Spatial Bloom Filters: Enabling Privacy in Location-Aware Applications

The wide availability of inexpensive positioning systems made it possible to embed them into smartphones and other personal devices. This marked the beginning of location-aware applications, where users request personalized services based on their geographic position. The location of a user is, however, highly sensitive information: the user's privacy can be preserved if only the minimum amount of information needed to provide the service is disclosed at any time. While some applications, such as navigation systems, are based on the users' movements and therefore require constant tracking, others only require knowledge of the user's position in relation to a set of points or areas of interest. In this paper we focus on the latter kind of services, where location information is essentially used to determine membership in one or more geographic sets. We address this problem using Bloom Filters (BF), a compact data structure for representing sets. In particular, we present an extension of the original Bloom filter idea: the Spatial Bloom Filter (SBF). SBF's are designed to manage spatial and geographical information in a space efficient way, and are well-suited for enabling privacy in location-aware applications. We show this by providing two multi-party protocols for privacy-preserving computation of location information, based on the known homomorphic properties of public key encryption schemes. The protocols keep the user's exact position private, but allow the provider of the service to learn when the user is close to specific points of interest, or inside predefined areas. At the same time, the points and areas of interest remain oblivious to the user

Efficient information theoretic multi-party computation from oblivious linear evaluation

Oblivious linear evaluation (OLE) is a two party protocol that allows a receiver to compute an evaluation of a sender’s private, degree 1 polynomial, without letting the sender learn the evaluation point. OLE is a special case of oblivious polynomial evaluation (OPE) which was first introduced by Naor and Pinkas in 1999. In this article we utilise OLE for the purpose of computing multiplication in multi-party computation (MPC). MPC allows a set of n mutually distrustful parties to privately compute any given function across their private inputs, even if up to t < n of these participants are corrupted and controlled by an external adversary. In terms of efficiency and communication complexity, multiplication in MPC has always been a large bottleneck. The typical method employed by most current protocols has been to utilise Beaver’s method, which relies on some precomputed information. In this paper we introduce an OLE-based MPC protocol which also relies on some precomputed information. Our proposed protocol has a more efficient communication complexity than Beaver’s protocol by a multiplicative factor of t. Furthermore, to compute a share to a multiplication, a participant in our protocol need only communicate with one other participant; unlike Beaver’s protocol which requires a participant to contact at least t other participants

Multiparty Proximity Testing with Dishonest Majority from Equality Testing

Motivated by the recent widespread emergence of location-based services (LBS) over mobile devices, we explore efficient protocols for proximity-testing. Such protocols allow a group of friends to discover if they are all close to each other in some physical location, without revealing their individual locations to each other. We focus on hand-held devices and aim at protocols with very small communication complexity and a small number of rounds. The proximity-testing problem can be reduced to the private equality testing (PET) problem, in which parties find out whether or not they hold the same input (drawn from a low-entropy distribution) without revealing any other information about their inputs to each other. While previous works analyze the 2-party PET special case (and its LBS application), in this work we consider highly-efficient schemes for the multiparty case with no honest majority. We provide schemes for both a direct-communication setting and a setting with a honest-but-curious mediating server that does not learn the users ’ inputs. Our most efficient scheme takes 2 rounds, where in each round each user sends only a couple of ElGamal ciphertexts.

Unconditionally secure distributed oblivious polynomial evaluation

Oblivious polynomial evaluation (OPE) was first introduced by Naor and Pinkas in 1999. An OPE protocol involves a receiver, R who holds a value, α and a sender, S with a private polynomial, f(x). OPE allows R to compute f(α) without revealing either α or f(x). Since its inception, OPE has been established as an important building block in many distributed applications. In this article we investigate a method of achieving unconditionally secure distributed OPE (DOPE) in which the function of the sender is distributed amongst a set of n servers. Specifically, we introduce a model for DOPE based on the model for distributed oblivious transfer (DOT) described by Blundo et al. in 2002. We then describe a protocol that achieves the security defined by our model. Our DOPE protocol is efficient and achieves a high level of security. Furthermore, our proposed protocol can also be used as a DOT protocol with little to no modification