A Study Of Three Confidential Computing And Statistical Problems

As a core driving force of the development of the times,data brings huge benefits to human,but data can also be eavesdropped,forged,tampered,or leaked,which will result in serious security incidents and losses.In order to ensure the security of data,it is necessary to encrypt data.However,the availability of encrypted data is greatly reduced.It has become an urgent problem to compute and analyze encrypted data.Secure multi-party computation is a key technology of privacy-preserving and cooperative computation.It makes some distrusted data owners be able to perform cooperate computation on their private data.After the computation,no party receives any information other than the expected computing result.In other words,secure multi-party computation makes us use private data without leaking the privacy of the data.According to different computing scenarios,secure multi-party computation protocols can be divided into specific protocols and general protocols.Specific protocols are designed to solve specific computing problems and are usually efficient.The general protocol focuses on the completeness of the solution,and theoretically proves that all secure multi-party computation problems can be solved.Because general protocols are not efficient in solving practical problems,the existing main protocols are specific and are constructed using a variety of cryptographic tools as building blocks.In this thesis,we deeply study the secure multi-party scientific computation and secure multi-party statistical analysis.The main works are as follows.1.We propose the blind millionaires' problem:Alice,Bob,Carol,and Dove have private numbers x,y,u and v,respectively.They want to compare x+ y and u+v without revealing x,y,u,v.We use the self-blinding property of probabilistic encryption algorithm and the idea of shift register to propose a secret shift-and-add method.Based on the method and probabilistic encryption algorithm,we design three secure protocols for blind millionaires' problem in small domain.The participants of the three protocols are 3,4 and n.We prove that the protocols are secure in the semi-honest model,and conduct theoretical analysis and experiment to test the efficiency of the protocols.2.We study the secure scalar product problem.For three kinds of vectors whose components are arbitrary integers,positive rational numbers,and arbitrary rational numbers,we propose three different encoding schemes to encode different vectors.Then,combined with the Paillier homomorphic encryption scheme,we propose three protocols to compute scalar product of these three kinds of private vectors.We finally prove the security of the protocols,analyze the efficiency of the protocols,and verify the analysis by experimental results.3.We introduce a new privacy-preserving statistical counting problem:n participants jointly compute the mean of their private data,and counting the number of data that is larger than the mean.Based on the threshold Lifted ElGamal cryptosystem and Paillier homomorphic encryption scheme,we design two secure multi-party statistical counting protocols,which are used for two scenarios where the range of private data is known and is not known.We prove that the protocols are secure in the semi-honest model by using the simulation paradigm.The efficiency of the protocols are analyzed and verified by experiments.