Fully homomorphic encryption (FHE), which allows arbitrary computation of ciphertexts without knowing the secret information, has become a hot research direction in the context of big data and cloud security and has made great progress in recent years. However, in practical applications, fully homomorphic encryption still faces many problems, among which the serious expansion of ciphertext brings great pressure to the transmission of ciphertext. This problem can be effectively solved by combining the full homomorphic encryption scheme with symmetric cipher. The GSW-type full homomorphic encryption scheme is more efficient, and does not need the re-linearization technique in homomorphic evaluations. This paper selects the MGSW15 scheme which supports parallel operations, and whose ciphertext can be transformed into the ciphertext of any FHE scheme based on LWE. We present the basic framework of achieving ciphertext compression based on MGSW15 scheme in the background of cloud computing, and implement homomorphic evaluations of the block cipher AES-128, PRINCE and SIMON-64/128 circuits respectively. According to the structural characteristics of each block cipher, we use various kinds of plaintext-slicing ways to improve the efficiency of homomorphic evaluation. Finally, we analyze efficiency and security. Combined with the security and generality of AES and the efficiency of lightweight block cipher algorithms PRINCE and SIMON, the work of this paper is more efficient, and more widely used in practical applications, in which the communication complexity of ciphertexts is approximately equal to the scale of plaintexts and only one homomorphic multiplications are needed every plaintext bit.
