Secure comparison and secure selection are two fundamental MPC (secure Multi-Party Computation) protocols. One important application of these protocols is the secure ReLU and DReLU computation in privacy preserving deep learning. In this paper, we introduce G-module, a mathematics tool, to re-design such protocols. In mathematics, given a group G, a G-module is an abelian group M on which G acts compatibly with the abelian group structure on M. We design three secure protocols for three G-module operations. i.e. "G-module action", "Cross G-module action" and "G-module recover". As far as we know, this is the first work on secure G-module operations. Based on them, we design secure comparison, selection, ReLU and DReLU protocols, which improve communication efficiency by 2X to 10X compared with state of arts. Our protocols are very computation efficient too. They do not require public key operations or any other expensive operations.

中文翻译：

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G-module的MPC协议及其在安全比较和ReLU中的应用

安全比较和安全选择是两个基本的 MPC（安全多方计算）协议。这些协议的一个重要应用是在隐私保护深度学习中的安全 ReLU 和 DReLU 计算。在本文中，我们介绍了一种数学工具 G-module 来重新设计此类协议。在数学中，给定一个群 G，一个 G 模是一个阿贝尔群 M，其中 G 与 M 上的阿贝尔群结构兼容。我们为三个 G 模运算设计了三个安全协议。即“G-module action”、“Cross G-module action”和“G-module recovery”。据我们所知，这是第一个关于安全 G 模块操作的工作。基于它们，我们设计了安全比较、选择、ReLU 和 DReLU 协议，与现有技术相比，将通信效率提高了 2 倍到 10 倍。我们的协议计算效率也很高。它们不需要公钥操作或任何其他昂贵的操作。