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

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