Secure two-party integer comparison protocol without any third party

Secure two-party integer comparison is a primitive problem of secure multiparty computations that enables two parties to decide whether $$x>y$$ without disclosing anything about $$x$$ and $$y$$ , where $$x$$ and $$y$$ are two integers held privately by two parties, respectively. This paper presents a novel and efficient quantum protocol for secure two-party integer comparison without any third party. This protocol tactfully adopts the ideas of quantum private query so that it achieves an exponential reduction in communication complexity because it only requires $$O(1)$$ communication cost.