Paper 2024/004

Practical Two-party Computational Differential Privacy with Active Security

Abstract

In this work we revisit the problem of using general-purpose MPC schemes to emulate the trusted dataholder in central differential privacy, to achieve same accuracy but without the need to trust one single dataholder. In particular, we consider the two-party model of having two computational parties (or dataholders) each with their own dataset wishing to compute a canonical differentially private mechanism on their combined data and to do so with active security. We start by remarking that available definitions of computational DP (CDP) for protocols are somewhat ill-suited for such a use-case, due to them using formalisms that either are much weaker than one can typically get for MPC protocols, or they are too strict in the sense that they need significant adjustment in order to be realisable by using common DP and MPC techniques. With this in mind we propose a new version of simulation-based CDP, called SIM$^*$-CDP, specifically geared towards being easy to use for MPC practitioners and more closely capture guarantees granted by using state-of-the-art MPC schemes to compute standard DP mechanism. We demonstrate the merit of the SIM$^*$-CDP definition by showing how to satsify it by use of an available distributed protocol for sampling truncated geometric noise. Further, we use the protocol to compute two-party inner products with computational DP and with similar levels of accuracy as in the central model, being the first to do so. Finally, we provide an open-sourced implementation and benchmark its practical performance.

Note: Major rewrite centered around reformulations of the main definitions and increased clarity and nuance in discussion thereof.