| Based on the basic ideas of LIU’s proposed Fully Homomorphic Encryption scheme for real number computation and Multi-key Homomorphic Encryption scheme,this paper proposes a Fully Homomorphic Encryption scheme that supports complex number computation based on the original scheme.We hope to meet the requirements of the project "Key Technologies and System Integration Research for Multi-Source Aviation Intelligence and Aviation Rule Information Fusion",while implementing Fully Homomorphic Encryption for complex numbers.The main research work carried out in this paper is as follows.1.For complex number data in the route planning project,the Fully Homomorphic Encryption of complex numbers was implemented in the current scheme.The scheme consists of two modules:Module 1 performs homomorphic operations on real number data and achieves Fully Homomorphic Encryption of real numbers.Module 2 performs homomorphic operations on complex number data and performs Fully Homomorphic operations on the input complex number data through an improved encryption and decryption process and homomorphic calculation process.The correctness,homomorphism,and security of the scheme were proved theoretically and through examples,and the scheme was implemented through coding.Finally,numerical experiments were conducted to verify that the implementation of fully homomorphic encryption of complex numbers meets the requirements of the project.For any function calculation,the decryption of the encrypted result is equivalent to the direct calculation of the function result,which satisfies the properties of Fully Homomorphic Encryption,and the error is controlled within a reasonable range.2.This article conducts experimental analysis on parameters that affect the efficiency of solutions for privacy computation in aviation planning,specifically for the concrete functions involved.The workflow between local and cloud platforms is simulated.Through experiments on privacy computation with complex power,it is concluded that the parameters that affect the time cost of solutions for specific functions include the logarithm of key pairs in the key K(m)and the value of n in the function(a+bi)n.The time complexity of the solution is O(mn).Through the privacy computation experiment of complex number division,it is found that for the specific function(a+bi)/(c+di)of the project,the parameter that affects the time cost of the scheme is the logarithm m of the key pair in the key K(m),and the time complexity of the scheme is O(m3);Finally,through the privacy computation experiment of cloud computing,it is found that the value range of k,m,t and r in the key pair K(m)and random array R can be arbitrarily large without affecting the efficiency of the scheme. |
