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An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps

Author

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  • Chen, Guo
  • Chen, Yong
  • Liao, Xiaofeng

Abstract

Tang et al. proposed a novel method for obtaining S-boxes based on the well-known two-dimensional chaotic Baker map. Unfortunately, some mistakes exist in their paper. The faults are corrected first in this paper and then an extended method is put forward for acquiring cryptographically strong S-boxes. The new scheme employs a three-dimensional chaotic Baker map, which has more intensive chaotic characters than the two-dimensional one. In addition, the cryptographic properties such as the bijective property, the nonlinearity, the strict avalanche criterion, the output bits independence criterion and the equiprobable input/output XOR distribution are analyzed in detail for our S-box and revised Tang et al.’s one, respectively. The results of numerical analysis show that both of the two boxes can resist several attacks effectively and the three-dimensional chaotic map, a stronger sense in chaotic characters, can perform more smartly and more efficiently in designing S-boxes.

Suggested Citation

  • Chen, Guo & Chen, Yong & Liao, Xiaofeng, 2007. "An extended method for obtaining S-boxes based on three-dimensional chaotic Baker maps," Chaos, Solitons & Fractals, Elsevier, vol. 31(3), pages 571-579.
    • Handle: RePEc:eee:chsofr:v:31:y:2007:i:3:p:571-579
    DOI: 10.1016/j.chaos.2005.10.022
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    Cited by:

    1. Yin, Ruming & Yuan, Jian & Wang, Jian & Shan, Xiuming & Wang, Xiqin, 2009. "Designing key-dependent chaotic S-box with larger key space," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2582-2589.
    2. Zhao, Liang & Liao, Xiaofeng & Xiao, Di & Xiang, Tao & Zhou, Qing & Duan, Shukai, 2009. "True random number generation from mobile telephone photo based on chaotic cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1692-1699.
    3. Zhou, Qing & Wong, Kwok-wo & Liao, Xiaofeng & Xiang, Tao & Hu, Yue, 2008. "Parallel image encryption algorithm based on discretized chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 38(4), pages 1081-1092.
    4. Hu, Yue & Liao, Xiaofeng & Wong, Kwok-wo & Zhou, Qing, 2009. "A true random number generator based on mouse movement and chaotic cryptography," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2286-2293.
    5. Muhammad Usama & Osama Rehman & Imran Memon & Safdar Rizvi, 2019. "An efficient construction of key-dependent substitution box based on chaotic sine map," International Journal of Distributed Sensor Networks, , vol. 15(12), pages 15501477198, December.
    6. Francisco Gonzalez & Ricardo Soto & Broderick Crawford, 2022. "Stochastic Fractal Search Algorithm Improved with Opposition-Based Learning for Solving the Substitution Box Design Problem," Mathematics, MDPI, vol. 10(13), pages 1-25, June.
    7. Chen, Guo, 2008. "A novel heuristic method for obtaining S-boxes," Chaos, Solitons & Fractals, Elsevier, vol. 36(4), pages 1028-1036.
    8. Lambić, Dragan, 2014. "A novel method of S-box design based on chaotic map and composition method," Chaos, Solitons & Fractals, Elsevier, vol. 58(C), pages 16-21.
    9. Xiang, Tao & Wong, Kwok-Wo & Liao, Xiaofeng, 2009. "On the security of a novel key agreement protocol based on chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 40(2), pages 672-675.

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