Secure multi-party computation is a focus in the international cryptographic community.This paper studies how to privately compute the minimum of some private numbers.We have not read a solution to this problem.In this study

we introduce a new encoding scheme

and then

based on this new encoding scheme and ElGamal multiplicatively homomorphic encryption scheme

using secret sharing and threshold decryption

devise protocols for this problem.We prove

using the simulation paradigm

that these protocols are secure in the semi-honest model.These protocols can resist collision attack.Based on the computing methods for minimum problem

secure multi-party computation for maximum and union of sets can also be solved.Efficiency analysis shows that these schemes are efficient.