The invention relates to the fields of cryptographic algorithms and
homomorphic encryption, in particular to an anti-
quantum-
attack homomorphic encryption method. Along with increasing demands of outsourcing computing and
privacy protection application in a multi-user scene, multi-key
homomorphic encryption becomes an important research direction. The construction of a traditional multi-key homomorphic
encryption scheme generally depends on a common random character string (CRS) model, and a trusted party needs to generate a common parameter for a public key so as to support calculation on a joint
ciphertext. Due to the dependence on the central trusted mechanism, the anti-
attack capability and the decentralization characteristic of the
system are greatly reduced. In order to avoid excessive dependence on trusted third parties and public parameters, a distributed
key generation protocol is used in the invention, all users are enabled to independently generate keys thereof, and ciphertexts of a plurality of users are expanded to the same dimension through a
ciphertext expansion technology, so that the
encryption efficiency is improved. Therefore, multi-key homomorphic
encryption in a multi-user scene is realized without depending on a
trusted third party, a lattice-based CRS-free multi-key homomorphic encryption method is provided, and the security and decentration characteristic of the scheme are enhanced. Furthermore, the invention provides a directional decryption mechanism and introduces the directional decryption mechanism into the scheme, the public key information of the target user is embedded into the
ciphertext, it is ensured that only the specific target user can decrypt the ciphertext after homomorphic operation, and more flexible
privacy protection is provided.