Encryption algorithm based on higher degree residues oriented to semantic security

Encryption algorithm based on higher degree residues is presented in this paper, including both deterministic and probabilistic. Since the algorithms have homomorphic properties, i.e., the ability to perform algebraic operations such as additions or subtractions directly on ciphertext, they can be applied in several specific fields. Except for ensuring semantic security, compared with the other probabilistic version, the algorithm in this paper has relatively smaller expansion rate.