Research On Ciphertext Search Based On Quantum Homomorphic Encryption

The existing classic ciphertext search scheme is developed mainly based on the classical homomorphic encryption technology,and its security mostly depends on the difficulty of mathematical problems.With the development of quantum computing,Shor proposes a polynomial quantum algorithm(shor algorithm)of prime factorization and discrete logarithm,which poses a fatal threat to the classical encryption algorithm that depends on the degree of difficulty of mathematical problems,and also threatens the security of ciphertext search algorithm based on homomorphic encryption.The efficiency of the existing ciphertext search algorithm based on quantum homomorphic encryption is relatively low.When there is a T gate in the circuit,an interactive process is required.In this paper,we first propose a quantum homomorphic encryption ciphertext retrieval scheme(QHECR)based on Grover search algorithm,which combines Grover quantum search algorithm with quantum homomorphic encryption.Grover search algorithm guarantees the efficiency of search,while quantum homomorphic encryption guarantees the perfect security of the scheme.Compared with the existing ciphertext search algorithm in the quantum cloud environment,the scheme adopts Grover parallel search algorithm,which improves the search efficiency.In addition,even if there is a T-gate in the search circuit,the interaction process is also not exist.In the existing quantum homomorphic encryption scheme,when there is a T-gate in the circuit,the key update algorithm is mostly too cumbersome and does not apply to the ciphertext search.Therefore,this paper presents a new ciphertext search scheme with decryption program.In this scheme,the trusted server is introduced to complete the operation of the T-gate and the key update algorithm,which reduces the pressure of the client.On the basis of this,an optimized semi-decrypted ciphertext search scheme is proposed.We have completed the ciphertext search experiment without T-gate in the case of two qubits on IBM quantum simulator and its real quantum devices.The experimental results show that our scheme is correct.In addition,we also verify the correctness of the key update algorithm of T-gate.The experimental results show that the scheme is still feasible when T-gate exists in the circuit.Finally,we complete the ciphertext search experiment with decryption program on the simulator,and the experiment of multi solution problem ciphertext search under the condition of three qubits.The experimental results show that the scheme is still feasible under the condition of multi solution.