BeeHive: Double Non-interactive Secure Multi-party Computation

In this paper, we focus on the research of non-interactive secure multi-party computation (MPC). At first, we propose a fully homomorphic non-interactive verifiable secret sharing (FHNVSS) scheme. In this scheme, shareholders can generate any-degree polynomials of shared numbers without interaction, and the dealer can verify the correctness of responses sent by servers without interaction. We implemented the FHNVSS scheme in Python with a detailed performance evaluation. According to our tests, the performance of FHNVSS is satisfactory. For instance, when the request is a 10-degree polynomial of secret value, generating a response takes about 0.0017263 s; verifying a response takes about 0.1221394 s; recovering a result takes about 0.0003862 s. Besides, we make an extension on the FHNVSS scheme to obtain a double non-interactive secure multi-party computation, called BeeHive. In the BeeHive scheme, distrustful players can jointly calculate a any-degree negotiated function, the inputs of which are inputs of all players, without interaction, and each player can verify the correctness of responses sent by players without interaction. To the best of our knowledge, it is the first work to realize that players can jointly calculate any-degree function, the inputs of which are inputs of all players, without interaction.