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International Conference on Wireless Communications, Networking and Mobile Computing

Privacy-Preserving Cooperative Linear System of Equations Protocol and its Application

Xuan Yang, Zhaoping Yu, Bin Kang

Published Oct 1, 2008• 3 citations
Publisher

Abstract

Privacy-preserving cooperative linear system of equations problem is an important scientific computation and widely used in many areas such as banking, manufacturing, and telecommunications. In this paper, we present a new privacy- preserving cooperative linear system of equations protocol under the semi-honest mode, which is more efficient as compared with existing schemes. The security of the newly devised protocol is also examined. Privacy-preserving cooperative linear system of equations protocol can be used to solve many privacy preserving scientific computation problems. As an example, a secure privacy-preserving polynomial interpolation protocol is developed based on the newly devised privacy-preserving cooperative linear system of equations protocol.

DOI
10.1109/wicom.2008.1131

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Privacy-preserving cooperative linear system of equations problem is an important scientific computation and widely used in many areas such as banking, manufacturing, and telecommunications. In this paper, we present a new privacy- preserving cooperative linear system of equations protocol under the semi-honest mode, which is more efficient as compared with existing schemes. The security of the newly devised protocol is also examined. Privacy-preserving cooperative linear system of equations protocol can be used to solve many privacy preserving scientific computation problems. As an example, a secure privacy-preserving polynomial interpolation protocol is developed based on the newly devised privacy-preserving cooperative linear system of equations protocol.
We propose several practical SMC protocols for privacy-preserving cooperative scientific computations. We consider two important scientific computations which involve linear equations: the linear systems of equations problem and the linear least-square problem. The protocols proposed in this paper achieve acceptable security in the sense of Du-Zhan's paradigm and t-wise collusion-resistance, and their communication complexity is O(tm), where t is a security parameter and m is the total number of participants. The complexity of our protocol is significantly better than the previous result O( m2/μm^2/{\mu}m2/μ ) of [4], in which the oblivious transfer protocol is used as an important building block.
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.
Private comparison is fundamental to secure multiparty computation. In this study, we propose novel protocols to privately determine [Formula: see text], or [Formula: see text] in one execution. First, a 0-1-vector encoding method is introduced to encode a number into a vector, and the Goldwasser-Micali encryption scheme is used to compare integers privately. Then, we propose a protocol by using a geometric method to compare rational numbers privately, and the protocol is information-theoretical secure. Using the simulation paradigm, we prove the privacy-preserving property of our protocols in the semi-honest model. The complexity analysis shows that our protocols are more efficient than previous solutions.
Outsourcing computation to cloud server has recently become popular in cloud computing. Cloud computing technologies enable clients with limited computational resources to outsource their massive computations to powerful cloud servers. Outsourcing computation has some new concerns, such as outsourced data and result privacy, verifiability and efficiency. Matrix multiplication is one of the most basic computational problems. In this paper, we are motivated to design a secure and efficient protocol for outsourcing the massive matrix multiplication computations to the cloud server. The existing works are mostly under amortized model that have an expensive phase as offline mode. Our proposed scheme does not have any expensive phase. So the client can outsource its matrices in online mode in which the efficiency of outsourcing will be increased. In our scheme, the client encrypts two matrices and sends them to a semi-honest cloud server. The cloud server computes matrix multiplication and a proof. After that, it sends the encrypted result to the client and finally the client checks the validity of the computation and decrypts the result. Our proposed scheme achieves privacy protection of outsourced data and multiplication result, unforgeability of proof, verification and high efficiency.
In order to improve efficiency and solve the security vulnerabilities of the secure set computation protocols in practical applications, two secure two-party protocols for set membership and set intersection were proposed based on discrete logarithm problem and the polynomial representation of sets with which the set operation problem could be transformed into a polynomial evaluation problem. Firstly, a latest efficient secure set membership protocol was analyzed, and a security vulnerability of leaking the privacy of the participants by obtaining the element of participants on the brute attack was found. To overcome the security vulnerability, a new method was introduced by representing sets by polynomials and randomizing the polynomials, which could ensure the security of the participants without any leakage of interactions. Based on the discrete logarithm problem and the new method, a new secure set membership protocol was presented. The protocol could judge set-element membership with high-efficiency, and did not leak any other information about the participants besides the size of the set. Further, a secure set intersection protocol was showed according to the same technique. The security proofs of both protocols were given under the semi-honest model by using the probability polynomial time simulator, which indicated that the simulator views were computationally indistinguishable from the original protocols’ execution views. Finally, the detailed analysis about the protocols’ performance was presented, showing that both protocols were more efficient than other protocols since their communication complexity and computational complexity were smaller.