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Secure comparison and secure selection are two fundamental MPC (secureMulti-Party Computation) protocols. One important application of theseprotocols is the secure ReLU and DReLU computation in privacy preserving deeplearning. In this paper, we introduce G-module, a mathematics tool, tore-design such protocols. In mathematics, given a group G, a G-module is anabelian group M on which G acts compatibly with the abelian group structure onM.  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 weknow, this is the first work on secure G-module operations. Based on them, wedesign secure comparison, selection, ReLU and DReLU protocols, which improvecommunication efficiency by 2X to 10X compared with state of arts. Ourprotocols are very computation efficient too. They do not require public keyoperations or any other expensive operations.

MPC Protocol for G-module and its Application in Secure Compare and ReLU