Research On High Dimensional Quantum Homomorphic Encryption

With the In-depth development of quantum communication and quantum computers,as an important means to guarantee quantum communication quantum homomorphic encryption has become more and more important.At present,the quantum homomorphic encryption algorithm mainly discusses quantum homomorphic encryption in low dimensional Hilbert space,and the research on quantum homomorphic encryption in arbitrary dimensions is insufficient.At the same time,the proposed quantum homomorphic encryption model has some shortcomings,which exposes the important information of the client too much,and there is no discussion about the simulation experiment of the quantum homomorphic encryption algorithm.In view of this,this thesis has proposed a d dimensional quantum homomorphic encryption algorithm based on phase transformation and a d dimensional(t,n)threshold quantum homomorphic encryption algorithm.The main research work and innovations of this thsis are as follows:1.Aiming at the current research on quantum homomorphic cryptography limited to low dimensional Hilbert space,this thesis proposes a d dimensional quantum homomorphic encryption algorithm based on phase transformation.In this algorithm,the phase-transformed d dimensional unitary operator has full interchangeability.In this thesis,two d dimensional quantum homomorphic encryption algorithms are constructed by using the commutability of this operator.One is the single-particle quantum homomorphic encryption algorithm,and the other is the multi-particle quantum homomorphic encryption algorithm.Because the d dimensional unitary operator based on phase transformation has exchangeable properties,the output state of the proposed algorithm has a totally mixed state,and the attacker can not obtain any useful information from the totally mixed state,which ensures the security of the algorithm.Finally,the simulation experiment is carried out on the proposed algorithm.The experimental results verify the correctness of the proposed algorithm.2.Aiming at the finite transform ability of d dimensional unitary operator based on phase transformation,this thesis proposed a d dimensional(t,n)threshold quantum homomorphic encryption algorithm.In this algorithm,the d dimensional unitary operator based on phase and state transformation has partial commutability.In order to protect the client’s initial evaluation parameters,the(t,n)threshold is used to decompose the initial evaluation parameters into n shares,and only t shares can be used to reconstruct the decrypted results.The security analysis shows that the algorithm has good security,and the algorithm simulation results verify the correctness of the algorithm.The biggest advantage of this quantum homomorphic encryption algorithm is that a d dimensional quantum homomorphic encryption algorithm based on phase and state transformation is constructed.At the same time,by adding the(t,n)threshold idea to the quantum homomorphic encryption algorithm,the quantum homomorphic encryption model is extended.The encryption model disperses the initial calculation information to ensure the security of the customer information.Finally,the simulation experiment verifies the correctness.