Research On Parallel Fully Homomorphic Encryption Algorithm Based On RLWE

Fully homomorphic encryption is a kind of encryption method with homomorphism, allowing one to compute arbitrary functions over encrypted data without the decryption key. The results of computation over encrypted data are equivalent to the encrypted results of corresponding computation over the plaintext. The nice property makes it have important application value in secure multi-party computation, cloud computing, digital watermarking, biometric features recognition and other related fields. Though the efficiency of FHE cryptosystem is improved continually, FHE has many defects, leading to low efficiency, such as large amount of calculation, large public-key size. The RLWE is a new problem with high security, while the low efficiency of involved algebraic polynomial modulo operation seriously restricts its performance; Outsourcing computing is an important secure multi-party computation problem. FHE can provide the underlying support for its implementation. However, its poor performance is the bottleneck problem.In view of above, the dissertation researches on fully homomorphic encryption, exploring the main work from high performance implementation and basic application as follows:(1) A brief survey on fully homomorphic encryption from basic construction method, high performance implementation and basic application was introduced, and the future research directions were pointed out.(2)A parallel accelerating scheme was proposed from RLWE.Chinese Remainder Theorem was employed to optimize algebraic polynomial modulo operation, decomposing high-dimensional polynomial into many small-dimensional polynomials. We focused on research on selecting reasonable parameters, meeting demand of security and performance;(3)The above-mentioned scheme was applied to fully homomorphic encryption; A parallel fully homomorphic encryption algorithm was designed. The implementation on the MPI clusters shows that the algorithm has high performance.(4)A secure outsourcing computing scheme was proposed based on the random reduction and fully homomorphic encryption algorithm. While meeting security requirement, the scheme has lower time complexity.Another secure outsourcing computing scheme was proposed based on MapReduce model.The implementation based on Hadoop platform shows that the scheme has high efficiency.The designed parallel accelerating scheme from RLWE has general applicability and is suitable for cryptography scheme designed from RLWE; The designed parallel fully homomorphic encryption algorithm and secure outsourcing computing scheme probe law from high performance implementation and basic application respectively, which provides a solution to efficient implementation of fully homomorphic encryption algorithm and the basic application.The experimental results show that the designed schemes have high efficiency and can satisfy the application requirements.