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Modern Physics Letters B

Continuous-time quantum hash function based on one-dimensional cycle lattice

Wei‐Min Shi, Wang Shou, Pan Tian, Yu‐Guang Yang, Yi‐Hua Zhou

Published Jun 17, 2022• 5 citations
Publisher

Abstract

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.

DOI
10.1142/s0217984921502419

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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.
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.
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.
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.
We propose a Quantum inspired Hash Function using controlled alternate quantum walks with Memory on cycles (QHFM), where thejjjth message bit decides whether to run quantum walk with one-step memory or to run quantum walk with two-step memory at thejjjth 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.
In this research article, we design a quantum hash function model from hybrid quantum walks on finite path graph. The hybrid evolution operator consisting of integrated framework of continuous time quantum walks and lackadaisical quantum walks as per choice of bits in binary input message, acts on initial quantum state and generate quantum hash values from probability distribution of final quantum state. The quantum hash values generated through the proposed method is showing strong cryptographic properties in sensitivity analysis, collision analysis, statistical features analysis, birthday attack and uniform analysis. Our proposed framework is showing successful results utilizing mathematically well defined structure of hybrid quantum walks based on quantum mechanics phenomena.
Quantum hash function is an important area of interest in the field of quantum cryptography. Quantum hash function based on controlled alternate quantum walk is a mainstream branch of quantum hash functions by virtue of high efficiency and flexibility. In recent development of this kind of schemes, evolution operators determined by an input message depend on not only coin operators, but also direction-determine transforms, which usually are hard to extend. Moreover, the existing works ignore the fact that improper choice of initial parameters may cause some periodic quantum walks, and further collisions. In this paper, we propose a new quantum hash function scheme based on controlled alternate lively quantum walks with variable hash size and provide the selection criteria for coin operators. Specifically, each bit of an input message determines the magnitude of an additional long-range hop for the lively quantum walks. Statistical analysis results show excellent performance in the aspect of collision resistance, message sensitivity, diffusion and confusion property, and uniform distribution property. Our study demonstrates that a fixed coin operator, along with different shift operators, can effectively work on the design of a quantum hash function based on controlled alternate quantum walks, and shed new light on this field of quantum cryptography.