Secure computing methods such as fully homomorphic encryption and hardware solutions such as Intel Software Guard Extension (SGX) have been applied to provide security for user input in privacy-oriented computation outsourcing. Fully homomorphic encryption is amenable to parallelization and hardware acceleration to improve its scalability and latency, but is limited in the complexity of functions it can efficiently evaluate. SGX is capable of arbitrarily complex calculations, but due to expensive memory paging and context switches, computations in SGX are bound by practical limits. These limitations make either of fully homomorphic encryption or SGX alone unsuitable for large-scale multi-user computations with complex intermediate calculations. In this paper, we present GPS, a novel framework integrating the Graphene, PALISADE, and SGX technologies. GPS combines the scalability of homomorphic encryption with the arbitrary computational abilities of SGX, forming a more functional and efficient system for outsourced secure computations with large numbers of users. We implement GPS using linear regression training as an instantiation, and our experimental results indicate a base speedup of 1.03x to 8.69x (depending on computation parameters) over an SGX-only linear regression training without multithreading or hardware acceleration. Experiments and projections show improvements over the SGX-only training of 3.28x to 10.43x using multithreading and 4.99x to 12.67 with GPU acceleration.

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