Research On Secure Multi-party Computing Protocols For Two Mathematical Application Problems

Secure multi-party computation means that the function calculation of input data can be completed correctly without divulging the input data of the participants.The concept of secure multi-party computing was first proposed by Yao,which successfully aroused the interest of researchers and became a research hotspot in the field of cryptography.At present,the research on secure multi-party computing is divided into two directions: one is to study the basic theory of secure multi-party computing,such as the definition of security,adversary model,the design method of general protocols for secure computing,and the other is to solve the privacy protection problems in specific applications.With the rapid development of network technology and more opportunities for multi-party cooperation,privacy protection becomes more and more important,this paper studies privacy protection in specific applications.Although Goldreich et al.have given a general solution to any secure multi-party computing problem,it is too inefficient to solve practical application problems,so specific solutions should be used for specific problems.For example,application issues such as confidential data mining and confidential auctions.Although many achievements have been made in the research of secure multi-party computing,there are still many contents worth studying.In this paper,the problem of parallel straight line distance and minimum value in safe computing space is deeply studied.The main research results and innovations are as follows:1.Aiming at the problem of secure computing of the distance between two different expressions of space parallel lines,two secure computing protocols of space parallel lines based on Paillier homomorphic encryption algorithm are proposed.The protocol uses the Paillier addition homomorphic encryption algorithm and basic mathematical knowledge to hide the confidential data,so that both parties can complete the calculation and ensure that their private data is not leaked.The simulation example demonstrates the security of the protocol under the semi-honest model and analyzes the correctness of the protocol and the computational complexity and communication complexity.Compared with the protocol for solving similar problems,the protocol does not need to call the inadvertent transmission and secret dot product protocol,but proposes a spatial parallel straight line secret computing protocol based on the Paillier homomorphic encryption algorithm.The analysis and experimental comparison show that the proposed protocol is lower in computational complexity and communication complexity than other protocols.2.In this thesis,two different protocols are proposed to solve the minimum value problem of multi-party secret computing:(1)By using G?del coding to map vectors into natural numbers,combined with ElGamal multiplicative homomorphic encryption algorithm and ciphertext segmentation,an efficient and simple secret computing minimum protocol is designed,which can resist some collusion attacks.(2)Combined with threshold decryption and addition homomorphic encryption,a secret computing minimum protocol based on threshold decryption is designed to resist any collusion attack.The correctness of the protocol is analyzed.The security of the protocol is proved under the semi-honest model,the efficiency of the protocol is analyzed.On the basis of solving the problem of minimum value of safety calculation,the problems of maximum value of safety calculation,maximum common divisor and least common multiple are solved,and an application example of safety calculation minimum is given.