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Chaotic hash function based on the dynamic S-Box with variable parameters

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Abstract

We present a chaotic hash function based on the dynamic S-Box with variable parameters in this paper. More specifically, we first exploit the piecewise linear chaotic map to obtain four initial buffers and an initial hash value. Then, we divide a randomly chosen message into message blocks and assign the four buffers and current message block to a transfer function to produce variable parameters and initial values of the PWLCM and logistic map for constructing a dynamic S-Box, which is then used for updating the four buffers. After all the message blocks are processed, the final hash value is generated by cascading the buffers and then applying XOR operation with the last hash value. Finally, we conduct performance evaluation on the proposed hash algorithm in terms of sensitivity, confusion and diffusion properties, collision resistances, speed analysis, randomness tests, and comparison with other algorithms, and the results demonstrate that the proposed algorithm has good statistical properties, strong collision resistances and better performance compared with other schemes.

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Acknowledgments

Our sincere thanks go to the anonymous reviewers for their valuable comments. This work was supported in part by the National Natural Science Foundation of China (Grant Nos. 61402380 and 61528206), the Natural Science Foundation of CQ CSTC (Grant No. cstc2015jcyjA40044), the Fundamental Research Funds for the Central Universities (Grant No. XDJK2015B030), the Science and Technology Foundation of Guizhou (Grant No. LH20147386) and the Scientific Project of State Ethnic Affairs Commission of the People’s Republic of China (Grant No. 14GZZ012).

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Authors and Affiliations

  1. College of Computer and Information Sciences, Southwest University, Chongqing, 400715, China

    Yantao Li, Guangfu Ge & Dawen Xia

  2. School of Information Engineering, Guizhou Minzu University, Guiyang, 550025, China

    Dawen Xia

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  1. Yantao Li
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  2. Guangfu Ge
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Correspondence to Yantao Li.

Appendix

Appendix

Lemma

Let \(\xi _1 \in (0,1), \xi _2 \in (0,1)\) be independent and uniformly distributed random variables, and another random variable \(\eta =|\xi _2 -\xi _1 |\), then expected value \(E(\eta )=1/3\).

Proof

$$\begin{aligned} E(\eta )= & {} \int _0^1 \int _0^1 |x-y|\mathrm{d}x\mathrm{d}y=\int _0^1 \mathrm{d}x\int _0^x (x-y)\mathrm{d}y\nonumber \\&+\int _0^1 {\mathrm{d}x\int _x^1 {(y-x)\mathrm{d}y} } \\= & {} \int _0^1 0.5x^{2}\mathrm{d}x+\int _0^1 (0.5-x+0.5x^{2})\mathrm{d}x\\= & {} 1/3 . \end{aligned}$$

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Li, Y., Ge, G. & Xia, D. Chaotic hash function based on the dynamic S-Box with variable parameters. Nonlinear Dyn 84, 2387–2402 (2016). https://doi.org/10.1007/s11071-016-2652-1

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