Private Sampling with Identifiable Cheaters

In this paper we study verifiable sampling from probability distributions in the context of multi-party computation. This has various applications in randomized algorithms performed collaboratively by parties not trusting each other. One example is differentially private machine learning where noise should be drawn, typically from a Laplace or Gaussian distribution, and it is desirable that no party can bias this process. In particular, we propose algorithms to draw random numbers from uniform, Laplace, Gaussian and arbitrary probability distributions, and to verify honest execution of the protocols through zero-knowledge proofs. We propose protocols that result in one party knowing the drawn number and protocols that deliver the drawn random number as a shared secret.