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Dianzi xuebao

Research on the Problem of Secure Multi-party Ranking Under Semi-honest Model

Bo Wu

Published Jan 1, 2008• 3 citations
OpenAlex

Abstract

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.

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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.
In this paper, we study a secure multi-party ranking problem: there are n parties, P1, P2, ... , Pn. Each party Pihas a secret input miisin {1, 2, ... ,N}. He wants to get the order of miin the ascending ranking sequence of the n parties' inputs, while not leaking the value of mi. This problem extends the famous Yao's millionaires' problem form two parties to n parties and is a multi-party Yao's Millionaires' problem. We propose a protocol for solving the secure multi-party ranking problem, using the encoding scheme and the El Gamal cryptosystem. We also prove the correctness and the security of our solution in the semi-honest model. The solution of secure multi-party ranking problem can make new-style electronic transactions, such as private bidding and auction, secret online transaction and so on, become better security.
In this paper, the problems of secure multi-party ranking and secure selection were studied. Two protocols were proposed. They were both based on Secure Sum protocol. Secure multi-party ranking problem is an extended problem from millionaires' problem. It can be applied to many fields, such as auctions, commercial enterprises and so on. Secure Sum protocol was used to calculate the sum of vectors. The security and complexity were analyzed in the semi-honest model. In some cases this protocol is better. This paper also studied the problem of secure selection and proposed a protocol using the protocols of Secure Sum and 1-n oblivious transfer. We analyzed the worst case and the average case.
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.
The secure multi-party comparing problem is generalized from the millionaires' problem,which is used to get whether the multi-party's secret inputs are all equal and if not,the number of users whose inputs are same as an indicated user's.Based on the F function and semantic addition homomorphic encryption,a protocol of secure multi-party comparing is proposed.The correctness,security and efficiency of the protocol are analyzed.This protocol can be used in many aspects of secure multi-party computation.
The multi-party comparing problem with no information leaking is generalized from the millionaires' problem, which is used to get whether these parties' secret inputs are all equal and if not, the number of users whose inputs are the same to a indicated user Pn's. Based on the semantic secure homomorphic encryption and the multi-threshold secret sharing scheme, a protocol of comparing multi-party information of equality is proposed. The correctness, security and efficiency are analyzed. The round complexity is two, the computation complexity is O(nk) modular exponentiations and the communication complexity is O(O2l) bits.