Secure multi-party computation (MPC) is an important research field of cryptography. Privately computing the k-th minimum element is an important problem of MPC (denoted by k-min problem). MPC protocol for k-min problem can be widely applied to secure voting, secure bid and auction, secure statistical analysis, etc. At present, most solutions to this problem need to repeatedly invoke secure sum protocol and secure comparison protocol. Therefore, the efficiency of the protocols is low. Some solutions designed for mobile network are not applicable to MPC settings. In this paper, we propose a new encoding scheme. Based on this encoding scheme and threshold Lifted ElGamal cryptosystem, we design a simple and efficient MPC protocol for k-min problem. The security of the protocol is strictly proved by using the simulation paradigm and the feasibility of the scheme is proved by the experiment. Using k-min protocol as a building block, we further design a protocol for privacy-preserving score statistics and sorting. Theoretical analysis and experimental result show that our protocols are secure and efficient. © 2021, Chinese Institute of Electronics. All right reserved.
