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Dianzi xuebao

An Efficient Solution to Yao's Millionaires' Problem

You Qi-you

Published Jan 1, 2005• 7 citations
OpenAlex

Abstract

AbstrcatThe protocols for Yao's Millionaires' problem have been building blocks of solutions to many secure multi-party computation problems.But known solutions are not efficient enough and thus affect the efficiency of many secure multi-party computation protocols.In this paper,we construct a new efficient solution to millionaires' problem based on length function and oblivious transfer.Compared with known solutions,our new solution has much less computational complexity.

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Secure multi-party computation is a focus of international cryptography in recent years. Protocols for Yao's millionaires' problem have become an important building block of many secure multi-party computation protocols. Their efficiency are crucial to the efficiency of many secure multi-party computation protocols. Unfortunately, known protocols for Yao's millionaries' problem have high computational complexity or communication complexity. In this study, based on the 1-out of-m oblivious transfer and set-inclusion problem, we propose a new protocol to solve this problem. This new protocol is very efficient in terms of both computational and communication complexities. Its privacy-preserving property is also proved by simulation patadigm which is generally accepted in the study of secure multi-party computation. We also compare the information leakage of our new protocol and the known protocols.

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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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Iranian Conference on Electrical Engineering•May 1, 2018•5 citations
AbstrcatThe protocols for Yao's Millionaires' problem have been building blocks of solutions to many secure multi-party computation problems.But known solutions are not efficient enough and thus affect the efficiency of many secure multi-party computation protocols.In this paper,we construct a new efficient solution to millionaires' problem based on length function and oblivious transfer.Compared with known solutions,our new solution has much less computational complexity.
Secure multi-party computation is a focus of international cryptography in recent years. Protocols for Yao's millionaires' problem have become an important building block of many secure multi-party computation protocols. Their efficiency are crucial to the efficiency of many secure multi-party computation protocols. Unfortunately, known protocols for Yao's millionaries' problem have high computational complexity or communication complexity. In this study, based on the 1-out of-m oblivious transfer and set-inclusion problem, we propose a new protocol to solve this problem. This new protocol is very efficient in terms of both computational and communication complexities. Its privacy-preserving property is also proved by simulation patadigm which is generally accepted in the study of secure multi-party computation. We also compare the information leakage of our new protocol and the known 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 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.
The increase in volume and sensitivity of data communicated and processed over the Internet has been accompanied by a corresponding need for e-commerce techniques in which entities can participate in a secure and anonymous fashion. Even simple arithmetic operations over a set of integers partitioned over a network require sophisticated algorithms. As apart of our earlier work, we have developed a secure protocol for computing dot products of two vectors. In this paper, we present a secure protocol for Yao's millionaires' problem. In this problem, each of the two participating parties have a number and the objective is to determine whose number is larger without disclosing any information about the numbers. This problem has direct applications in on-line bidding and auctions. Furthermore, combined with a secure dot-product, a solution to this secure multiparty computation provides necessary building blocks for such basic operations as frequent item-set generation in association rule mining. Although an asymptotically optimal solution for the secure multiparty computation of the 'less-or-equal' predicate exists in literature, this protocol is not suited for practical applications. Here, we present a protocol which has a much simpler structure and is more efficient for numbers in ranges practically encountered in typical e-commerce applications. Furthermore, advances in cryptanalysis and the subsequent increase in key lengths for public-key cryptographic systems accentuate the advantage of the proposed protocol. We present experimental evidence demonstrating the efficiency of the proposed protocol both in terms of time and communication overhead.
In this paper, we present a protocol for generalized secure comparison problem. Yao's millionaire problem is for comparing the wealth of two parties by preserving their privacy. Ifnnnparties want to compare their wealth by using Yao's protocol, it should be run$n(n-1)2times;iftheirwealthintervalisaslargeasN,thecomplexityofYao′sprotocolfor2 times; if their wealth interval is as large as N, the complexity of Yao's protocol for2times;iftheirwealthintervalisaslargeasN,thecomplexityofYao′sprotocolfornpartiesisinorderofN.parties is in order of N.partiesisinorderofN.\mathbf{n}^{2}, \mathbf{i}.\mathbf{e}...\mathbf{O}\ (\mathbf{N}.\mathbf{n}^{2})$. In this paper, we present a generalized secure comparison protocol, which need not to be run by every two parties separately. We use an easy knapsack problem for distinguishing parties' indices. Our protocol computation and communication complexities are bounded by 0 (n).