Abstract:

The existing quantum homomorphic encryption algorithm is limited to two-dimensional or three-dimensional Hilbert space. This paper breaks through this low-dimensional limitation and proposes two [d]dimensional quantum homomorphic encryption algorithm based on the exchange ability of any two [d]dimensional operators. One is a[d]dimensional quantum homomorphic encryption algorithm on a single particle, and the other is a[d]dimensional quantum homomorphic encryption algorithm on a multi-particle. Each algorithm includes a key generation sub-algorithm, an encryption sub-algorithm, an evaluation sub-algorithm and a decryption sub-algorithm, which proves the correctness of the two quantum homomorphic encryption algorithms and gives an example to verify the feasibility of the algorithm. Since the evaluation algorithm does not depend on the client’s key and the output state has a fully mixed state property, the security of the two algorithms is guaranteed. The simulation results show that the output of the decryption sub-algorithm and the evaluation sub-algorithm are completely consistent with the direct calculation results of the plaintext, and the homomorphic characteristics of the two algorithms are verified.

Key words: quantum homomorphic encryption, [d]dimensional operators, totally mixed state

摘要：

现有量子同态加密算法局限于二维或三维的希尔伯特空间，突破这种低维度的限制，基于任意两个[d]维酉算子的可交换性提出了两个[d]维量子同态加密算法。一种是单粒子上的[d]维量子同态加密算法，另一种是多粒子上的[d]维量子同态加密算法。每个算法包括密钥生成子算法、加密子算法、评估子算法和解密子算法，证明了两个量子同态加密算法的正确性并举例予验证算法的可行性。由于评估算法不依赖于客户端的密钥，并且输出态具有完全混合态性质，保证两个算法的安全性。仿真结果显示解密子算法的输出与评估子算法对明文的直接计算结果完全一致，验证了两个算法的同态特性。

关键词: 量子同态加密, d维酉算子, 完全混合态