CRT-Based Homomorphic Encryption over the Fraction

Abstract

Homomorphic encryption technology is the holy grail of cryptography and has a wide range of applications in practice. This paper proposes a homomorphic encryption scheme over the fraction based on the Chinese remainder theorem (CRT) Dayan qiuyi rule. This homomorphic scheme performs encryption and decryption operations by forming congruence groups and has homomorphism. The solution in this paper first combines the traditional CRT algorithm with the Dayan qiuyi rule to obtain the CRTF algorithm that can be operated on the fraction field. Finally, in the decryption process, modulo arithmetic is used twice to obtain the correct plaintext components, restored to plaintext by CRTF. The scheme’s security is related to a decisional version of an approximate GCD problem. The proof of theoretical derivation shows that this paper’s homomorphic encryption scheme can realize the homomorphic addition operation in the fraction field. Compared with the CKKS scheme, efficiency is improved.