Privacy-Preserving Greater-Than Integer Comparison without Binary Decomposition

Three-Party Integer Comparison and Applications

“…The communications and computations are inefficient requiring many rounds of interaction. In contrast to bitwise comparisons, more efficient protocols were given in [7,8,9,10] to compare multiple bits simultaneously with a single ciphertext by a somewhat homomorphic encryption.…”

“…Two constant-round constructions are given against semi-honest and malicious adversary respectively. One is built on [7] for semi-honest competitors, and has low communication and computation cost (it can be improved by the method in [9,10] to reduce one round), while the other is built on the technique of Fischlin [5] for malicious competitors. In both, the judge is assumed to be semi-honest and non-colluding with competitors to maintain the comparison result.…”