Research And Application Of Homomorphic Encryption Over Integer

The rapid development of cloud computing,mobile edge computing(MEC)has brought great challenges to data privacy.It is one of the most urgent problems for cloud computing and MEC to data privacy and computability.The ciphertext arithmetic operation of homomorphic encryption over integer is an important method to solve the data privacy problem.Now,the ciphertext operation schemes cannot implement ciphertext division or ciphertext of multibit integer arithmetic operation.This paper presents the ciphertext operation process of multi-bit integer based on the operation rules of complement,addition,subtraction,multiplication and division of plaintext integer.Homomorphic evaluation of addition,subtraction,multiplication and division of multibit integer ciphertext are redesigned,according to the homomorphic multiplication and homomorphic addition.Then,this paper proposes a homomorphic evaluation of the integer arithmetic operations(HE-IAO)that implements data with integer homomorphic encryption to ensure data privacy and computability.The HE-IAO can not only implement ciphertext division,but also implement homomorphic evaluation of the multi-bit integer arithmetic operations.Last,this paper discusses the complexity and security of HE-IAO scheme.The noise ceiling of this scheme is obtained by analyzing the growth process of homomorphic encryption noise over integer.The noise ceiling of homomorphic evaluation of the complement,addition and subtraction operations is a function of the noise length,and the homomorphic evaluation of the multiplication and division is an exponential function of the length of the ciphertext vector.According to the characteristics of MEC,this paper optimizes the calculation process of HE-IAO and applies HE-IAO to calculation of privacy data in MEC.According to the general scenario of MEC,this paper designs experiments to verify the feasibility of MEC.The experimental results show that: divide the ciphertext vector of integer encryption into subvectors of length 2 and increase the length of private key of FHE to support the 3-multiplication level additional,except for the 15-multiplication level required by Bootstrapping.We test optimized our scheme in DGHV and CMNT.In the number of ciphertext refreshes,the optimized scheme is reduced by 2/3 compared to the original scheme,and the time overhead of our scheme is reduced by 1/3.We also examine our scheme in CNT of without Bootstrapping.The time overhead of optimized scheme over DGHV and CMNT is close to the original scheme over CNT.