Research On Two Types Of Privacy-preserving Scientific Computing Problems

Since the third industrial revolution,information technology has developed rapidly all over the world,and our lives have also undergone earth-shaking changes.The distance between people is getting closer and closer.Compared with the previous underdeveloped communication,it greatly facilitates people's communication.But everything has two sides,and information security risks are deeply lurking in our lives.Cryptography is an important guarantee for information security.With the in-depth study of cryptography by experts and scholars,secure multi-party computing has been proposed and regarded as one of the current research hotspots in cryptography.The concept of secure multiparty computation was first proposed in 1982 by Professor Yao,who is the winner of the Turing Award.The so-called secure multiparty computation means that two or more participants use their own confidential information to perform cooperative computing under the premise of not divulging the confidential information of each party to obtain the desired result.During the entire calculation process,it is impossible for each participant to know the confidential information of other participants.At present,there are a lot of secure multiparty computation protocols in the world of cryptography.but some protocols' efficiency is not ideal,it needs to be improved strongly,and many new secure multiparty computation issues have yet to be studied.The problem of confidential scientific computing is an important part of secure multiparty computation.The main problems studied in this paper are the millionaires' problem and the confidential calculation problem of collective membership.The specific work is as follows:For the millionaires' problem,this article uses 0-1 coding to encode one party's private data into a vector consisting of 0 and 1.and the other party does not perform coding operations.He needs to calculate the sum of two adjacent elements in the vector,and then judge the result of the millionaires' problem by the value of the sum.The problem of millionaires was reduced to the sum of elements,and the original problem was solved;then,combined with the Paillier homomorphic encryption algorithm to protect privacy,a safe and efficient protocol was designed.The agreement can judge the equality of the two confidential data;finally,the agreement is analyzed in three aspects,not only to prove the security of the agreement based on the security definition,but also to ensure the correctness of the agreement result.The third is to ensure the agreement of this article It is better than the existing millionaire problem protocol,so it is necessary to analyze the computational complexity and communication complexity of these protocols and compare them with each other.For the privacy-preserving calculation problem of the set membership,this article uses 0-1 coding to encode the confidential data and the confidential set of the two parties into two vectors with the same dimension,and then multiply a certain corresponding position element of the two vectors,and pass the value of the product To judge whether the confidential data is in the confidential collection,the problem of confidential calculation of the membership relationship of the collection is reduced to the element integration;then the Paillier homomorphic encryption algorithm and the elliptic curve cryptography system are used to protect privacy,and two safe and efficient protocols are designed;Finally,in order to ensure the correctness and safety of the protocol designed in this article,we have attached an accurate proof process.It also sorts out the complexity of the agreement,and compares its efficiency with the agreement on the confidential calculation problem of the existing collective membership.This article addresses the above two issues while designing a new security protocol,but also provides corresponding applications.