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.

翻译：我们考虑一个完全去中心化的场景，其中不存在任何可信中心实体，且所有客户端均为诚实但好奇的。当前解决该问题的主流方法通常依赖密码学协议（如多方计算），这些协议需要将实值数据映射到离散字母表（具体为有限域）。然而，此类方法因计算溢出可能导致显著的精度损失。为解决该问题，我们提出A-MPC——一种在模拟域中执行全部计算的私有模拟多方计算协议。我们基于$(\epsilon, \delta)$-本地差分隐私刻画个体数据集的隐私性，其中每个客户端数据集中单条记录的隐私性受到针对其他参与方的保证。具体而言，我们通过求解优化问题，以所需$(\epsilon,\delta)$-本地差分隐私参数来表征高斯机制中的噪声方差。此外，相较于现有去中心化协议，A-MPC能够抵御其他所有参与方合谋对个体数据集隐私的威胁，因此，在协议中允许合谋客户端的最大数量相比当前最先进的协作学习协议提升了三倍，这一改进极为显著。实验表明，使用A-MPC以完全去中心化方式训练的$(\epsilon,\delta)$-本地差分隐私逻辑回归与线性回归模型的精度，紧密跟随由单个可信实体执行的集中式模型精度。