Distributed computing has been widely applied in distributed edge networks for reducing the processing burden of high-dimensional data centralization, where a high-dimensional computational task is decomposed into multiple low-dimensional collaborative processing tasks or multiple edge nodes use distributed data to train a global model. However, the computing power of a single-edge node is limited, and collaborative computing will cause information leakage and excessive communication overhead. In this paper, we design a parallel collaborative distributed alternating direction method of multipliers (ADMM) and propose a three-phase parallel collaborative ADMM privacy computing (3P-ADMM-PC2) algorithm for distributed computing in edge networks, where the Paillier homomorphic encryption is utilized to protect data privacy during interactions. Especially, a quantization method is introduced, which maps the real numbers to a positive integer interval without affecting the homomorphic operations. To address the architectural mismatch between large-integer and Graphics Processing Unit (GPU) computing, we transform high-bitwidth computations into low-bitwidth matrix and vector operations. Thus the GPU can be utilized to implement parallel encryption and decryption computations with long keys. Finally, a GPU-accelerated 3P-ADMM-PC2 is proposed to optimize the collaborative computing tasks. Meanwhile, large-scale computational tasks are conducted in network topologies with varying numbers of edge nodes. Experimental results demonstrate that the proposed 3P-ADMM-PC2 has excellent mean square error performance, which is close to that of distributed ADMM without privacy-preserving. Compared to centralized ADMM and distributed ADMM implemented with Central Processing Unit (CPU) computation, the proposed scheme demonstrates a significant speedup ratio.

翻译：分布式计算已被广泛应用于分布式边缘网络，以减轻高维数据集中化处理负担，其通常将高维计算任务分解为多个低维协同处理任务，或由多个边缘节点利用分布式数据训练全局模型。然而，单个边缘节点的计算能力有限，且协同计算易导致信息泄露与通信开销过大。本文设计了一种并行协同分布式交替方向乘子法（ADMM），并提出一种面向边缘网络分布式计算的三阶段并行协同ADMM隐私计算（3P-ADMM-PC2）算法，其中利用Paillier同态加密保护交互过程中的数据隐私。特别地，引入一种量化方法，在不影响同态运算的前提下将实数映射至正整数区间。针对大整数运算与图形处理器（GPU）计算之间的架构失配问题，我们将高比特宽度计算转换为低比特宽度的矩阵与向量运算。从而可利用GPU实现长密钥的并行加解密计算。最终，提出一种GPU加速的3P-ADMM-PC2算法以优化协同计算任务。同时，在具有不同数量边缘节点的网络拓扑中进行了大规模计算任务实验。结果表明，所提出的3P-ADMM-PC2算法具有优异的均方误差性能，其接近无隐私保护的分布式ADMM算法。与基于中央处理器（CPU）实现的集中式ADMM及分布式ADMM相比，本方案展现出显著的加速比。