关键词: 量子同态加密, d维酉算子, 完全混合态

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