Grover algorithm-based quantum homomorphic encryption ciphertext retrieval scheme in quantum cloud computing

Abstract

Existing classical ciphertext retrieval schemes are mainly developed according to the homomorphic encryption that is a cryptographic technique based on computational complexity theory of mathematical puzzles. In quantum computing, on the one hand, most of traditional asymmetric encryption can be quickly cracked as the computational capacity of quantum computer is much higher than that of traditional digital computer. Hence, the quantum homomorphic encryption scheme is widely used in data encryption for the issue of privacy protection in quantum computing. But on the other the retrieval efficiency of homomorphic encrypted data is insufficient especially in quantum cloud computing. Therefore, this paper proposes a novel quantum homomorphic encryption ciphertext retrieval (QHECR) scheme basing on the Grover algorithm to solve the problem of homomorphic encrypted ciphertext data retrieval in quantum cloud computing. Our scheme is to improve such retrieval efficiency mentioned above where the interaction process is not required even if the T-gate exists in the circuit. In the experiment, two qubits without the T-gate are conducted on both simulations and real quantum devices by using IBM quantum information science kit (Qiskit). The results show that the proposed QHECR scheme is capable of achieving the retrieval encrypted data when the T-gate does not exist in the evaluation circuit in ciphertext environment. Moreover, a verification experiment about the T-gate key update algorithm is implemented to verify the feasibility and reliability of the proposed scheme in the Qiskit as well, which indicates that the QHECR is still available when the T-gate exists in the circuit. Since the decryption is inefficient when there are exponential T-gates in the circuit, our proposed scheme is suitable for low T-gate complexity.