Research On Privacy-preserving Statistical Computation

The high-speed development of network opened a new era of information processing. With the magical increasing of shared data resource, the security issues attracted more and more people's attention. On one hand, each group is gathering valuable data during its growing up and protecting it strictly as a special form of wealth. On the other hand, the interest of maximizing the value of information is driving the collaboration beteween different groups. Under such situation, privacy-preserving techniques for calculation coopratively are shining up and warmly welcomed by all the social circles.In order to meet the above security demands, secure multi-party computation (SMC) emerged. In 1982, A.C. Yao brought forward the millionares' protocol and first introduced the field of SMC. Then, Oded Goldreich enriches its theory and formalized model. After a long time of expanding, SMC techniques become to be used to design special protocols for special work. Nowadays, it is showing a big potential for the applications in the areas of data mining, electronic transactions, scientific computation, information retrieval, computational geometry etc. And it is attracting more and more scholars and teams launching into this research.Privacy-preserving statistical computation is an important branch of secure multi-party computation, it helps two or more users who are distrustful of one another to carry out statistical analysis without leaking private information. Since privacy-preserving statistical analysis is cited as one of the applications of SMC by Du Wenliang in 2001, a few preliminary problems such as mean value, variance analysis and linear regression have been solved by some researchers. However, statistics is multiform and shows wide prospect of applications in military affairs, politics, finance and medical treatment. So, it is also a problem for urgent solution under the popular use of privacy-preserving techniques.For the importance of discribing sample data, matrix operation is considered firstly. Then, a few basic problems of statistical analysis are solved securly. At last, practical issues are studied. With this concern, the main research content of this dissertation consists of:1. An efficient pro rata protocol is improved by the use of SMC techniques. And the privacy-preserving rank computation protocol is brought forward. After that, the security of the protocols is proven in the form of iteration.2. Protocols to compute eigenvalue are proposed. They can be carried out without leaking any message to each one of the two parties. One will solve the problem efficiently for a special kind of matrix, and another is a scheme to gain all the eigenvalues securely. They are designed with the flexible use of mathematical calculation and SMC skills according to different situations. On the basis of eigenvalue, the calculation of eigenvector and exponentiation are also considered in this dissertation.3. A few statistical measurements' computation are discussed under the demand of privacy-preserving which includes harmonic mean, weighted mean, geometric mean, mode and root mean square. The characters of computing them are summarized systemly to organize into three kinds. For each one, we adopt an efficient tool of SMC techniques to slove it and verify its security rigorously.4. Multiple linear regression in secure two-party model is considered in this dissertation. After the maximum likelihood estimate has been solved, the sum of squared residuals and regression sum of square are deduced securely. In order to improve performance, simplification of matrix continued product is summarized. Through this method, the difficulty of never leaking two pivate data's sum is overcomed and the calculation of multiple linear regression securly is realized.