Verifiable Security Outsourcing Computing Method For Large Matrix In Cloud Environment

With the rapid development of the Internet and the enhancement of users' security awareness,protecting users' privacy and security has become the demand of most people.However,with the emergence of cloud computing,more and more users outsource the storage and calculation of their private data to untrusted clouds.How to ensure user privacy and security while enabling users to use the powerful cloud service provider Computing power has become an urgent problem to be solved.In this context,the fully homomorphic encryption technology emerged as the times require,and the fully homomorphic encryption technology allows certain operations to be performed on the ciphertext,so as to obtain the corresponding operation result of the plaintext.The good features enable the fully homomorphic encryption technology to be applied in various fields,such as electronic voting,ciphertext retrieval,and secure multi-party computing.Among them,electronic voting technology,as a major emerging technology,has quickly become the focus of research in various countries due to its convenient voting process and the powerful computing power provided by cloud servers.The feature of fully homomorphic encryption technology that can calculate plaintext by calculating ciphertext also makes the electronic voting technology based on homomorphic encryption shine.Therefore,this article has done the following work:First,analyze and study the key generation algorithm,encryption algorithm,decryption algorithm and homomorphic operation algorithm of the fully homomorphic encryption algorithm GSW-FHE scheme.Since the GSW-FHE scheme is mainly based on approximate feature vectors to construct public and private keys,it is At this time,all those involved in the calculation are matrices or vectors.Naturally,the GSW-FHE scheme is extended to the encryption and decryption of matrices.A matrix addition outsourcing scheme based on the GSW-FHE scheme is proposed,and the proposed scheme is simulated.And test,by comparing the calculation time of the encryption and decryption algorithm and the homomorphic calculation algorithm of the two schemes,the analysis shows that the scheme proposed in this paper can effectively outsource the addition of the matrix to the cloud for calculation.Then,based on the matrix addition outsourcing scheme proposed in the previous article,by constructing a characteristic voting matrix,a multi-candidate anonymous electronic voting system based on a trusted third party is given.The system uses the NTRU-Prime algorithm based on the lattice password to generate the public and private key pairs in the digital certificate,and performs identity authentication and key exchange through the structure of the message authentication code,which effectively guarantees the security and traceability of the voting process.In addition,,Because a trusted third party is the vote-counting party,it is impossible to obtain the votes of every voter,thus achieving anonymity.Finally,since the GSW-FHE scheme itself is only a hierarchical homomorphic encryption algorithm,the original algorithm can only be optimized through Bootstrapping,so as to achieve a fully homomorphic operation of any level.The anonymous electronic voting system proposed in this article is also just a hierarchical matrix addition outsourcing scheme.After simulation tests,it can only provide 400 voters at the same time voting,which limits the efficiency of voting.In order to solve this defect,this article finally gives a Bootstrapping scheme based on this system,which increases the number of homomorphic calculation stages of this electronic voting system,so that the original system can count more voters' votes at the same time.Compared with the existing matrix outsourcing scheme,this scheme does not reduce the upper limit of noise,but because of the need to encrypt n data,the ciphertext space is increased to twice the original scheme.Compared with the original scheme,which can only perform homomorphic operations on one bit,this scheme has better practicability.