BLIP: Non-interactive Differentially-Private Similarity Computation on Bloom Filters

International audienceIn this paper, we consider the scenario in which the profile of a user is represented in a compact way, as a Bloom filter, and the main objective is to privately compute in a distributed manner the similarity between users by relying only on the Bloom filter representation. In particular, we aim at providing a high level of privacy with respect to the profile even if a potentially unbounded number of similarity computations take place, thus calling for a non-interactive mechanism. To achieve this, we propose a novel non-interactive differentially private mechanism called BLIP (for BLoom-and-flIP) for randomizing Bloom filters. This approach relies on a bit flipping mechanism and offers high privacy guarantees while maintaining a small communication cost. Another advantage of this non-interactive mechanism is that similarity computation can take place even when the user is offline, which is impossible to achieve with interactive mechanisms. Another of our contributions is the definition of a probabilistic inference attack, called the ''Profile Reconstruction attack'', that can be used to reconstruct the profile of an individual from his Bloom filter representation. More specifically, we provide an analysis of the protection offered by BLIP against this \mbox{profile reconstruction} attack by deriving an upper and lower bound for the required value of the differential privacy parameter $\epsilon$