Verifiable privacy-preserving cox regression from multi-key fully homomorphic encryption

While it is well known that privacy-preserving cox regression generally consists of a semi-honest cloud service provider (CSP) who performs curious-but-honest computations on ciphertexts to train the cox model. No one can verify the behaviors of CSP when he performs computations dishonestly in reality. Focusing on this problem, we propose a verifiable privacy-preserving cox regression algorithm tailored with the semi-malicious CSP, where all his behaviors are recorded on a witness tape fulfilling the requirement of transparency. To be specific, a multi-key fully homomorphic encryption (FHE) is used to protect the information of different data owners. The verifiability of our proposed multi-key homomorphic message authenticator (HMAC) ensures CSP sends correct results back to data owners. Furthermore, the compactness of FHE and succinctness of HMAC both under multi keys make the cox regression scheme more feasible. The efficiency of our proposed cox regression scheme is also proved by both theoretical analyses and experimental evaluations. After 21 iterations, it costs no more than 10 min to evaluate our cox regression scheme.