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Simple hash function using discrete-time quantum walks

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Abstract

Hash functions play an essential role in many cryptographic applications such as digital signature, integrity authentication, and key derivation. Most of them are iteratively built based on the Merkle–Damgård (MD) structure. Unfortunately the traditional MD structure is suffering from various attacks, and thus the design of new hash functions is emerging. In this paper, inspired by quantum computation, we present a new hash function by introducing alternate single-qubit coin operators into discrete-time quantum walk. The present hash function is classical with classical input and output. The compressive function can be implemented by performing alternate single-qubit coin operators on the coin state controlled by a classical input binary message and then applying the global conditional shift operator on the position state and the coin state. The classical output hash value is generated by making amplification, truncation, and modular operation on the final probability distribution. Numerical simulation and performance comparison show that the present hash function has an excellent property of collision resistance and easier implementation than existing quantum-walk-based hash functions. It promotes more applications of quantum computation in the design of hash functions.

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Acknowledgements

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

    Yu-Guang Yang, Jing-Lin Bi, Yi-Hua Zhou & Wei-Min Shi

  2. Information Security Center, State Key Laboratory of Networking and Switching Technology, Beijing University of Posts and Telecommunications, Beijing, 100876, China

    Xiu-Bo Chen

  3. Beijing Electronics Science and Technology Institute, Beijing, 100070, China

    Zheng Yuan

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  1. Yu-Guang Yang
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Correspondence to Yu-Guang Yang.

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Yang, YG., Bi, JL., Chen, XB. et al. Simple hash function using discrete-time quantum walks. Quantum Inf Process 17, 189 (2018). https://doi.org/10.1007/s11128-018-1954-2

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