Abstract — Comparing information secretly is the fundamental to secure multiparty computation. The knownprivate comparison protocols without a third party canonly resolve the Greater than (GT) problem and can onlycompare two integers. In this paper, we develop an improved cross products protocol by using the Paillier's additive homomorphic encryption at first. Then, we propose a three-round protocol for solving the private comparison problem in the semi-honest setting based on theproperty of the cross products. In comparison with theknown private comparison protocols, our method can determine whether a > b, a < b or a = b for two numbers a andb by running our proposed protocol only once. Moreover,our protocol can compare two real numbers in additionto integers. The analysis shows that our method is morepowerful than previous methods.