关键词: 量子同态加密, 量子同态算子, 量子代理计算, 对称量子加密, 量子密码

Abstract: Through studying quantum homomorphic encryption, this paper proposes a general construction method for quantum homomorphic operator, thus sets up a universal construction framework for quantum homomorphic encryption scheme. Compared with existing quantum homomorphic encryption schemes, the schemes constructed by the universal construction framework according to the binary and ternary quantum unitary transformations, are more feasible. This paper analyzes the security of the universal framework from two respects. One is the security of quantum encryption scheme. The other is the security of the secret key. In the universal construction framework, the symmetric quantum encryption scheme is used and the evaluation algorithm is dependent on the secret key in the process of constructing the corresponding quantum homomorphic operator. As a result, the universal construction framework is a kind of weak symmetric quantum homomorphic encryption framework. Finally, it is generalized to the case of the quantum public key encryption.

Key words: quantum homomorphic encryption, quantum homomorphic operator, quantum delegated computation, symmetric quantum encryption, quantum cryptography