Analog Multi-Party Computing: Locally Differential Private Protocols for Collaborative Computations

We consider a fully decentralized scenario in which no central trusted entity exists and all clients are honest-but-curious. The state-of-the-art approaches to this problem often rely on cryptographic protocols, such as multiparty computation (MPC), that require mapping real-valued data to a discrete alphabet, specifically a finite field. These approaches, however, can result in substantial accuracy losses due to computation overflows. To address this issue, we propose A-MPC, a private analog MPC protocol that performs all computations in the analog domain. We characterize the privacy of individual datasets in terms of $(\epsilon, \delta)$-local differential privacy, where the privacy of a single record in each client's dataset is guaranteed against other participants. In particular, we characterize the required noise variance in the Gaussian mechanism in terms of the required $(\epsilon,\delta)$-local differential privacy parameters by solving an optimization problem. Furthermore, compared with existing decentralized protocols, A-MPC keeps the privacy of individual datasets against the collusion of all other participants, thereby, in a notably significant improvement, increasing the maximum number of colluding clients tolerated in the protocol by a factor of three compared with the state-of-the-art collaborative learning protocols. Our experiments illustrate that the accuracy of the proposed $(\epsilon,\delta)$-locally differential private logistic regression and linear regression models trained in a fully-decentralized fashion using A-MPC closely follows that of a centralized one performed by a single trusted entity.