Secure multiparty computation of a comparison problem

Private comparison is fundamental to secure multiparty computation. In this study, we propose novel protocols to privately determine [Formula: see text], or [Formula: see text] in one execution. First, a 0-1-vector encoding method is introduced to encode a number into a vector, and the Goldwasser-Micali encryption scheme is used to compare integers privately. Then, we propose a protocol by using a geometric method to compare rational numbers privately, and the protocol is information-theoretical secure. Using the simulation paradigm, we prove the privacy-preserving property of our protocols in the semi-honest model. The complexity analysis shows that our protocols are more efficient than previous solutions.