Design And Applications Of Secure Multi-party Computation Protocol Based On Homomorphic Encryption

The secure multi-party computation was first proposed by Chinese scientist and Turing Award winner Professor Andrew Chi-Chih Yao in 1982.After more than 30 years of development and enrichment,it has become one of the hotspots in the field of international cryptography.Now it has become an important branch,of the cryptography.Therefore,studying the secure multi-party computation has important theoretical significance and practical application value.This paper focuses on the Millionaires' problem,multi-party secret computing set intersection problem,and multi-party secret computing maximum and minimum problem.The main work is as follows:The millionaires' problem is a classic problem of the secure multi-party computation.However,so far the existing solutions are not efficient and affect the practical application.Moreover,most previous schemes do not distinguish whether the two numbers are equal.Aiming at these drawbacks,a new solution,in this paper,is proposed to solve the millionaires' problem.The scheme first gives a new l-r enc.oding method to construct a vector according to a given confidential data.The encoding guaranteed a kind of one-to-one correspondence between the con,fidential data and the vector.Then,Based on what mentioned above,the millionaires' problem is transformed into the product of two elements in the vector.Thus,The initial problem was solved by calculating the product result to distinguish the size of the two confidential data.Subsequently,a secure protocol was designed to solve the Millionaires' problem by taking advantage of the EIGamal homomorphic encryption algorithm.Finally,the correctness,security,complexity and performance of the new protocol are analyzed.compared with the existing related protocol,the protocol of this paper is not only simple and efficient,but also the compare was more fine-grained.The multi-party secure set intersection problem and the multi-party secure computing maximum and minimum problem,and the both of them are the basic problems that need to be solved in the privacy-preserving data mining and statistical analysis,respectively.The research status about these two problems and the advantages and disadvantages of many existing solutions are analyzed.most of the previous solutions cannot resist quantum attacks,the efficiency is not efficient,and the solutions using cloud outsourcing are less.Aiming at these issues above,two new solutions to solve these two problems are proposed in this paper.In the scheme,two kinds of 0-1 encoding methods are first given.Subsequently,the two problems are solved utilizing the 0-1 encoding methods and combining with NTRU homomorphic encryption,respectively,and new protocols are designed.At last,the correctness,security,complexity and performance of the new protocols are analyzed,the two protocols designed in this paper,compared with the previous schemes,are not only secure against the quantum attack but also more efficient.In addition,it is in the cloud computing environment that the new corresponding protocols are given to solve the these two problems at the first time.The new solutions are proposed aiming at the three problems mentioned above in this paper,the corresponding secure protocols are designed,and then related applications based on these protocols are given.