Research On The Related Theory And Application Of Quantum Encryption

Quantum cryptography originated in Wiesner's pioneering paper “Conjugate Coding”,is a combination of quantum theory,information science and computer science.After more than 30 years of development,it has gradually formed a systematic quantum cryptography theory architecture,which involves quantum key distribution and management,quantum encryption,quantum authentication,multi-party secure quantum cryptography protocol,quantum information theory and quantum cryptoanalysis,etc.Unconditional security and detectability of eavesdropper are the two-significant characteristics of quantum cryptography.Furthermore,the important foundations ensure that quantum cryptography is unconditionally secure due to the uncertainty principle and no cloning theorem of quantum mechanics.First of all,we proposed a quantum key distribution protocol based on retransmission mechanism,which greatly improves the distribution efficiency of the secret key.Then,through studying ternary quantum state,quantum homomorphic encryption and synthesis technology of quantum circuits,we proposed a symmetric weak ternary quantum homomorphic encryption scheme,and established an universal quantum homomorphic encryption framework.Meanwhile the correctness and universality of the proposed framework are verified though two examples of qubit and qutrit.And then,through optimizing ternary XHZ encryption scheme,we obtained some interesting conclusions.Finally,a practical quantum public key encryption model is proposed.These contents are divided into five parts shown as follows in detail.1)Quantum key distribution based on retransmission mechanism.Through studying the execution process of BB84 protocol,we found that some transmitted photons are lost,which has a serious influence on the secret key distribution efficiency.Therefore,we proposed a QKD scheme based on retransmission mechanism.Then,we described the execution process of new QKD protocol,which is similar to BB84 protocol.The main difference between them is: when the numbers of the lost photons exceed a specific threshold,the retransmission process of the lost photons will be started.Meanwhile,we acted as an eavesdropper to simulate the new protocol with interception-resend strategy.The result shows that any disturbance of the quantum states can be detected by the receiver.Finally,we analyzed the new protocol from three aspects: security,data reconciliation and privacy amplification,and we concluded that the new protocol can improve the distribution efficiency of the secret key,especially for deterministic QKD protocol,and is unconditionally secure.2)Symmetric weak quantum homomorphic encryption scheme.Based on ternary quantum logic circuit,four symmetric weak ternary quantum homomorphic encryption schemes were proposed.First,for a one-qutrit rotation gate,a quantum homomorphic encryption scheme was constructed.Second,in view of the synthesis of a general 3?3 unitary transformation,another one-qutrit quantum homomorphic encryption scheme was proposed.Third,according to the one-qutrit scheme,the two-qutrit quantum homomorphic encryption scheme about GCX(m,n)gate was constructed and further generalized to the n-qutrit unitary matrix case.Finally,the security of these schemes was analyzed in two respects.It could be concluded that the attacker can correctly guess the encryption key with a maximum probability pk=1/33 n,thus it can better protect the privacy of users' data.Moreover these schemes can be well integrated into future quantum remote server architecture,thus the computational security of the users' private quantum information can be well solved in a distributed computing environment.3)Universal quantum homomorphic encryption framework.Through studying quantum homomorphic encryption,a general construction method for quantum homomorphic operator was proposed,and thus a universal construction framework for quantum homomorphic encryption scheme was setup.Compared with the existing quantum homomorphic encryption schemes,our schemes constructed by the universal construction framework according to the binary and ternary quantum unitary transformations,are correct and more feasible.The security of the universal framework was analyzed from two respects.One is the security of quantum encryption scheme.The other is the security of the secret key.In our universal construction framework the symmetric quantum encryption scheme is used and the evaluate algorithm is dependent on the secret key in the process of constructing the corresponding quantum homomorphic operator.As a result,our universal construction framework is a kind of weak symmetric quantum homomorphic encryption framework.Finally,it was generalized to the case of the quantum public key encryption.4)Optimal symmetric ternary quantum encryption schemes.In this section,we present two definitions of the orthogonality and orthogonal rate of the encryption operator,and we provide a verification process for the former.Then,four improved ternary quantum encryption schemes are constructed.Compared with Scheme 1,these four schemes demonstrate significant improvements in term of calculation and execution efficiency.Especially under the premise of the orthogonal rate ? as secure parameter,Scheme 3 shows the highest level of security among them.Through custom interpolation functions f(s,k)or f(s),the ternary secret key source,which is composed of the digits 0,1 and 2,is securely constructed.Finally,we discuss the security of both the ternary encryption operator and the secret key source,and both of them show a high level of security and high performance in execution efficiency.5)Practical quantum public key encryption model.In this section,a practical quantum public-key encryption model is proposed by studying the recent quantum public-key encryption.This proposed model makes explicit stipulations on the generation,distribution,authentication,and usage of the secret keys,thus forms a black-box operation.Meanwhile,this proposed model encapsulates the process of encryption and decryption for the users,and forms a black-box client-side.In our models,each module is independent and can be replaced arbitrarily without affecting the proposed model.Therefore,this model has a good guiding significance for the design and development of the quantum public key encryption schemes.Finally,we summarized the whole dissertation,and proposed the future research tasks: constructing these schemes,such as the QKD scheme based on ternary quantum entanglement state,ternary quantum homomorphic signature and authentication schemes,and ternary QPKE scheme.Furthermore we also hoped to revisit the relevant quantum encryption protocol by mean of the latest quantum blockchain technology.