Researches On Private Set Intersection Computation Protocols For The Cloud Environments

Secure Multi-party Computation(SMC)is a hot topic in cryptography which provides a universal solution for distributed collaborative computing with privacy protection.As a specific example in SMC,the Private Set Intersection(PSI)computation problem can ensure users to obtain set intersections without revealing their private set information.With the development of cloud computing,more and more users save their set information on cloud servers,and then complete the intersection computation with the assistance of the cloud.However,many PSI protocols for the cloud environments still exist the following problems: inefficiency,hidden security risks,and the inability to provide natural and safe data storage.In this paper,we apply set representation technology to convert set operation problems into mathematical problems,and then combine cryptographic tools such as pseudo-random function and homomorphic cryptosystem to propose efficient privacy-preserving set intersection computation protocols for the cloud environments.First,based on the set's polynomial and point-value pair representation,we convert the set intersection computation into polynomials solution: Represent set elements as the roots of the polynomials,calculate their point-value pair vectors,randomize the point-value pair vectors,and then send the hidden point-value pair vectors to the cloud server.Then,combined with cryptographic tools such as pseudo-random function and homomorphic cryptosystem,a privacy-preserving two-party set intersection computing protocol is designed for the cloud environments.At the same time,a strict formal security proof of the protocol is given under the semi-honest model.After that,we further combine the hash mapping technology to design an optimization scheme to reduce the running time of the two-party protocol by tens of times,greatly improving the efficiency.Meanwhile,a strict form security proof of the hash optimization protocol is given under the semi-honest model.Finally,we use GMP,NTL and other C++ libraries to implement those protocols and similar protocols,and compare performance and security.The results show that the new protocols enjoy the following advantages:(a)provides a natural secure data storage;(b)normal channels are suitable to our protocol;(c)compared with other similar protocols,the communication and calculation complexity are greatly improved,and the protocol is efficient and practical;(d)provides detailed and formal security proof based on a standard simulation simulator.Finally,in order to make the protocols more applicable,we design a multi-party set intersection computing protocol for the cloud environments.And a strict formal security proof under the semi-honest model is given,while the protocol and similar protocols are implemented under the C++ environment.Finally,the performance and security are compared while results show that the multi-party protocol also has the advantages of the two-party protocol along with the following advantages: the protocol is more scalable because intersection computation is more delegated to the server,and protocol is more suitable for calculating set intersections for large-scale sets.