LAUSR

In this paper, we focus on the research of non-interactive secure multi-party computation. At first, we propose a fully homomorphic non-interactive verifiable secret sharing (FHNVSS) scheme. In this scheme, shareholders can generate shares of any-degree polynomials of shared numbers without interaction, and the dealer can verify the correctness of shares sent by shareholders 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 fully non-interactive secure multi-party computation, called AntNest. In the AntNest scheme, distrustful parties can jointly calculate a any-degree negotiated function, the inputs of which are inputs of all parties, without interaction, and each party can verify the correctness of responses sent by parties without interaction. To the best of our knowledge, it is the first work to realize that parties can jointly calculate any-degree function, the inputs of which are inputs of all parties, without interaction.