Applying the Shuffle Model of Differential Privacy to Vector Aggregation

In this work we introduce a new protocol for vector aggregation in the context of the Shuffle Model, a recent model within Differential Privacy (DP). It sits between the Centralized Model, which prioritizes the level of accuracy over the secrecy of the data, and the Local Model, for which an improvement in trust is counteracted by a much higher noise requirement. The Shuffle Model was developed to provide a good balance between these two models through the addition of a shuffling step, which unbinds the users from their data whilst maintaining a moderate noise requirement. We provide a single message protocol for the summation of real vectors in the Shuffle Model, using advanced composition results. Our contribution provides a mechanism to enable private aggregation and analysis across more sophisticated structures such as matrices and higher-dimensional tensors, both of which are reliant on the functionality of the vector case.