An Efficient Threshold Access-Structure for RLWE-Based Multiparty Homomorphic Encryption

We propose and implement a multiparty homomorphic encryption (MHE) scheme with a t-out-of-N -threshold access-structure that is efficient and does not require a trusted dealer in the common reference-string model. We construct this scheme from the ring-learningwith-error (RLWE) assumptions, and as an extension of the MHE scheme of Mouchet et al. (PETS 21). By means of a specially adapted shareresharing procedure, this extension can be used to relax the N -out-ofN -threshold access structure of the original scheme into a t-out-of-N threshold one. This procedure introduces only a single round of communication during the setup phase to instantiate the t-out-of-N -threshold access structure. Then, the procedure requires only local operations for any set of t parties to compute a t-out-of-t additive sharing of the secret key; this sharing can be used directly in the scheme of Mouchet et al. We show that, by performing the re-sharing over the MHE ciphertextspace with a carefully chosen exceptional set, this reconstruction procedure can be made secure and has negligible memory and CPU-time overhead. Hence, in addition to fault tolerance, lowering the corruption threshold also yields considerable efficiency benefits, by enabling the distribution of batched secret-key operations among the online parties. We implemented and open-sourced our scheme in the Lattigo library.