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Computer Technology and Development

A Security Protocol for Points-Rectangle Area Inclusion

Lei Shi

Published Jan 1, 2009• 0 citations
OpenAlex

Abstract

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.

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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.
The relationship of a point and a range is that two parties based on the input of information 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 many fields,such as military field and commerce field.In this paper,two protocols for the points-range inclusion problem are developed.One is based on comparison,and the other is based on homomorphic encryption schemes.At the same time,their correctness,security and complexity are analysed.
Secure multiparty computation is a very important research topic in cryptography. The sub-problem of secure multiparty computation that has received special attention by researchers because of its close relation to many cryptographic tasks is secure two-party computation. This area of research is concerned with the question: ldquoCan two party computation be achieved more efficiently and under weaker security assumptions than general multiparty computation?rdquo Yaopsilas protocol provided security against passive adversaries, while Lindell and Pinkas proposed secure two party protocols that are secure against active adversaries. In this paper, we would like to propose a set of information theoretically secure protocols based on scalar product protocol. The detailed complexity analysis is also provided.
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.
It is well known that, in theory, the general secure multi-party computation problem is solvable using circuit evaluation protocols. However, the communication complexity of the resulting protocols depend on the size of the circuit that expresses the functionality to be computed and hence can be impractical. Hence special solutions are needed for specific problems for efficiency reasons. The point inclusion problem in computational geometry is a special multiparty computation and has got many applications. Previous protocols for the secure point inclusion problem are not adequate. In this paper we modify some known solutions to the point inclusion problem in computational geometry to the frame work of secure two-party computation.
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.
Scalar product protocol and privacy preserving add to multiply protocol (PPAtMP) are two significant basic secure multiparty computation protocols. In this paper, we claim that the two protocols are equivalent to each other and we can achieve one based on the other with the same communication and computation complexity. Then, we propose Secure Two-party Mean Protocol, Secure Shared x ln x Protocol and Secure Shared Generic Polynomial Protocol based on scalar product protocol and PPAtMP. Additionally, we analyze the correctness, security, communication overheads and computation complexity of each protocol proposed in this paper.