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International Conference on Management and Service Science (MASS)

Secure Two-Party Multi-Dimensional Vector Comparison Protocol

Lei Shi, Yonglong Luo, Caiyun Zhang

Published Sep 1, 2009• 3 citations
Publisher

Abstract

Secure two-party vector dominance means that the two sides of the computation want to judge whether their vectors have the dominance relation securely, a new problem which is called multi-dimensional vector comparison problem is proposed based on the vector dominance in this paper, it can be applied in many commercial areas, such as auction, bidding and so on. Two solutions are provided for this problem, using multiplication protocol and scalar products protocol respectively. Furthermore, we introduce the random algorithm to solve the problem, analyze the security, correctness and complexity, point out the differences between these two methods, and simulate by experiments.

DOI
10.1109/icmss.2009.5302846

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Secure two-party vector dominance means that the two sides of the computation want to judge whether their vectors have the dominance relation securely, a new problem which is called multi-dimensional vector comparison problem is proposed based on the vector dominance in this paper, it can be applied in many commercial areas, such as auction, bidding and so on. Two solutions are provided for this problem, using multiplication protocol and scalar products protocol respectively. Furthermore, we introduce the random algorithm to solve the problem, analyze the security, correctness and complexity, point out the differences between these two methods, and simulate by experiments.
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.
The millionaire’s problem is the origin of secure multi-party computation. This problem has always been the focus of scholars' research, and it is also the design basis and important part of other secure multi-party computation protocols. An in-depth study of the millionaires’ problem is of great significance to promote the further development of secure multi-party computation. Based on millionaires’ problem and secure vector dominance protocol, we propose an improved protocol and an extended protocol. The improved protocol solves the problem of coarse granularity when comparing elements in the original protocol, and can realize that two parties can compare the relationships of greater than, equal to or less than between their elements by executing the protocol once. The improved protocol and the extended protocol are further applied to solve the problem of finding the cardinality of the intersection of the two-party sets in two cases. In addition, based on the integer division problem, we give a method to privately evaluate the greatest common factor of two integers.
The relationship of a point and a rectangle area is that two parties based on the input of information to complete the security of the points-range inclusion problem,and they can't get information from each other.It is a secure two-party computation problem,and can be applied in commerce field.In this paper,a protocol for the points-rectangle area inclusion problem which is based on scalar product protocol is developed,and its correctness,security and complexity are analyzed,and the corresponding algorithms for determining the relative position of point and rectangle area are also presented.
Private integer comparison has been an essential computation function for many applications, including online auction, credential identification, data mining, and joint bidding. In the setting of two-party computation, two parties with private inputs (x and y) want to jointly compare them without revealing the value of those inputs to others (also known as the Millionaires’ problem) while the output should ensure correctness and preserve data privacy. The private inputs only can be revealed if they are equal, i.e., x = y. Many related works have been proposed to solve the integer comparison problem in various settings, focusing on different properties such as round and computation complexity. Most solutions decompose integers into bitwise representation and then securely evaluate the function in a Boolean circuit on encrypted bits. However, this type of solution is costly (especially for large integers) as each bit requires encryption and decryption. In this paper, we transform the private integer comparison into a block comparison problem. In particular, we employ a block vectorization mechanism to encode the private inputs into blocks. We show the security of our two-party protocol in the semi-honest model. Also, we implement the protocol to demonstrate its efficiency using block vectorization mechanism and homomorphic encryption. The experimental result proves that our proposed solution achieves high efficiency, particularly for large integer comparisons.
At present, research on secure multi-party computation is of great interest in modern cryptography. It should be acknowledged that if any function can be computed securely, then it results in a very powerful tool. In fact, all natural protocols are, or can be rephrased to be, special cases of the multi-party computation problems. Design and analysis of the special multi-party computation protocols is meaningful and has attracted much interest in this field. Based on the combination of a public-key cryptosystem of the homomorphic encryption and on the theoretic construction relying on the F-hiding assumption, a protocol for comparing information of equality is proposed. The protocol needs only a single round of interaction and ensures fairness, efficiency and security. The protocol is fair, which means that one party knows the sound result of the comparison if and only if the other one knows the result. The protocol is efficient with the help of an oblivious third party for calculating. However, the third party cannot learn any information about the participant抯 private inputs and even about the comparison result, and cannot collude with any participant. The protocol is secure for the two participants, that is, any information about their secret input will not leak except the final computation result. A precise proof of security of the protocol is presented. Applications of this protocol may include private bidding and auctions, secret ballot elections, commercial business, identification in a number of scenarios and so on. It is believed that the protocol may be of practical significance for electronic transaction.
Secure scalar product protocol is an important fundamental protocol in secure multi-party computation. Serving as a basic building block for many other secure protocols, it is widely used in data mining, statistical analysis and scientific computation. Based on additive homomorphism public key cryptosystem, we develop a new secure scalar product protocol under semi-honest model with low communication complexity which is easy to implement and understanding. Furthermore, we firstly apply it to position relationship decision for privacy preserving space vectors.