Abstract: The present disclosure provides practical communication-efficient and low-error algorithms for aggregation of private data. For example, the proposed algorithms can be implemented in the shuffled DP model. Specific example operations that can be performed using the proposed algorithms include summation (e.g., binary summation, integer summation) and histograms over a moderate number of buckets. The proposed algorithms achieve accuracy that is arbitrarily close to that of central DP algorithms with an expected communication per user essentially matching what is needed without any privacy constraints.