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arXiv:1707.07389 · Scientific Reports

Controlled Alternate Quantum Walks based Quantum Hash Function

Dan Li, Yu‐Guang Yang, Jing-Lin Bi, Jiabin Yuan, Juan Xu

Published Jan 3, 2018• 49 citations
arXivHTMLPDF

Abstract

Through introducing controlled alternate quantum walks, we present controlled alternate quantum walks (CAQW) based quantum hash function. CAQW based quantum hash function have excellent security, outstanding statistical performance and splendid expansibility. Furthermore, due to the structure of alternate quantum walks, implementing CAQW based quantum hash function significantly reduces the resources necessary for its feasible experimental realization than implementing other quantum hash functions.

DOI
10.1038/s41598-017-18566-6

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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.
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In this paper, we develop a generic controlled alternate quantum walk model (called CQWM-P) by combining parity-dependent quantum walks with distinct arbitrary memory lengths and then construct a quantum-inspired hash function (called QHFM-P) based on this model. Numerical simulation shows that QHFM-P has near-ideal statistical performance and is on a par with the state-of-the-art hash functions based on discrete quantum walks in terms of sensitivity of hash value to message, diffusion and confusion properties, uniform distribution property, and collision resistance property. Stability test illustrates that the statistical properties of the proposed hash function are robust with respect to the coin parameters, and theoretical analysis indicates that QHFM-P has the same computational complexity as that of its peers.
In this paper, we develop a generic controlled alternate quantum-walk model (called CQWMP) by combining parity-dependent quantum walks with distinct arbitrary memory lengths and propose a hash function (called QHFM-P) based on this model. The statistical properties of the proposed scheme are stable with respect to the coin parameters of the underlying controlled quantum walks; with certain parameter values, the collision resistance property of QHFM-P is better than that of the state-of-the-art hash functions based on discrete quantum walks. Moreover, the proposed hash function can also maintain near-ideal statistical performance when the input message is of small length. Additionally, we derive a type of inappropriate initial states of hash functions based on one-dimensional one-particle quantum walks (with ordinary shift operator) on cycles, with which all messages will be mapped to the same hash value, regardless of the angles adopted by the coin parameters.
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.