Research On Key Agreement Schemes Based On Quantum Entangled States

With the advent of Internet and big data era,the safe storage and transmission of data has attracted more and more attention.Classical cryptography has played a vital role in protect-ing the privacy and integrity of data.However,the emergence of quantum algorithms has brought tremendous impact on classical cryptography.Once the quantum computer comes out,the widely used RSA cryptosystem based on the large integer decomposition problem and ElGamal cryptosystem based on the discrete logarithm problem on finite fields will be quickly destroyed.Quantum cryptography is the organic integration of quantum technology and classical cryptography.It can theoretically achieve unconditional security.Quantum cryptography protocol is the best choice for information security protection.Following the research frontier of quantum cryptography,this dissertation explores the ap-plication of quantum entangled states in the design of quantum cryptography protocols.Four multi-party quantum key agreement protocols with good properties,two threshold quantum state sharing protocols and one multi-party quantum secret comparison protocol are pro-posed.The specific contents include:1.An important property of the quantum search algorithm,Grover algorithm,is general-ized,and a multi-party quantum key agreement protocol based on quantum search algorithm is proposed by using the generalized properties and taking two-particle entangled state as quantum channel.This protocol is the first application of quantum search algorithm in con-structing quantum key agreement protocol.Theoretical analysis shows that this protocol is more efficient than the known protocols of the same type.It can resist not only external attacks,but also the most threatening collusion attacks from internal participants.2.Taking two-particle Bell entanglement states as quantum channels,two multi-party quan-tum key agreement protocols with additional bits are proposed by using the method of hid-ing participants' private keys with additional classical bits.In the former protocol,a trusted party is introduced,which randomly assigns a random classical bits sequence to each par-ticipant to cover up the participant's key.In the key extraction phase,the trusted party helps each participant to extract the shared key by publishing the XOR values of those random bit sequences.In the latter protocol,each participant directly chooses additional classical bit sequences to hide their keys,and finally extracts the shared key by publishing these addi-tional classical bit sequences.Security analysis shows that both protocols can resist external attacks and collusion attacks from internal participants.3.A multi-party quantum key agreement protocol based on non-orthogonal quantum en-tanglement pairs is proposed by using the hybrid coding technique of Pauli transform and Hadamard transform and taking two-particle Bell entanglement pairs and their dualities as quantum channels.Based on the hybrid coding technique of Pauli transform and Hadamard transform,an important property between unitary transform and non-orthogonal quantum pairs(including Bell States and their dualities)is given,and a multi-party quantum key a-greement protocol with traveling structure is proposed.Security analysis and efficiency analysis show that the protocol is superior to all known protocols.4.A threshold quantum state sharing protocol and a verifiable threshold quantum state sharing protocol are proposed by introducing a single-particle unitary transformation with special properties and combining the solution characteristics of linear equations.The former protocol is the first case in which linear equation is applied to the construction of quantum state sharing protocol.Compared with the known threshold quantum state sharing protocol,it has a certain improvement in efficiency and feasibility.In addition,in view of the above protocol can not test the dishonest behavior of a dishonest participant,the above protocol is improved.On the basis of not affecting the implementation process of the original protocol,using a special property of Bell entanglement,a method of dishonest detection of quantum pairs is designed,and a verifiable threshold quantum state sharing protocol is proposed.5.Based on the entanglement properties of level multi-particle GHZ quantum states,a multi-party quantum privacy comparison protocol is proposed,which can effectively deter-mine the size of multiple secret values.This protocol can make up for the shortcomings of most current multi-party quantum secret comparison protocols,which are limited to judging the equality of secrets and seldom used to judge the size of the relationship between secrets.Theoretical analysis shows that the protocol not only guarantees security,but also greatly improves efficiency compared with known protocols.