Construction of noiseless leveled fully homomorphic encryption scheme

Based on the hardness of AGCD problem, we construct a new noiseless leveled fully homomorphic encryption scheme that can homomorphically evaluate all the higher degree integer polynomials, real polynomials and complex polynomials. We also provide a natural procedure for the applications of our homomorphic encryption scheme to the practical privacy-preserving computations arising from real world business and industry problems. We would like to emphasize that our encryption scheme recovers exactly the same original plaintexts after going through encryption, homomorphic evaluation and decryption algorithms.