Confidentially judging the relationship between an integer and an interval against malicious adversaries and its applications

Abstract

With the growing prominence of privacy protection issues in big data, artificial intelligence and blockchain, secure multi-party computation has become a research hotspot. Confidentially computing the set problem is an important branch of secure multi-party computation. The relationship between an integer and an interval is the most basic problem in the study of computing set problems. At present, there are many research solutions for secure multi-party computation against malicious adversaries. In this paper, we analyze some possible malicious attacks in the protocol of determining an integer and an interval relationship under the semi-honest model. By using the Goldwasser–Micali encryption scheme, Paillier encryption algorithm, zero-knowledge proof and cut-choose method, we design the secret judgment protocol of an integer and an interval relationship under the malicious model. Finally, an ideal-practical example proof method is used to prove that the protocol is secure under the malicious model. Compared with the existing schemes, it not only keeps good efficiency, but also can resist the attack of malicious opponents, and the protocol is more fair. The scheme has a wide application prospect.