Homomorphic Evaluation of the Integer Arithmetic Operations for Mobile Edge Computing

With the rapid development of the 5G network and Internet of Things (IoT), lots of mobile and loT devices generate massive amounts of multisource heterogeneous data. Effective processing of such data becomes an urgent problem. However, traditional centralised models of cloud computing are challenging to process multisource heterogeneous data effectively. Mobile edge computing (MEC) emerges as a new technology to optimise applications or cloud computing systems. However, the features of MEC such as content perception, real-time computing, and parallel processing make the data security and privacy issues that exist in the cloud computing environment more prominent. Protecting sensitive data through traditional encryption is a very secure method, but this will make it impossible for the MEC to calculate the encrypted data. The fully homomorphic encryption (FHE) overcomes this limitation. FHE can be used to compute ciphertext directly. Therefore, we propose a ciphertext arithmetic operation that implements data with integer homomorphic encryption to ensure data privacy and computability. Our scheme refers to the integer operation rules of complement, addition, subtraction, multiplication, and division. First, we use Boolean polynomials (BP) of containing logical AND, XOR operations to represent the rulers. Second, we convert the BP into homomorphic polynomials (HP) to perform ciphertext operations. Then, we optimise our scheme. We 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. We test our optimised scheme in DGHV and CMNT. In the number of ciphertext refreshes, the optimised 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 optimised scheme over DGHV and CMNT is close to the original scheme over CNT.