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

摘要： 研究了量子同态加密，提出了一种通用的构造量子同态加密算子的方法，进而建立了构造量子同态加密方案的一种通用框架；通过二值和三值量子态的酉变换，利用该框架构造了相应的量子同态加密方案，与现有文献的构造方案相比，利用该框架构造的量子同态加密方案更具有普遍性；通过安全性分析，该框架的安全性是基于加密算法的安全性和密钥的安全性。由于该框架采用了对称量子加密算法，导致构造量子同态算子时需要加密密钥,从而该框架是一种弱的对称量子同态加密框架。最后，该框架被推广到了量子公钥加密的情形。

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