MuEOC: Efficient SGX-Based Multi-Key Homomorphic Outsourcing Computation for E-Health System

While techniques such as Homomorphic Encryption (HE) and Intel Software Guard Extensions (SGX) have been leveraged to secure outsourced electronic health record (EHR) computation, there are a number of known limitations (e.g., performance bottlenecks, lack of desired functionalities, or the reliance on a trusted third party). To address these challenging issues, this paper proposes MuEOC, an SGX-based multi-key homomorphic outsourcing computation scheme without a trusted third party. MuEOC is designed to support arbitrary depth multiplication and multi-key setup. In our approach, we first propose an SGX-assisted fully homomorphic encryption scheme (XFHE) under the randomized AGCD assumption. This allows us to replace costly bootstrapping with re-encryption in the enclave, and enable key-switching and Galois automorphism. Using XFHE as a building block, we construct a high-performance multi-key outsourcing computing protocol without the trusted third-party setup. Leveraging SGX, the MuEOC incorporates efficient sub-protocols of secure ciphertext transformation, secure polynomial evaluation, secure inner product, and secure non-linear function evaluation. We also present formal security proof which shows that our proposal guarantees the privacy of input EHR data and medical analysis results under the semi-honest model. Finally, experimental results demonstrate the outstanding efficiency of MuEOC.