Study On Construction Of Hash Function Based On Discrete Quantum Walking

Today,with the rapid development of the Internet,information has become a vital resource,and the competition for information resources has become increasingly fierce,and the security of information has become a top priority.Therefore,while the Internet has brought about the rapid development of society,it has also brought enormous challenges,which requires us to devote more energy to maintenance.Cryptography is the core technology for encrypting information and ensuring the secure transmission of information.It is also an important direction for people to study information security.In recent years,the continuous improvement of machine performance and the increasing computing power,especially the emergence of quantum parallel algorithms,continue to impact the status of classic cryptographic protocols,and computational complexity is no longer an unbreakable problem.Therefore,the focus of attention has turned to quantum cryptography.Quantum cryptography is a combination of quantum mechanics and cryptography.Its security is the principle of quantum physics to ensure that the attacker's computing power is stronger and will not threaten it.Quantum computing is a new way of computing based on quantum mechanics.Quantum entanglement effects and coherent superposition effects can improve computational performance and also contribute to the resolution of some problems.Quantum advantage with shallow circuits,published in Science,demonstrates this.It has been confirmed in the text that the quantum computing performance is higher than the classical calculation for the same limitation of computing power.The Hash function is an indispensable part of the cryptosystem.It has also been applied to many fields.It is a key technology for cryptographic applications such as pseudo-random number generation,message authentication code,digital signature,and data integrity protection.Any length of data transformed by the Hash function will be converted to a fixed-length data output,and this process is irreversible.In this paper,we have done the following work on how to construct a new Hash function to improve the security of data:(1)We studied the entanglement entropy of the walkers and coins based on quantum walks,analyzed each of the influencing factors,and found their influence on the entanglement entropy.It is hoped that a high-performance quantum hash function canbe constructed.We analyzed the entanglement entropy of the walker and the coin.And,we want to track the correlation between coins and walkers.In order to study the correlation,we analyzed three indicators: mutual information(MI),quantum mutual information(QMI)and measurement-induced disturbance(MID).These related functions will help us study the movement of the coin exchange for the walker.(2)We proposed a 1coin1 walker Hash function by introducing the alternating single qubit coin operator into the discrete time quantum walker(Quantum Walker).Our suggestion makes the implementation of the Hash function simpler because there is no need for a two-particle interaction or a 4x4 coin operator.We tested its various performances through experimental simulation,including anti-collision testing,sensitivity testing,statistical testing of diffusion and chaos,uniform distribution testing,image information sensitivity testing and anti-birth attack testing,etc.The constructed hash function has better performance.(3)A quantum hash function of 2coin1 walker based on quantum random walk was constructed and its detailed performance analysis was carried out.We presented DHF(Discrete Hash Function)by using two alternating coins and a single walker.Through experimental simulation,we obtained its various performances,including anti-collision testing,sensitivity testing,statistical testing of diffusion and chaos,uniform distribution testing,image information sensitivity testing and anti-birth attack testing,etc.The constructed hash function has better performance.