A secure quantum homomorphic encryption ciphertext retrieval scheme
摘要
In a recent paper (Gong et al. Quantum Inf Process 19:3, 2020), a novel ciphertext retrieval scheme based on the Grover algorithm and quantum homomorphic encryption was presented. In this scheme, when the server performs the operation of marking the solution on the user’s encrypted state in the Grover iteration, it needs to remove many gate-errors generated in the homomorphic evaluation of the T gate. And the server could judge this specific solution from the quantum circuit of marking the solution. It makes this scheme unable to achieve the low-cost and secure ciphertext retrieval. Therefore, we improve the Gong et al.’s scheme and propose a secure quantum homomorphic encryption ciphertext retrieval scheme. In our scheme, the trusted third party is introduced to cooperate with the server to execute the Grover algorithm. In each Grover iteration, the trusted third party can quickly mark the solution on the plaintext state, encrypt the marked state, and transmit it to the server. Then the server performs the remaining operations of this Grover iteration on the encrypted state. The trusted third party finally decrypts the iterated state. This cooperative approach ensures that the number of auxiliary qubits required and extra quantum gates executed in our scheme are lower than the Gong et al.’s scheme. By analyzing the security of our scheme, we confirm that the server and the trusted third party will not be informed of this solution. Thus, our scheme realizes the secure ciphertext retrieval with low computational overhead. We utilize IBM’s Qiskit framework to simulate our scheme, and the experimental result shows that our scheme is correct. It is worth noting that the low-cost and secure ciphertext retrieval will play a crucial role in modern information security and privacy protection.