Research On (Fully) Homomorphic Encryption And Its Application In Cloud Computing

With the rapid development of network technology,security situation of network is deteriorating day by day.With the help of cloud computing platform,users can store and process data.With the development of big data and popularization of cloud computing,how to realize secure and effective use of big data in the cloud compouting and privacy protection of users are also the focus of research in the field of network security.In particular,with the rapid development of quantum computing technology,how to implement secure data processing in the quantum computing is also particularly urgent.In the face of such a complex situation,implementation of cryptographic algorithm of anti-quantum attack,which supports directly processing encrypted data,is urgent for network security,privacy protection of user,big data processing and cloud computing.Therefore,this paper researches homomorphic encryption and its application:1.Optimization and implementation of homomorphic encryption algorithm.In order to meet the growing demand for encrypted data processing,this paper implemented,tested and optimized the existing(fully)homomorphic encryption algorithm.This paper firstly implemented multi-bit homomorphic addition and multiplication computing in multiple(fully)homomorphic encryption schemes based on plaintext packaging technology.The basic solutions of this paper have implemented including BGV,FV,YASHE and LTV schemes.In the implementation of basic(fully homomorphic encryption)schemes,this paper mainly used the batch homomorphic evaluation of SIMD.Based on SIMD technology,this paper supports homomorphic additive and multiplicative evaluation of multi-bit data.Then,based on the automorphism algebric structure in the algebraic number theory,this paper implemented a parallel homomorphic encryption scheme based on SSE instruction.In the implementation scheme that supports the SSE instruction,the arbitrary movement of data in the plaintext slot is realized.This paper implemented parallel homomorphic evaluation with multithreading.Optimized(fully)homomorphic encryption scheme can implement multi-bit plaintext packaging and parallel computing under SSE instruction.On the basis of maintaining security of the original scheme,efficiency of the implementation is greatly improved.The improved(fully)homomorphic encryption scheme is nearly 60 times more efficient than the previous original scheme.At the same time,the expanded rate of ciphertext for the improved scheme is greatly reduced.2.Application of(fully)homomorphic encryption for the encrypted image processing.In order to realize privacy-preserving multimedia data(image)processing,this paper applied the improved(fully)homomorphic encryption and provided a homomorphic encryption scheme that supports more computing types.Based on the above homomorphic encryption schemes,this paper implemented homomorphic comparison of encrypted data,homomorphic division operation based on encrypted data and computation of partial derivatives based on encrypted data.The above homomorphic evaluation types do not require or requires only a small amount of interaction between user and cloud server.These extended homomorphic evalution types can meet the needs of practical applications.Based on the extended computing types,this paper have implemented efficient feature extraction of encrypted image,encrypted image matching and retrieval.3.Privacy-preserving statistical learning and machine learning based on encrypted data.Based on the requirement of data utilization for big data,this paper first provided a statistical learning scheme based on a leveled(fully)homomorphic encryption scheme.In this scheme,this paper constructed a non-interactive protocol for encrypted data comparison.Based on this protocol,our scheme can achieve the acquisition of a part of the statistical learning model based on encrypted training data and classification of the new encrypted data.These models only need to carry out homomorphic addition,homomorphic multiplication and encrypted data comparison.For most statistical learning models,because of complexity of the model,they can not carry out model training with encrypted training data.These models can perform classification of new encrypted data using a trained model in the plaintext domain.In order to support more learning models,this paper also provided machine learning scheme based on functional encryption.This paper first constructed a new attribute-based encryption scheme using fully homomorphic encryption.According to the attribute-based encryption scheme,combined with garbled circuit,this paper provided a concrete functional encryption scheme.Based on concrete functional encryption scheme,this paper provided machine learning scheme in the encrypted domain.This scheme can train encrypted training data set for most machine learning models,and obtain encrypted machine learning models.Then,using the new obtained machine learning models,cloud server can classify the new encrypted data.In the execution of entire scheme,communication costs between user and cloud server has been greatly reduced.This scheme can achieve more efficient applications of statistical learning and machine learning.The model training supported by this scheme almost covers all the commonly used models in machine learning.