| With the development of information technology,while the information age has brought convenience to people,how to ensure information security is also the focus of research by domestic and foreign scholars.Cryptography is an important subject of information security,and it plays an important role in information security.However,the development of quantum computers has threatened cryptographic protocols with computational complexity,and quantum cryptography has become the focus of attention.As an important core part of quantum cryptography,quantum hashing has been widely used in various quantum hash functions based on discrete quantum walks that have been proposed so far.In the construction process,additional coin space and resource consumption are required.Compared with discrete-time quantum walk,continuous-time quantum walk has the advantages of high efficiency,no extra coin space,and easy preparation of quantum states.In order to further improve the performance of quantum hash function,this paper mainly studies how to apply continuous-time quantum walk to the construction of quantum hash function.The main research contents of this thesis are as follows:（1）A quantum hash function based on continuous-time quantum walk is proposed.Firstly,the classical information is mapped to time t according to certain mapping rules,then the continuous quantum walk is controlled by time t,and finally the probability value of the walk to each node is taken as the output of the quantum hash function.Experimental results show that the constructed quantum hash function has good security,and compared with the existing quantum hash function with the best diffusion and confusion performance,the diffusion and confusion performance of the constructed quantum hash function is improved.（2）A quantum hash function based on continuous-time quantum walk in onedimensional cycle lattice is proposed.This method controls the Hamiltonian of continuous-time quantum walk in a certain time interval according to one bit of classical information,and then obtains the final probability distribution of continuous-time quantum walk as the output of quantum hash function.Experimental results show that the collision rate of the constructed quantum hash function is 40% lower than that of the existing quantum hash function based on discrete-time quantum walk model with the lowest collision rate.（3）A quantum hash function based on dense coded Hamiltonian for continuoustime quantum walk is proposed.In order to improve the efficiency of quantum hash function,dense coding is introduced into the construction method of quantum hash function,and a construction method of continuous-time quantum walk quantum hash function based on Hamiltonian dense coding is proposed.This method controls the Hamiltonian of continuous-time quantum walk in a certain time interval according to the two bits of classical message,and then obtains the final probability distribution of continuous-time quantum walk as the output of quantum hash function.Numerical simulation and theoretical analysis show that the constructed quantum hash function satisfies the corresponding security,and the efficiency of quantum hash function is doubled.In addition,the above method is extended,that is,the Hamiltonian of continuous-time quantum walk in a certain time interval is controlled according to the multiple bits of the classical message.The final numerical simulation and theoretical analysis show that the extended quantum hash function not only meets the corresponding security,but also improves the efficiency by more times. |
