The existing hash functions based on quantum walk construction are all proposed under the ideal closed environment. In order to better conform to the actual situation and improve the relevant performance of Hash functions, we propose a quantum hash function constructed by continuous quantum walk on the basis of broken-line noise model. We first propose a continuous-time quantum walk model on cycle under the influence of broken-line decoherence, after that apply this model to the construction process of the quantum hash function and put forward a building method of the hash function on the basis of the broken-line decoherent continuous-time quantum walk on the one-dimensional cycle. The safety analysis and numerical simulation indicate that our hash function has greater anti-collision performance than the existing hash function based on the quantum walk.
The existing hash functions based on quantum walk construction are all proposed under the ideal closed environment. In order to better conform to the actual situation and improve the relevant performance of Hash functions, we propose a quantum hash function constructed by continuous quantum walk on the basis of broken-line noise model. We first propose a continuous-time quantum walk model on cycle under the influence of broken-line decoherence, after that apply this model to the construction process of the quantum hash function and put forward a building method of the hash function on the basis of the broken-line decoherent continuous-time quantum walk on the one-dimensional cycle. The safety analysis and numerical simulation indicate that our hash function has greater anti-collision performance than the existing hash function based on the quantum walk.
Abstract At present, decoherence continuous-time quantum walks are only based on measurement decoherence, but a new broken-line noise model for continuous-time quantum walks on the cycle is proposed. In this scheme, we first construct the Hamiltonian H according to four cases including no broken links, the link to the left of the node is broken, the link to the right of the node is broken, and both links are broken, and then the probability of a walker is reconstructed. The analysis shows that with the increase of the probability of disconnection, the oscillation of the walk gradually weakens and becomes a peak distribution, and with the continuous increase of the walk time, the probability distribution of each vertex tends to be uniform. In addition, we also analyze the mixing time of this walk model and find that a small amount of broken chain decoherence can help reduce the mixing time, thereby improving the performance of quantum walks.
A method of constructing a quantum hash function (QHF) based on continuous-time quantum walk is proposed, in which the time of quantum walk is controlled by the binary string message, namely, a binary string message as the input of the constructed QHF and the probability value of finally walking to the nodes on the cycle is used as the output of the QHF. Numerical simulation and performance analysis show that our QHF has obvious advantages in the efficiency of the QHF compared with the existing QHF based on the discrete-time quantum walk, that is, the efficiency of our scheme is nearly 4 times faster in computing the hash value of the same size file compared with the most efficient scheme. Besides, the QHF has also better collision resistance compared with the existing QHF based on the discrete-time quantum walk.
Quantum walk based hash functions have attracted a lot of attention in recent years because of its faster execution time and robust resistance against attacks compared to classical hash functions. It has been observed that the underlying graph and the way message controls the quantum walk iteration steps play a crucial role for the robustness of the hash function. We propose a quantum hash function based on the discrete-time quantum walk on a Hanoi network--a one dimensional periodic lattice with extra long-range edges of a specific form--which is highly collision resistant. The message bits of our scheme control the flow of probability amplitude through the extra long-range edges and the conditional shift operators. Our method even works for messages with small bit-lengths, contrary to most of the quantum walk based hash functions defined on a cycle, which usually work for messages with bit-lengths more than the length of the cycle.
The proposed quantum hash function (QHF) based on the discrete-time quantum walk (DTQW) structure requires enlarging the coin state space and the preparation of continuous quantum states is less difficult. Hence, a new construction method of QHF is proposed based on the continuous-time quantum walk (CTQW) of the one-dimensional (1D) lattice with boundary constraints and without additional coin space. In the scheme, the input of the QHF is an arbitrary binary string message which is used to control the selected Hamiltonian of CTQW at each time interval, and the output of the QHF is the final probability distribution of CTQW. Under the same computing environment, simulation and analysis indicate that our QHF can satisfy the same security requirements such as sensitivity, diffusion and confusion, collision, birthday attack, but the collision rate is reduced by 40% without reducing effectiveness.
We propose a new hash function QHFM based on controlled alternate quantum walks with memory on cycles, where the jth message bit decides whether to run quantum walk with one-step memory or to run quantum walk with two-step memory at the jth time step, and the hash value is calculated from the resulting probability distribution of the walker. Numerical simulation shows that the proposed hash function has near-ideal statistical performance and is at least on a par with the state-of-the-art hash functions based on quantum walks in terms of sensitivity of hash value to message, diffusion and confusion properties, uniform distribution property, and collision resistance property; and theoretical analysis indicates that the time and space complexity of the new scheme are not greater than those of its peers. The good performance of QHFM suggests that quantum walks that differ not only in coin operators but also in memory lengths can be combined to build good hash functions, which, in turn, enriches the construction of controlled alternate quantum walks.
We propose a Quantum inspired Hash Function using controlled alternate quantum walks with Memory on cycles (QHFM), where thejth message bit decides whether to run quantum walk with one-step memory or to run quantum walk with two-step memory at thejth time step, and the hash value is calculated from the resulting probability distribution of the walker. Numerical simulation shows that the proposed hash function has near-ideal statistical performance and is at least on a par with the state-of-the-art hash functions based on quantum walks in terms of sensitivity of hash value to message, diffusion and confusion properties, uniform distribution property, and collision resistance property; and theoretical analysis indicates that the time and space complexity of the new scheme are not greater than those of its peers. The good performance of QHFM suggests that quantum walks that differ not only in coin operators but also in memory lengths can be combined to build good hash functions, which, in turn, enriches the construction of controlled alternate quantum walks.