A New Protocol for the Nearby Friend Problem

Abstract

The question of location privacy has gained a special significance in the context of location-based services for mobile devices. The challenge is to allow the users to benefit from location-based services without disclosing their private location information unless necessary and that too only to the party eligible to receive that information. In this work, we investigate the so-called nearby friend problem. The problem has emerged in the context of location-based services such as social networking and is closely related to the issue of location privacy. In particular, we are interested in the question of how Alice can efficiently determine whether a friend Bob is at a nearby location or not. This has to be achieved without a third party and where Alice neither reveals any information about her own location nor can she extract any information about Bob’s actual location when they are not nearby. Similarly, no eavesdropper should be able to gain any information about their actual locations, whether they are actually nearby or not. The problem becomes more challenging as both Alice and Bob are restricted in computational power and communication bandwidth. Starting from an earlier work by Zhong et al., we formalize the protocol definition and the security model and then propose a new protocol that solves the problem in the proposed security model. An interesting feature of the protocol is that it does not depend on any other cryptographic primitive, thus providing a new approach to solve the nearby friend problem. Our basic protocol and its extensions compare favorably with the earlier solutions for this problem. The protocol might be of use in other privacy-preserving applications.