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When collecting information, local differential privacy (LDP) alleviates privacy concerns of users because their private information is randomized before being sent it to the central aggregator. LDP imposes large amount of noise as each user executes the randomization independently. To address this issue, recent work introduced an intermediate server with the assumption that this intermediate server does not collude with the aggregator. Under this assumption, less noise can be added to achieve the same privacy guarantee as LDP, thus improving utility for the data collection task. This paper investigates this multiple-party setting of LDP. We analyze the system model and identify potential adversaries. We then make two improvements: a new algorithm that achieves a better privacy-utility tradeoff; and a novel protocol that provides better protection against various attacks. Finally, we perform experiments to compare different methods and demonstrate the benefits of using our proposed method. 

Multi-dimensional analytical (MDA) queries are often issued against a fact table with predicates on (categorical or ordinal) dimensions and aggregations on one or more measures. In this paper, we study the problem of answering MDA queries under local differential privacy (LDP). In the absence of a trusted agent, sensitive dimensions are encoded in a privacy preserving (LDP) way locally before being sent to the data collector. The data collector estimates the answers to MDA queries, based on the encoded dimensions. We propose several LDP encoders and estimation algorithms, to handle a large class of MDA queries with different types of predicates and aggregation functions. Our techniques are able to answer these queries with tight error bounds and scale well in high-dimensional settings (i.e., error is polylogarithmic in dimension sizes). We conduct experiments on real and synthetic data to verify our theoretical results, and compare our solution with marginal-estimation based solutions.