called either provers, verifiers, or other actors.…”

“…Then, two parallel models were developed: the BMV model [6,8,9] and the DFKO model [16]. There exist many symmetric distance-bounding protocols but so far only the SKI protocol [5,6,7,9] (based on the BMV model), the Fischlin-Onete (FO) protocol [18] (based on the DFKO model), and DB1, DB2, and their extensions [10,24] (combining both SKI and FO in the BMV model) provide an all-encompassing proven security.…”

“…-We adapt the framework of [10] in the BMV model to provide a full formalization of public-key distance-bounding. We specify our new primitive: the proof of proximity of knowledge (PoPoK).…”

“…We specify our new primitive: the proof of proximity of knowledge (PoPoK). -We change the definition of soundness from [10] and [25] to make it closer to the one of interactive proofs. So, our model is pretty natural and nicely connects recent work on distance bounding (such as the BMV model [6,8,9]) and interactive proofs.…”