The Theoretical Research On Cryptographic Protocols Based On Quantum Entanglement

Quantum cryptography,which uses the properties of quantum mechanics to realize cryptographic tasks,is a discipline based on modern cryptography and quantum mechanics.It uses the quantum properties of microscopic particles to achieve information protection and it has been proven to be unconditional security in theory.Compared with the classical cryptography based on hard mathematical problems,quantum cryptography has obvious advantages in security,so it has been paid more and more attention and has made rapid development.Quantum entanglement,as a resource,is often used in the design and security analysis of cryptographic protocols,which plays an important role in the research of quantum cryptography.Based on quantum entanglement,this paper focuses on the research of quantum homomorphic signature protocols,quantum private comparison protocols and quantum anonymous ordering protocols.The main research contents are divided into three parts,the main research results are as follows:1.Quantum homomorphic signature protocols(1)A quantum homomorphic signature protocol based on quantum coherent states is proposed.Firstly,the definition of quantum homomorphic signature is given according to the existing quantum homomorphic signature protocols and the definition of homomorphic signature in classical cryptography.Secondly,we analyze the interference properties of the quantum coherent state in a balanced beam splitter and proposed a new quantum homomorphic signature protocol based on these properties.And then the proposed quantum signature is proved to be a group homomorphic signature and the security and the communication complexity of the protocol are analyzed.Compared with the existing quantum homomorphic signature protocols,it can be concluded that the protocol is more efficient and easier to be implemented.Finally,the relationship between the quantum coherent states used in the protocol and the entangled states used in quantum fingerprinting is discussed.(2)A quantum homomorphic signature protocol based on complete Bell state measurement and a protocol based on partial Bell state measurement are proposed.Firstly,the work principle of Bell state measurement is analyzed and how to realize partial Bell state measurement by using linear opticals is described.Secondly,a quantum homomorphic signature protocol based on the complete Bell state measurement is proposed and it is further discussed how to present the protocol based on partial Bell state measurement and the protocol is given.And then the proposed quantum signature is proved to be a group homomorphic signature and the security of the protocol is analyzed.In the security analysis,an ”intercept-retransmission” attack is proposed for the existing quantum homomorphic signature protocols,and it is proved that the decoy state method used in this protocol can effectively resist this attack.Finally,it can be concluded that the proposed protocol has higher security and efficiency compared with the existing quantum homomorphic signature protocols.2.Quantum private comparison protocols(1)The first quantum private comparison protocol that multiple paricipants can sort their private information in size is proposed.Firstly,a multi-party and high-dimensional entangled state is found and the properties of the entanled state are analyzed.Further,we use the method of group theory to prove that the relationship between the two positive integers can be described by using modulo d subtraction.Secondly,a quantum prvate comparison protocol based on these properties is proposed.If l participants want to know the relation of size among their secret inputs,the two-participant protocols have to be executed repeatedly (?) times,however,the proposed protocol needs to be executed only one time.Finally,the security of the protocol is analyzed in detail and the efficiency of the protocol is analyzed by calculating the quantum resources used in the protocol.(2)A quantum private comparison protocol based on the work principle of linear optics is proposed.Due to the most existing quantum private comparison protocols are presented and analyzed from a purely abstract point of view,it is far away to implement these protocols in practice.Firstly,the work principle of linear optics,mainly the principle of beam splitter and the post-selected entanlement of polarization states in a balanced beam splitter,are analyzed.Secondly,A quantum private comparison protocol that two participants can determine whether or not their private information is equal based on these principles is proposed,and this is the first step to implement quantum private comparison protocol in practice.Finally,the security of the proposed protocol is analyzed in detail.3.Quantum Anonymous Ranking ProtocolsA quantum anonymous multiparty,multidata ranking protocol with single-particle states is proposed.Firstly,the design principle and security requirements of quantum anonymous ranking protocols are analyzed.Secondly,a new quantum anonymous ranking protocol based on high-dimensional single particle states is proposed and the security of the protocol is analyzed.By comparing this protocol with the existing quantum entanglement-based anonymous rinking protocols,this protocol is more efficient.Finally,it is discussed that the protocol can be completed with lower dimension single particle states by using the Chinese residual theorem,and a concrete method is given.