Homomorphism Encryption Algorithm for Elementary Operations over Real Number Domain

Based on the homomorphism of Lee et al, Xiang Guangli et al proposed similar module and implemented encrypting operations of addition, subtraction, multiplication and division over real number domain. There was additive and multiplicative homomorphism heretofore. But their cipher text leaks the information of decimal fraction, sign and relationship of big and small. We propose additive, subtractive, multiplicative and divisive homomorphism over real number domain based on representation of real number by positive integer and Fermat's Little Theorem. We prove the security and correctness of the proposed homomorphism encryption system. The results of instances show that there are no the problems mentioned above in our algorithm.