A General Framework of Homomorphic Encryption for Multiple Parties with Non-interactive Key-Aggregation

Abstract

Homomorphic Encryption (HE) is a useful primitive for secure computation, but it is not generally applicable when multiple parties are involved, as the authority is solely concentrated in a single party, the secret key owner. To solve this issue, several variants of HE have emerged in the context of multiparty setting, resulting in two major lines of work – Multi-Party HE (MPHE) and Multi-Key HE (MKHE). In short, MPHEs tend to be more efficient, but all parties should be specified at the beginning to collaboratively generate a public key, and the access structure is fixed throughout the entire computation. On the other hand, MKHEs have relatively poor performance but provide better flexibility in that a new party can generate its own key and join the computation anytime. In this work, we propose a new HE primitive, called Multi-Group HE (MGHE). Stated informally, an MGHE scheme provides seamless integration between MPHE and MKHE, and has the best of both worlds. In an MGHE scheme, a group of parties jointly generates a public key for efficient single-key encryption and homomorphic operations similar to MPHE. However, it also supports computation on encrypted data under different keys, in the MKHE manner. We formalize the security and correctness notions for MGHE and discuss the relation with previous approaches. We also present a concrete instantiation of MGHE from the BFV scheme and provide a proof-of-concept implementation to demonstrate its performance. In particular, our MGHE construction has a useful property that the key generation is simply done by aggregating individual keys without any interaction between the parties, while all the existing MPHE constructions relied on multi-round key-generation protocols. Finally, we propose a general methodology to build a multi-party computational protocol from our MGHE scheme.