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Information Sciences

Symmetric cryptographic solution to Yao’s millionaires’ problem and an evaluation of secure multiparty computations

Shundong Li, Wang Daoshun, Dai Yiqi, Ping Luo

Published Jul 25, 2007• 39 citations
Publisher
DOI
10.1016/j.ins.2007.07.015

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Secure comparison problem, also known as Yao's Millionaires' problem, was introduced by Andrew Yao in 1982. It is a fundamental problem in secure multi-party computation. In this problem, two millionaires are interested in determining the richer one between them without revealing their actual wealth. Yao's millionaires' problem is a classic and fundamental problem in cryptography. The design of secure and efficient solutions to this problem provides effective building blocks for secure multi-party computation. However, only a few of the solutions in the literature have succeeded in resisting attacks of malicious adversaries, and none of these solutions has been proven secure in malicious model under ideal/real simulation paradigm. In this paper, we propose two secure solutions to Yao's millionaires' problem in the malicious model. One solution has full simulation security, and the other solution achieves onesided simulation security. Both protocols are only based on symmetric cryptography. Experimental results indicate that our protocols can securely solve Yao's millionaires' problem with high efficiency and scalability. Furthermore, our solutions show better performance than the state-of-the-art solutions in terms of complexity and security. Specifically, our solutions only require O(|U|) symmetric operations at most to achieve simulation-based security against malicious adversaries, where U denotes the universal set and |U| denotes the size of U.

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Secure comparison problem, also known as Yao's Millionaires' problem, was introduced by Andrew Yao in 1982. It is a fundamental problem in secure multi-party computation. In this problem, two millionaires are interested in determining the richer one between them without revealing their actual wealth. Yao's millionaires' problem is a classic and fundamental problem in cryptography. The design of secure and efficient solutions to this problem provides effective building blocks for secure multi-party computation. However, only a few of the solutions in the literature have succeeded in resisting attacks of malicious adversaries, and none of these solutions has been proven secure in malicious model under ideal/real simulation paradigm. In this paper, we propose two secure solutions to Yao's millionaires' problem in the malicious model. One solution has full simulation security, and the other solution achieves onesided simulation security. Both protocols are only based on symmetric cryptography. Experimental results indicate that our protocols can securely solve Yao's millionaires' problem with high efficiency and scalability. Furthermore, our solutions show better performance than the state-of-the-art solutions in terms of complexity and security. Specifically, our solutions only require O(|U|) symmetric operations at most to achieve simulation-based security against malicious adversaries, where U denotes the universal set and |U| denotes the size of U.
Millionaire's problem is the base of secure multiparty computation, and its solutions have become basic blocks of many secure multi-party computation solutions. Unfortunately, most solutions to millionaire's problem are based on public key cryptography, and thus are inefficient. Furthermore, all solutions are designed to solve millionaire's problem for natural number case to privately determine which natural number is larger. If the numbers are real, these solutions do not directly work. In this paper, we first propose a symmetric key cryptographic solution to millionaire's problem for natural numbers case, and then generalize it to the case of real numbers, that is to privately determine which real number is larger. We further prove, by simulation paradigm, that these solutions are private. These solutions are really efficient.
Secure multiparty computation is a key privacy-preserving technology in cyberspaces and a research focus in the international cryptographic community.We first present a new encoding scheme to encode private data.By using this encoding scheme together with homomorphic encryption scheme,we construct a new scheme for Yao′s millionaires′ problem and prove its privacy-preserving property.This new scheme is more concise,more general and can be applied to compare any two objects on which a total order can be defined.We finally utilize the new scheme to propose a solution to the coprime problem and prove the privacy-preserving properties of the solution.