Abstract: As one of the ideal implementations of secure multi-party computing, multi-key homomorphic encryption has significant advantages in resisting quantum attacks and facilitating the construction of secure multi-party computing solutions. However, the existing BGV-type multi-key homomorphic encryption algorithm has problems such as complex key calculation and large ciphertext size. Therefore, a multi-key homomorphic encryption scheme is constructed using a single-key homomorphic encryption scheme, which encrypts the main operation part with a single-key homomorphic encryption scheme, and uses the existing multi-key homomorphic encryption to complete the common key and common decryption. Theoretical analysis shows that the encryption scheme can reduce the key size, reduce the complexity of homomorphic multiplication, and improve the efficiency of encryption operations.

Key words: multi-key homomorphic encryption, evaluation key, homomorphic multiplication