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Multiparty Reach and Frequency Histogram: Private, Secure, and Practical

Abstract Consider the setting where multiple parties each hold a multiset of users and the task is to estimate the reach (i.e., the number of distinct users appearing across all parties) and the frequency histogram (i.e., fraction of users appearing a given number of times across all parties). In this work we introduce a new sketch for this task, based on an exponentially distributed counting Bloom filter. We combine this sketch with a communication-efficient multi-party protocol to solve the task in the multi-worker setting. Our protocol exhibits both differential privacy and security guarantees in the honest-but-curious model and in the presence of large subsets of colluding workers; furthermore, its reach and frequency histogram estimates have a provably small error. Finally, we show the practicality of the protocol by evaluating it on internet-scale audiences.