| With the rapid development of network technology,how people can share a set of keys without meeting has become an important research problem,and the key agreement scheme provides the possibility to solve this problem.The key agreement refers to the process in which two or more members communicate on a public channel to jointly generate a set of keys.Any one of the communicating parties will have an impact on the value of the key.The communicating party can use the generated key to encrypt and decrypt.The key agreement schemes are divided into the classical key agreement(CKA)schemes and the quantum key agreement(QKA)schemes.The first proposed CKA scheme is the Diffie-Hellman algorithm,or DH algorithm for short.In this scheme,two communicating parties perform the same operation through the interaction of the classical channel,to generate a set of classical bit strings as the key of both parties.However,the security of DH algorithm depends on the difficulty of computing discrete logarithm problems on finite fields,and it cannot resist the attack of quantum algorithms.The BB84 protocol is the first proposed QKA scheme.The protocol lets both parties send information through classical channels and quantum channels to achieve the purpose of sharing a set of classical bit strings.The principle of quantum mechanics guarantees the unconditional security of the BB84 protocol,but there is a dominant problem in this scheme,that is,the one communication party occupies the dominant position in the key agreement process,and the other communication parties cooperate with him or her to implement the agreement,which is not fair for other communication parties;at the same time,the qubit efficiency of the protocol,that is,the ratio of the length of the generated key to the length of the qubit string initially prepared by the communicating party to generate the key,is only 25%.In this thesis,based on the assumption of a noise-free channel,a new general scheme for quantum key agreement with unconditional security is proposed,and we give two secure specific schemes.The two communicating parties share a set of quantum state keys by means of symmetric operation,and neither party or both parties can individually pre-determine the key.The utilization rate of qubits can reach 50%.Compared with the existing CKA scheme,the new scheme uses quantum channels to transmit information,realizes the detectability of any external disturbance based on the basie principles of quantum mechanics,which improves the security of the scheme;compared with the existing QKA scheme,the new scheme solves the dominance problem in the scheme while ensuring the same unconditional security,and the two communicating parties can jointly generate a set of keys fairly;at the same time,the new scheme reduces the disturbance caused by the measurement operation to the photon,and improves the efficiency of the qubit.In the proposed new scheme,both communicating parties need to agree on a 2n-bit qubit string,and then use their own secret values to interactively perform unitary operations on the qubit string to generate an initial key,in which we require the unitary operators of both sides of the communication should be commutative,which lays the foundation for the correctness of the scheme.By comparing whether the n qubits randomly selected in the initial keys of both parties are the same,the communicating parties can detect whether the quantum state has been tampered with.If not,the two communicating parties will successfully jointly generate a set of keys.Then we use the Hadamard matrix and the operator function exp(iθn·σ)to give two unconditionally secure QKA schemes respectively.The analysis results show that it is more difficult for the eavesdropper to recover the key correctly in the second specific scheme than in the first specific scheme. |
