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International Conference on Computer Information Science and Application Technology (CISAT)

Improvement of the protocol for millionaires’ problem

Zhengtao Jiang, Ye Chen, Huiqiang Li, Ting Yu

Published Oct 20, 2022• 0 citations
Publisher

Abstract

As the basic problem that introduces the idea of secure multi-party computation (SMC), millionaires’ problem (MP) is one of the research highlights in the field of SMC. However, most of current protocols for MP are only secure in semi-honest model, which using public key cryptography schemes, and there are few secure schemes in malicious model exist security defects. Therefore, this paper analyzes the Li et al.’s protocol for MP that secure in malicious model. Firstly, we point out several behaviours that can be successfully implemented in Li et al.’s protocol. Secondly, by using the zero-knowledge proof (ZKP) for the equality of discrete logarithm (DL), cut-and-choose method etc. We propose the improved protocol and show how to detect malicious behaviours. Finally, we analyze the correctness and security against malicious behaviours of the improved protocol.

DOI
10.1117/12.2656657

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As the basic problem that introduces the idea of secure multi-party computation (SMC), millionaires’ problem (MP) is one of the research highlights in the field of SMC. However, most of current protocols for MP are only secure in semi-honest model, which using public key cryptography schemes, and there are few secure schemes in malicious model exist security defects. Therefore, this paper analyzes the Li et al.’s protocol for MP that secure in malicious model. Firstly, we point out several behaviours that can be successfully implemented in Li et al.’s protocol. Secondly, by using the zero-knowledge proof (ZKP) for the equality of discrete logarithm (DL), cut-and-choose method etc. We propose the improved protocol and show how to detect malicious behaviours. Finally, we analyze the correctness and security against malicious behaviours of the improved protocol.
Secure multi-party computation is a hotspot in the cryptography field, and it is also a significant means to realize privacy computation. The Millionaires’ problem is the most fundamental problem among them, which is the basic module of secure multi-party computation protocols. Although there are many solutions to this problem, there are few anti-malicious adversarial protocols besides protocols based on Yao’s garbled circuit. Only a few solutions have low efficiency, and there is no protocol for rational numbers comparison under the malicious model, which restricts the solution of many secure multi-party computation problems. In this paper, the possible malicious behaviors are analyzed in the existing Millionaires’ problem protocols. These behaviors are discovered and taken precautions against through the triangle area formula, zero-knowledge proof, and cut-and-choose method, so the protocol of comparing confidentially rational numbers is proposed under the malicious model. And this paper adopts the real/ideal model paradigm to prove the security of the malicious model protocol. Efficiency analysis indicates that the proposed protocol is more effective than existing protocols. The protocol of rational numbers comparison under the malicious model is more suitable for the practical applications of secure multi-party computation, which has important theoretical and practical significance.
Secure multiparty computation is a focus of the international cryptographic community. The millionaires problem is the most important problem in secure multiparty computation and is a building block for constructing other secure multiparty computation protocols. Several solutions are available to solve this problem, but except for protocols based on garbled circuits, the existing solutions based on public key cryptosystems are only secure in semihonest models. No solution based on a public key cryptosystem is secure against malicious adversaries. This state restricts the resolution of many secure multiparty computation problems in malicious scenarios. A solution that is secure in malicious models is highly applicable in practical application scenarios and is generally appealing. Therefore, the study of the solution to the millionaires problem in a malicious model is of great theoretical and practical significance. In this work, we propose a multiparty computation protocol for the millionaires problem that is secure in a semihonest model. The proposed protocol is simple and easily understandable. We analyze the possible malicious behaviors in this protocol and use zero-knowledge proof and cut-and-choose techniques to resist possible malicious behaviors and thereby convert the protocol into one that is secure in the malicious model. We prove that the proposed protocol is secure in the malicious model by using the well-accepted ideal-real paradigm. Theoretical efficiency analysis shows that the efficiency of our protocol is at least six times that of existing protocols.
Secure multi-party computation is a hot research topic in cryptography in recent years, and has become an important research direction in cryptography. This paper studies the millionaires’ problem in secure multi-party computation, and its essence is a comparison issue about the size of two encrypted data. Yao offered a solution to the millionaires’ problem, but his protocol can’t accurately compare two numbers. We improved Yao’s protocol and proposed two generic protocols to solve the millionaires’ problem. Our first protocol has one more round of communication between participants than Yao’s, but our protocol can accurately compare the size of two numbers. The second protocol improved the first protocol, and only one round of communication is needed to get accurate comparison results. Finally, we realized the second protocol based on RSA encryption algorithm, and analyze the security under the semi-honest model.
Secure comparison is an important problem in the field of secure computing. A classic example is the Millionaires' problem, which is securely compares the wealth of two millionaires without revealing their wealth. However most traditional secure comparison protocol requires autonomous computation among the participants. It is necessary to ensure that the model of the participants is a semi-honest model, otherwise the protocol will not be able to execute correctly. In this paper, we introduce a semi-honest judge to improve the Damgård-Geisler-KrØigaard(DGK) comparison protocol by using techniques such as zero-knowledge proof and homomorphic encryption. The improved protocol is not only applicable to the malicious participant model, but also the introduced judge would not get any information of data. At last, the security analysis shows that the proposed scheme in this paper can guarantee the data fairness of the comparison protocol while ensuring the privacy security of the participants.
Secure multiparty computation (SMC) is a research focusing in the international cryptographic community. The protocols used to address the millionaires' problem are the basic building blocks of most SMC protocols and their efficiency dominates that of many other SMC protocols. To the best of our knowledge, almost all protocols used to address the millionaires' problem are based on integers, which means that their applications are limited. In this study, we propose precise and efficient protocols for rational numbers based on additively homomorphic encryptions. One of our protocols is inspired by computational geometry and it reduces the millionaires problem to computing the area of a triangle formed by three private points. This approach can determine whether the relationship between two private inputs is greater than, equal to or less than, and it has a much lower computational complexity compared with existing methods. We proved that these protocols are secure using simulation paradigm. Our approaches can be used in many SMC protocols that involve rational numbers and integers, and they can also be used directly to solve some secure multiparty computational geometry problem in rational number field.
Secure multi-party ranking is a problem generalized from the millionaires' problem,which can be used by n people to know about their secrets' order among all their inputs without leaking further information.Through the study on millionaires' protocol,we presented a secure two-party ranking protocol under semi-honest model based on homomorphic encryption.Then we generalized it to secure multi-party ranking,and we presented two algorithms whose efficiency are both improved.Finally,we gave a secure multi-party ranking protocol based on fuzzy nearness degree,and we analyzed the efficiency and security of these protocols.