Faster Secure Arithmetic Computation Using Switchable Homomorphic Encryption

Secure computation on encrypted data stored on untrusted clouds is an important goal. Existing secure arithmetic computation techniques, such as fully homomorphic encryption (FHE) and somewhat homomorphic encryption (SWH), have prohibitive performance and/or storage costs for the majority of practical applications. In this work, we investigate a new secure arithmetic computation primitive called switchable homomorphic encryption (or SHE) that securely switches between existing inexpensive partially homomorphic encryption techniques to evaluate arbitrary arithmetic circuits over integers. SHE is suited for use in a two-cloud model that is practical, but which makes stronger assumptions than the standard single-cloud server model. The security of our SHE solution relies on two non-colluding parties, in which security holds as long as one of them is honest. We benchmark SHE directly against existing secure arithmetic computation techniques—FHE and SWH—on real clouds (Amazon and Rackspace) using microbenchmarks involving fundamental operations utilized in many privacy-preserving computation applications. Experimentally, we find that SHE offers a new design point for computing on large data—it has reasonable ciphertext and key sizes, and is consistently faster by several (2–3) orders of magnitude compared to FHE and SWH on circuits involving long chain of multiplications. SHE exhibits slower performance only in certain cases, when batch (or parallel) homomorphic evaluation is possible, only against SWH schemes (which have limited expressiveness and potentially high ciphertext and key storage costs).