Abstract: To lower the sizes of keys, a certificateless encryption scheme is put forward by using a trapdoor sampling algorithm over a selected NTRU lattice to extract partial private keys and using Ring Learning With Errors (RLWE) problem to generate public keys. Its security is based on both assumptions of the decisional ring learning with errors problem and the decisional Small Polynomial Ratio (SPR) problem. To further improve efficiency, a certificateless parallel encryption scheme with more efficient algorithms only using arithmetic in integers is also given by respectively using the Chinese Remainder Theorem (CRT) to decompose the enlarged plaintext space into the product of distinct prime ideals and to break down the ring, over which encryption operations work, for obtaining the Chinese Remainder basis. The given results show that the proposed schemes are characterized by low computation complexity and small communication complexity.