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

Abstract We propose and implement a multiparty homomorphic encryption (MHE) scheme with $$t$$ t -out-of- $$N$$ N -threshold access-structure that is efficient does not require trusted dealer in the common random string model. construct this from ring-learning-with-error assumptions as an extension of MHE Mouchet et al. (PETS 21). By means specially adapted share re-sharing procedure, can be used to relax original into one. This procedure introduces only single round communication during setup phase, after which any set at least t parties compute additive sharing secret-key no interaction; new directly show that, by performing Shamir over ciphertext-space ring carefully chosen exceptional set, reconstruction made secure has negligible overhead. Moreover, it requires store constant-size state its phase. Hence, addition fault tolerance, lowering corruption threshold also yields considerable efficiency benefits, enabling distribution batched operations among online parties. implemented open-sourced our Lattigo library.