On Implementing Linear Regression on Homomorphically Encrypted Data: A Case-Study

Fully Homomorphic Encryption (FHE) is a key technological enabler for secure computations as it allows a third-party to perform arbitrary computations on encrypted data learning neither the input nor the results of a computation. Notwithstanding the recent theoretical breakthroughs in FHE, building a secure and efficient FHE-based application is still a challenging engineering task where optimal choices are heavily application-dependent. Taking linear regression as a case-study, we investigate the programming and configuration solutions to implement FHE-based applications. We show that, although obviously slower than the non-homomorphic version, the implementation of linear regression on homomorphically encrypted data is viable provided the programmer adopts appropriate programming expedients and parameters selection.