Secure multiparty computation is a key privacy-preserving technology in cyberspaces and a research focus in the international cryptographic community.We first present a new encoding scheme to encode private data.By using this encoding scheme together with homomorphic encryption scheme

we construct a new scheme for Yao's millionaires' problem and prove its privacy-preserving property.This new scheme is more concise

more general and can be applied to compare any two objects on which a total order can be defined.We finally utilize the new scheme to propose a solution to the coprime problem and prove the privacy-preserving properties of the solution.