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Constructing quantum Hash functions based on quantum walks on Johnson graphs

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Abstract

We present a quantum hash function in a quantum walk framework on Johnson graphs. In this quantum hash function, the message bit decides which coin operator, i.e., Grover operator or DFT operator, is applied on the coin at each step. Then a fixed conditional shift operator is applied to decide the movement of the walker. Compared with existing quantum-walk-based hash functions, the present hash function has a lower collision rate and quantum resource cost. It provides a clue for the construction of other cryptography protocols by introducing the quantum walk model into hash functions.

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Acknowledgements

We thank Dr. Xiu-Bo Chen and Dr. Zheng Yuan for reviewing the original manuscript. This work was supported by the National Natural Science Foundation of China (Grant Nos. 61572053, 61671087, U1636106, 61602019, 61571226, 61701229, 61702367), Beijing Natural Science Foundation (Grant Nos. 4162005, 4182006), Natural Science Foundation of Jiangsu Province, China (Grant No. BK20170802), Jiangsu Postdoctoral Science Foundation.

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Authors and Affiliations

  1. College of Electric and Information Engineering, Zhengzhou University of Light Industry, Zhengzhou, 450002, China

    Wei-Feng Cao

  2. Faculty of Information Technology, Beijing University of Technology, Beijing, 100124, China

    Yong-Ce Zhang, Yu-Guang Yang, Yi-Hua Zhou & Wei-Min Shi

  3. College of Computer Science and Technology, Nanjing University of Aeronautics and Astronautics, Nanjing, 210016, China

    Dan Li

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  1. Wei-Feng Cao
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  2. Yong-Ce Zhang
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  3. Yu-Guang Yang
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  4. Dan Li
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  5. Yi-Hua Zhou
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  6. Wei-Min Shi
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Correspondence to Wei-Feng Cao.

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Cao, WF., Zhang, YC., Yang, YG. et al. Constructing quantum Hash functions based on quantum walks on Johnson graphs. Quantum Inf Process 17, 156 (2018). https://doi.org/10.1007/s11128-018-1923-9

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