Linear multi-secret sharing schemes based on multi-party computation

In multi-secret sharing schemes, publishing shares during the process of reconstructing partial secrets may leak some information of the secrets unrecovered yet. By using a multi-party computation (MPC) protocol, we solve this problem for any linear multi-secret sharing scheme (MSSS). We also show that LMSSS usually involve more complicated reconstruction algorithms than “direct sum” schemes, but from the point of reducing share expansion, the former is preferred.