Quantum Hash Function Based On Discrete Quantum Walk Framework

Hash functions play an important role in cryptographic applications such as digital signatures and integrity authentication.Most Hash functions are based on the Merkle-Damg?rd(MD)structure.Unfortunately,this MD structure suffers from various attacks,so it is necessary to design a new type of Hash function to solve the threat to the security of a series of cryptosystems based on Hash functions based on computational complexity theory.Quantum walk is a quantum correspondence of classical random walks.It is a new type of quantum computation model proposed in recent years.Discrete quantum walk is the basis for constructing many quantum algorithms,so it has attracted the attention of scholars at home and abroad.At present,scholars at home and abroad have conducted extensive and in-depth research on the topological properties of quantum walks,localization of Anderson,applications,and experiments,and have achieved many important results.However,these studies are limited to the quantum level.In order to expand the application of quantum walk,this paper proposes to apply the quantum walk model to the construction of Hash function,so as to provide a good basis for key technologies such as digital signature,message authentication code,and pseudo-random number generation.The main achievements and innovations are as follows:(1)We propose a quantum random walk simulation model based on quantum walk in two-dimensional lattices,and derive a discrete-time quantum walk algorithm based on the standard quantum walk formula,which can be significantly increased to a specified position.Quantum walking probability.The visualized simulation software was used to make the process of discrete quantum walk and searching on the two-dimensional lattice.(2)Constructing a quantum Hash function based on discrete quantum walks on a two-dimensional lattice,sensitive to messagesSex,diffusion and confusion analysis,collision testing,uniform distribution,and anti-birthday attacks were tested,showing that it has good performance in resisting threats and compressing messages.(3)In order to further enhance security,we constructed a quantum hash function based on discrete quantum walk on the Johnson graph.We tested the sensitivity,diffusion and confusion analysis,collision testing,uniform distribution,and anti-birthday attacks of the message.It shows that it has better performance than the discrete quantum walk Hash function on the two-dimensional lattice.The visual Hash function based on Quantum Walk on Johnson graph is made into visual simulation software,which can realize the efficient compression function of Hash function on message.