Position-Based Cryptography from Noisy Channels

Abstract

We study the problem of constructing secure positioning protocols (Sastry et. al, 2003). Informally, the goal of such protocols is to enable a party P to convince a set of verifiers about P’s location in space, using information about the time it takes P to respond to queries sent from different points. It has been shown by Chandran et al (2009) that in general such task is impossible to achieve if the adversary can position his stations in multiple points in space. Chandran et al proposed to overcome this impossibility result by moving to Maurer’s bounded-storage model. Namely, they construct schemes that are secure under the assumption that the memory of the adversary is bounded. Later Buhrman et al (2010) considered secure positioning protocols schemes in quantum settings.

In this paper we show how to construct secure positioning schemes in the so-called noisy channel scenario, i.e.: in the setting where the parties participating in a protocol have access to a source of random bits sent to them via independent noisy channels. We argue that for some practical applications such assumptions may be more realistic than those used before.

This work was supported by the WELCOME/2010-4/2 grant founded within the framework of the EU Innovative Economy (National Cohesion Strategy) Operational Programme.