An LDP Compatible Sketch for Securely Approximating Set Intersection Cardinalities

Given two sets of elements held by two different parties separately, computing the cardinality (i.e., the number of distinct elements) of their intersection set is a fundamental task in applications such as network monitoring and database systems. To handle large sets with limited space, computation, and communication costs, lightweight probabilistic methods (i.e., sketch methods) such as the Flajolet-Martin (FM) sketch and the HyperLogLog (HLL) sketch are extensively used. However, when a set's probabilistic data summary and the hash functions used to construct the sketch are disclosed to an untrusted third party, the set's privacy is compromised. Directly applyingLocal Differential Privacy (LDP) techniques to safeguard the sketch collection results in extremely large estimation errors of set intersection cardinalities. To address this issue, we propose a novel sketch method that makes it easier to incorporate noise into the constructed sketch to achieve differential privacy. More importantly, our sketch method is compatible with the LDP noise. In other words, the probabilistic model underlying our LDP-based data summary is quite basic, allowing us to eliminate the estimation error generated by the noise. We perform extensive experiments on various synthetic and real-world datasets and the experimental results demonstrate that our method is orders of magnitude more accurate and several times faster than state-of-the-art methods.