Research On Secure Multi-party Computation Of Several Set Problems

With the rapid development of network technology,multiparty collaborative computation has become an increasingly common computation mode in computer networks.Due to the virtuality of the network environment,the slightest careless-ness in the collaborative computation process may lead to privacy disclosure of data,so protecting the privacy of the participants’ data in the collaborative computation is a key issue.The application of secure multiparty computation technology can not only give full play to the role of private data,but also protect the confidentiality and privacy of data,which makes secure multiparty computation become a main method of privacy-preserving computation,and has been widely studied.Secure multiparty computation of set,problems is an important,research content in cryptography,and it has been widely used in many fields.The existing secure computation of set problems mainly studies two-party set computation on integer set,and there are many related research results.In other research directions,there are still many important,set problems have not,been solved.On the one hand,the existing research results of the set problem are mainly aimed to the computation of two-party set.There are few research schemes about the computation of multi-party set,and the computational efficiency of the existing schemes are not ideal,which has no practical application.On the other hand,the secure computation of set problems on the rational number field have not been studied,which limits the applicable scope of the secure set computation.Therefore,it is necessary to design schemes with higher efficiency and wider applicability.In this paper,we focus on the above two aspects of set problems,deeply explore the multiparty set problem on the integer set,and the two-party set problem on the rational number field,and design efficient and secure protocols for above two problems.The main research contents of this paper are as follows:(1)We design two different encoding schemes for integer set and rational set,so that each participant’s private set is hidden in a special array.Combining with the homomorphic encryption algorithm,the secure set computation problem is trans-formed into that of secure array computation.(2)We design secure and efficient computation protocols for several basic set operations.These protocols are suitable for the secure computation of two-party sets and multiparty sets.Then,we strictly prove that these schemes are secure in the semi-honest model and can resist any collusion attacks by using simulation paradigm.Finally,we modify the protocol under the semi-honest model and design the related protocol in the malicious model.(3)We propose and solve a new problem of privacy preserving two-party set computation on the rational number fields.Firstly,we use computational geometry to transform the set problem into an array problem.Combining with homomorphic encryption algorithm,we design secure computation protocols for several basic set problems on the rational number field.These protocols can guarantee the privacy of set elements and set cardinality.The efficiency analysis show that the proposed protocols have obvious advantages in computational efficiency.Then,we give an application example of the above protocols in rational point set problem.