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，其中不存在任何中心化可信实体，且所有客户端均为诚实但好奇的。当前处理该问题的最先进方法通常依赖于密码学协议，例如需要将实值数据映射到离散字母表（特别是有限域）的多方计算（MPC）。然而，这些方法可能因计算溢出而导致显著的精度损失。为解决此问题，我们提出A-MPC（一种私有模拟MPC协议），该协议在模拟域中执行所有计算。我们使用$(\epsilon, \delta)$-局部差分隐私来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对其他参与者得到保障。特别地，我们通过求解优化问题，以所需$(\epsilon,\delta)$-局部差分隐私参数的形式刻画高斯机制中的噪声方差。此外，与现有去中心化协议相比，A-MPC能够保护个体数据集免受所有其他参与方共谋的攻击，从而显著提升协议能容忍的最大共谋客户端数量——相较于最先进的协作学习协议，提升了三倍。实验表明，使用A-MPC以完全去中心化方式训练的$(\epsilon,\delta)$-局部差分隐私逻辑回归和线性回归模型的精度，与由单一可信实体执行的集中式训练模型精度高度一致。