Abstract: A new protocol for the task that give two secrets 0, 1 shared among 3 players, compute the product 0 1 but without any exposure about the secrets except the product is presented. It is a two-round protocol if new error occurs. The protocol uses the non-interactive distributed approach for multiplication of the shared secrets and the Welch-Berlekamp decoder for product reconstruction, which results in a more efficient protocol. To achieve provable security, the simulator protocol is given in the security proof.

Key words: secure multiparty computation, distributed cryptography, veriable secret sharing, provable security, robustness