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ACIS International Conference on Software Engineering, Artificial Intelligence, Networking and Parallel/Distributed Computing (SNPD)

A Study of Secure Multi-party Ranking Problem

Wen Liu, Shoushan Luo, Ping Chen

Published Jul 1, 2007• 23 citations
Publisher

Abstract

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.

DOI
10.1109/snpd.2007.367

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•Jan 1, 2007•19 citations
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.
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, 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.
In the present paper, a secure multi-party protocol for sorting the private values, without disclosing them, is presented. We extend the Yao's millionaire problem to n parties. Secure comparison and sorting the wealth of n parties using the Yao's protocol requires running it n×(n-2)/2 times. For a wealth interval of N, the complexity the Yao's protocol execution for these n parties has an order of N × n2. The Secure Multi-party Computation method is utilized to develop the protocol of secure multi-party sorting. We also employ an easy knapsack problem to distinguish the corresponding indices of different participants. Moreover, a modified version of the distributed oblivious transfer protocol is proposed to improve our proposed protocol and reduce its overall compexity. The computational and communication complexities of our protocol for secure multiparty sorting based on the distributed oblivious transfer, are both equal to n. Finally, the security of the proposed protocol against adversaries of semi-honest type is proved.
Consider several parties that do not trust each other, yet they wish to correctly compute some common function of their local inputs while keeping these inputs private. This problem is known as "Secure Multi-Party Computation", and was introduced by Andrew Yao in 1982. Secure multi-party computations have some real world examples like electronic auctions, electronic voting or fingerprinting. In this thesis we consider the case where there are only two parties involved. This is known as "Secure Two-Party Computation". If there is a trusted third party called Carol, then the problem is pretty straightforward. The participating parties could hand their inputs in Carol who can compute the common function correctly and could return the outputs to the corresponding parties. The goal is to achieve (almost) the same result when there is no trusted third party. Cryptographic protocols are designed in order to solve these kinds of problems. These protocols are analyzed within an appropriate model in which the behavior of parties is structured. The basic level is called the Semi-Honest Model where parties are assumed to follow the protocol specification, but later can derive additional information based on the messages which have been received so far. A more realistic model is the so-called Malicious Model. The common approach is to first analyze a protocol in the semi-honest model and then later extend it into the malicious model. Any cryptographic protocol for secure two-party computation must satisfy the following security requirements: correctness, privacy and fairness. It must guarantee the correctness of the result while preserving the privacy of the parties’ inputs, even if one of the parties is malicious and behaves arbitrarily throughout the protocol. It must also guarantee fairness. This roughly means that whenever a party aborts the protocol prematurely, he or she should not have any advantage over the other party in discovering the output. The main question for researchers is to construct new protocols that achieve the above mentioned goals for secure multi-party computation. Of course, such protocols must be secure in a given model, as well as be as efficient as possible. In 1986, Yao presented the first general protocol for secure two-party computation which was applicable only to the semi-honest model. He uses a tool called "Garbled Circuit". Yao’s protocol uses the underlying primitives ("Pseudorandom Generator" and "Oblivious Transfer") as blackboxes which lead to efficient results. After Yao’s work many variants and improvements have been proposed for the malicious model. In this thesis, we design several new protocols for secure two-party computation based on Yao’s garbled circuit. Before we present the details of our new designs, we first show several weaknesses, security flaws or problems with the existing protocols in the literature. We first work in the semi-honest model and then extend it into the malicious model by presenting new protocols. Finally we add fairness to our protocol. Oblivious transfer (OT) is a fundamental primitive in modern cryptography which is useful for implementing protocols for secure multi-party computation. We study several variants of oblivious transfer in this thesis. We present a new protocol for the so-called "Committed OT". This protocol is very efficient in the sense that it is quite good in comparison to the most efficient committed OT protocols in the literature. The abovementioned flaw with the use of OT can be fixed with our committed oblivious transfer protocol. Furthermore, it is more general than all previous protocols, and, therefore, it is of independent interest. We also deal with fairness in this thesis. For protocols based on garbled circuit, so far only Benny Pinkas has presented a protocol in the literature for achieving fairness. We show a subtle problem with this protocol where the privacy of the inputs of one party can be compromised. We also describe this problem in detail which is in fact related to the fairness, and finally propose a more efficient scheme that does achieve fairness.