Homomorphic Encryption Based on Post-Quantum Cryptography

The development of Shor's algorithm makes it possible to solve some of the problems that are currently NP-intermediate, e.g. the prime factorization problem and discrete logarithm problem, in polynomial time. Hence, the homomorphic encryption algorithms that are designed based on prime factorization may be vulnerable to quantum computing attacks. Considering the post-quantum cryptography, this study proposes a homomorphic encryption method which is devised based on nonnegative matrix factorization (NMF) owing to the NP-hardness of the NMF problem and constructs the homomorphic encryption function through the code-based cryptography method for withstanding the quantum computing attacks. The feasibility of the proposed method is demonstrated by the derived mathematical models coupled with some calculation examples illustrating the detailed method steps. Our conducted experiments show that the proposed method has a shorter encryption/decryption time than the mainstream cryptographic algorithms based on the RSA or elliptic-curve cryptography.