Multi-key fully homomorphic encryption from NTRU and (R)LWE with faster bootstrapping

Abstract

Multi-Key Fully Homomorphic Encryption (MKFHE) supports homomorphic evaluation on ciphertexts encrypted under different keys, guaranteeing data privacy in the case of multiple mutually untrusted parties. In ASIACRYPT 2019, Chen et al. designed an LWE-based MKFHE scheme, which evaluates a boolean gate on ciphertexts followed by a bootstrapping procedure in the dynamic multi-key setting. In this paper, we propose a new MKFHE scheme from NTRU and (R)LWE, achieving better bootstrapping performance. To that end, we adapt Chen et al.'s bootstrapping algorithm to the NTRU setting and construct an efficient conversion from multi-key NTRU to multi-key RLWE ciphertexts. With appropriate parameter choice, our scheme avoids the sublattice attacks that broke previous NTRU-based MKFHE schemes. Finally, we implement a proof-of-concept of our construction and conduct experiments to test its performance. Our experiments indicate that gate bootstrapping in our scheme for 2 parties takes 0.18 seconds, which is faster than with Chen et al. by around 5.3 times, but unfortunately does not scale beyond that. It is however practical for uses such as oblivious neural network inference.