Research On Parallelization Of Homomorphic Encryption Algorithm And Its Applications

The homomorphic encryption technique supports direct processing of encrypted data,which can not only effectively guarantee the security of user's data,but also prevent the encrypted data from statistical analysis.This technique has broad applications on the aspects of encrypted data retrieval,data privacy protection,secure multi-party computation and encrypted database,which has attracted great public concern.However,with the continuously increasing demand for big data inquiry and processing,and the requirement for data privacy protection from the user,we are faced with the challenge of how to design effective homomorphic encryption technique.The parallel encryption technique has provided a new approach to address this issue,which makes it possible to further expand the application scenarios for homomorphic encryption algorithm.In this dissertation,the addition homomorphism of encryption algorithm,the exponential block and preprocessing method,the block matrix,the Map Reduce parallel framework and other related techniques are employed to conduct systematic research on the homomorphism of partial homomorphic encryption algorithm,somewhat homomorphic encryption algorithm and fully homomorphic encryption algorithm.Considering that most current homomorphic encryption algorithms only support integers,a floating-point fully homomorphic encryption(FFHE)algorithm which supports floating-point operation is proposed,and the parallel FFHE algorithm is designed.Then,this homomorphic encryption algorithm is further utilized to design and implement the data privacy protection scheme for financial users in the Internet based on the parallel FFHE algorithm,and further expand the application scope of fully homomorphic encryption algorithm.The main achievements in this dissertation are as follows:1.A parallel partial homomorphic encryption scheme that supports the Paillier and El Gamal encryption algorithms is proposed.First of all,for the encryption algorithm with addition homomorphism,the addition homomorphism of Paillier algorithm is utilized to divide the plaintext data into multiple relatively smaller data to reduce the size of index.Then,multiple groups of data are encrypted simultaneously based on the parallel characteristics of Map Reduce,which can realize the parallelism of algorithm,and the encryption speed of algorithm is increased.Secondly,for the El Gamal encryption algorithm with multiplication homomorphism,the exponential block technique and preprocessing technique are incorporated in this dissertation,and the line parallelism method is used to realize parallelism of algorithm.Both the theoretical and experimental results show that the preprocessing time is unrelated to the size of plaintext data,and the bigger the plaintext data volume is,the higher the efficiency of this parallel encryption scheme.2.The LWE-based BGN type parallel class homomorphic encryption algorithm is put forward.Because this algorithm has the characteristic that the main operation is matrix multiplication during the encryption process,the block matrix is employed to realize the parallelism of homomorphic encryption algorithm.During the partitioning process of matrix,the size of each block is determined based on boundary division;at the Map stage,the encryption of plaintext is mainly conducted through matrix multiplication and matrix addition operations,and during this process,the parallel performance of algorithm is mainly controlled by specifying the number of available kernels and block number;furthermore,the time-consuming problem of single Reduce can be alleviated by setting multiple parallel executions of Reduce.3.A fully homomorphic encryption algorithm that supports floating-point number is proposed,which can realize the parallelism of encryption algorithm using the plaintext data block method.Because most current homomorphic encryption schemes only support the homomorphic operation of integer data,a fully homomorphic encryption algorithm which supports floating-point operation is proposed in this dissertation.It is aimed at extending the encryption algorithm from integer to floating-point number,and expanding the application scenarios of fully homomorphic encryption algorithm.In order to improve the efficiency of encryption algorithm,the cloud computing environment is integrated to implement the Map Reduce-based parallel floating-point fully homomorphic encryption scheme.This scheme utilizes the cluster advantage to realize efficient encryption and decryption,which can effectively reduce the time of homomorphic operation,provide high security and great practicality,and well adapt to the cloud computing scenarios.4.The data privacy encryption scheme for Internet financial users is presented,which is based on the parallel FFHE algorithm.In this scheme,the RSA encryption algorithm is employed to encrypt the basic information of user for the convenience to query the encrypted database.In the meantime,the FFHE algorithm is used for encryption of transaction amount and to implement the floating-point operation of ciphertext.The data is in the form of ciphertext during storage and homomorphic computation,which can effectively protect the privacy of user data.In order to improve the efficiency of encryption scheme,the private cloud service provided by the trusted computing center can be utilized to realize parallel homomorphic operation and encryption.