Research On Privacy Preserving Linear Algebra Problems And Extended Model

Secure multi-party computation (shorted for SMC) is one of the most important research fields in modern cryptography. In a distributed network environment, to achieve security of multi-party in collaborative computing is a core problem in SMC. As computional model has changed and the privacy protection during the calculation process has become increasingly prominent, furthermore, most existing network security protocols can be reduced to a particular SMC protocol, so SMC attracts many researchers’attention.Although SMC has got rich results both in theoretical study and practical application, there are still many open problems are worthy of study. For underlying protocols, because they will affect the efficiency of the application protocols which calls them, therefore efficient and practical underlying protocols are needed to be designed. For specific secure protocols design, lacking methods to simplify protocol design, additionally, the diversity of applications makes SMC application protocols are far away from needs, new protocols for solving new problems are needed. For basic theory, further research is demanded so that useful theoretical model to expand the scope of SMC, and it can solve some problems of specific scenarios.Based on the above analysis, this thesis mainly focuses on the following three aspects:(1) Research on underlying protocols in SMCThe underlying protocols are not only the basic tools in designing application protocols, but also the cornerstone of SMC, they are abstracted from application. This paper designs a set of efficient underlying protocols, they solve some basic SMC problems. It mainly include three aspects:first, this paper uses data confusion technique, an efficient permutation protocol is designed, then secure scalar protocol is deeply studied, two improved protocols under semi-honst model and malicious model are proposed. At last, based on data block and random numbers, a secure sum protocol which can anti two-party conspiracy is proposed, the protocol get high security while remain low complexity.At the same time, these protocols are analyzed, additionally, this paper gives efficiency comparision, the results show that these protocols get a good balance during security and efficiency.(2) Research on private linear algebraLinear algebra has a wide application, this paper propose some building blocks of vector computation and matrix computation under secure linear algebra. Through building these blocks, this paper convert many SMC problems to their composable. Specifically, by using the properties of inverse matrix, the building block of SMC vectors rank is proposed, compare to existing protocol, the complexity are decreased efficiently. This paper uses it as a building block, a non-homogeneous linear equations, least square protocol and linear programming are designed. By introducing privacy reductions and composition theorem, this paper analyze the security of these two protocols, and analyze the protocols’efficiency.(3) Research on extended multi-party computation modelSMC is unable to solve the protocols which participants can’t carry out the computation task. The reasons maybe lie in the partners are short of computation resources, or maybe the users can’t take the protocols immediately. Secure outsourcing computation and proxy multiparty computation compensate these shortcomings on some degree. After deeply study these two models, this paper propose extended proxy multi-party computation model, its features are the protocols which are secure under this model must also be secure under the above two models. Therefor the SMC problems which want to use the proxy temporarily, only need to analyze the protocol under this model. This model expand the content of SMC, that is, SMC can not only solve preserve the partnes’ privacy problems, and it can also protect the partners’ privacy when they can’t complete the computations by themselves. Furthermore, this paper gives formal definition of functionality and protocol, and depicts the general solution and phases, by using this general solution strategy, this paper design a secure union set protocol, its correctness, security and discuss its efficiency are also proved.