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International Conference on Systems and Informatics (ICSAI)

Enhancing security for two-party comparison over encrypted data

Ching‐Nung Yang, Zong-Xuan Yeh, Shen-Chieh Hsu, Zhangjie Fu

Published Nov 1, 2016• 2 citations
Publisher

Abstract

The so-called Yao's millionaire problem (YMP) is about securely comparing two numbers held by two parties, respectively. After comparison, the actual values of these two numbers are still unknown to both parties. Recently, Kaghazgaran and Sadeghyan propose a variant of YMP, the two-party multiple comparison (TPMC) protocol, that determines the greatest one over multiple (more than two) encrypted data between two parties. However, in Kaghazgaran and Sadeghyan's TPMC (KS-TPMC) protocol, one of two parties may guess the original data with a probability. In this paper, we introduce a new TPMC protocol to enhance the security by reducing this guess probability, and meanwhile has the same computation cost compared with KS-TPMC protocol. Additionally, the proposed TPMC protocol is more effective on reducing the attack probability for the large number of encrypted data. Thus, our TPMC protocol is suitable for applications on multiple comparison over encrypted data.

DOI
10.1109/icsai.2016.7810995

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The so-called Yao's millionaire problem (YMP) is about securely comparing two numbers held by two parties, respectively. After comparison, the actual values of these two numbers are still unknown to both parties. Recently, Kaghazgaran and Sadeghyan propose a variant of YMP, the two-party multiple comparison (TPMC) protocol, that determines the greatest one over multiple (more than two) encrypted data between two parties. However, in Kaghazgaran and Sadeghyan's TPMC (KS-TPMC) protocol, one of two parties may guess the original data with a probability. In this paper, we introduce a new TPMC protocol to enhance the security by reducing this guess probability, and meanwhile has the same computation cost compared with KS-TPMC protocol. Additionally, the proposed TPMC protocol is more effective on reducing the attack probability for the large number of encrypted data. Thus, our TPMC protocol is suitable for applications on multiple comparison over encrypted data.
Yao's classical millionaires' problem is about securely determining whether x>y, given two input values x, y, which are held as private inputs by two parties, respectively. The output which is result of comparison becomes known to both parties. In this paper we consider a variant of comparison problem in which the inputs x, y are encrypted and the actual values are not known to the parties. Our first solution deals with single comparison; however, in many applications, we encounter situations where it is necessary to make multiple comparisons to find the maximum among several encrypted data, so we make a modification to our first protocol to solve the multiple comparisons problem. Such a secure comparison is an important building block for applications like privacy preserving data mining and secure business. Our second protocol is based on Homomorphic encryption which achieves very low communication and computational complexities. Also our protocols can be performed in constant rounds and do not use general circuit evaluation techniques so they are more efficient than circuit based ones but not general. Implementation is easy and fast.
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.
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).
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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.
We give an efficient symmetric--key based protocol to solve Yao'smillionaire problem. We assume a semi--honest server assists incomparing values held by two different parties. We assume thisserver only executes the protocol precisely and does not colludewith any other participants. We protect the participants against theserver getting any information about the numbers or theirrelationship, by using encryption and hash chains. The protocol hasthree communication phases; initialisation, computation andannouncement. Each of the two parties and the server sends twomessages during the protocol. Each phase requires the two parties torun one of their three algorithms. We discuss the correctness,security properties and efficiency of our scheme. We compare thecommunication and computational costs against other solutions to themillionaire problem, using an RSA based implementation and using anAES based implementation. The computational cost is generally verylow by comparison with other methods, even when we use the lessefficient RSA.