Secure Noise Sampling for DP in MPC with Finite Precision

While secure multi-party computation (MPC) protects the privacy of inputs and intermediate values of a computation, differential privacy (DP) ensures that the output itself does not reveal too much about individual inputs. For this purpose, MPC can be used to generate noise and add this noise to the output. However, securely generating and adding this noise is a challenge considering real-world implementations on finite-precision computers, since many DP mechanisms guarantee privacy only when noise is sampled from continuous distributions requiring infinite precision. We introduce efficient MPC protocols that securely realize noise sampling for several plaintext DP mechanisms that are secure against existing precision-based attacks: the discrete Laplace and Gaussian mechanisms, the snapping mechanism, and the integer-scaling Laplace and Gaussian mechanisms. Due to their inherent trade-offs, the favorable mechanism for a specific application depends on the available computation resources, type of function evaluated, and desired ( µ, d)-DP guarantee. The benchmarks of our protocols implemented in the state-of-the-art MPC framework MOTION (Braun et al., TOPS'22) demonstrate highly efficient online runtimes of less than 32 ms/query and down to about 1ms/query with batching in the two-party setting. Also the respective offline phases are practical, requiring only 51 ms to 5.6 seconds/query depending on the batch size.