Systems and methods for determining the union of the set of user identifiers across multiple publishers are described. Each publisher computing device can use a list of hash functions to hash the respective set of de-duplicated user identifiers. Each publisher can assemble a vector of counts using the respective hashed set of user identifiers, where each coordinate in the vector of counts corresponds to a select of bit positions from the hashed set of user identifiers. Each publisher can add noise to each of the vector of counts to enhance the privacy of the system. Each publisher can transmit the respective vector of counts to a server to compute the union of the multiset without exposing any private or protected information about the user identifiers to any third-party. The server can compute the union of the sets described by the vectors of counts from each of the publishers using at least one of the methods described herein.

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This work is licensed under a Creative Commons Attribution 4.0 License.