Modified Multi-Key Fully Homomorphic Encryption Scheme in the Plain Model

Multi-key fully homomorphic encryption (MFHE) supports arbitrary meaningful computations on encrypted data under different public keys even without access to the secret key, which is well tailored for the secure multiparty computation scenarios. Based on the Gentry-Sahai-Waters scheme (a single-key FHE in Crypto 2013) with the underlying learning with errors problem, MW16 scheme (Eurocrypt 2016) utilizes the method of 'linear combination procedure' (LCP) as a subroutine to construct the auxiliary information for the expanded ciphertexts of MFHE scheme. However, every party shares a common random string (CRS) to be distributed by a trusted setup, which is unpractical. Meanwhile, the noise in the auxiliary information is too much compared with the one in fresh ciphertexts. In this paper, we propose a modified MFHE scheme in the plain model, i.e. without CRS, to enhance the practicability of MFHE. Specifically, every involved party generates his own public key independent on a CRS. Then a potential improvement on the LCP is developed to provide auxiliary information, which largely reduces the noise and leads to a smaller modulus for our MFHE. Furthermore, the feasibility of our proposal is also proved by theoretical performance comparisons.