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From Collatz Conjecture to chaos and hash function

Author

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  • Rasool, Masrat
  • Belhaouari, Samir Brahim

Abstract

The non-linear property of Chaos is a promising approach to information security, and many accomplishments have been made by combining Chaos with several sub-security domains, including chaos-based stream ciphers, block ciphers, image encryption, and hash functions. Most Chaos-based hash functions are insecure or inefficient due to their dependence on complex, attacked multi-dimensional maps or uncertain, weak one-dimensional maps like logistic and tent. The Collatz Conjecture is a mystery that has stumped mathematicians for decades and still has not been solved. This paper aims to introduce a novel approach to addressing current security challenges by utilizing our generalized Collatz process to create a chaos-based hash function. By leveraging the unpredictable behaviour of the Collatz sequence, the proposed hash function aims to enhance ergodicity and entropy properties, thereby making it well-suited for cryptographic applications. In the proposed method, the chaotic variables are governed by cryptographic keys, crucial in generating data sequences. These sequences are then utilized within the diffusion and confusion structures of the hashing function. The design of the chaos-hash model is carefully optimized to exhibit desirable characteristics such as randomness, collision resistance, uniformity, sensitivity to initial conditions, speed, and resistance against cryptanalysis.

Suggested Citation

  • Rasool, Masrat & Belhaouari, Samir Brahim, 2023. "From Collatz Conjecture to chaos and hash function," Chaos, Solitons & Fractals, Elsevier, vol. 176(C).
    • Handle: RePEc:eee:chsofr:v:176:y:2023:i:c:s0960077923010044
    DOI: 10.1016/j.chaos.2023.114103
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    References listed on IDEAS

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    1. Yang, Huaqian & Wong, Kwok-Wo & Liao, Xiaofeng & Wang, Yong & Yang, Degang, 2009. "One-way hash function construction based on chaotic map network," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2566-2574.
    2. Aslan, Nisa & Şeker, Saliha & Saltan, Mustafa, 2022. "The investigation of chaos conditions of some dynamical systems on the Sierpinski propeller," Chaos, Solitons & Fractals, Elsevier, vol. 159(C).
    3. Akhavan, A. & Samsudin, A. & Akhshani, A., 2009. "Hash function based on piecewise nonlinear chaotic map," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1046-1053.
    4. Li, Yantao & Li, Xiang, 2016. "Chaotic hash function based on circular shifts with variable parameters," Chaos, Solitons & Fractals, Elsevier, vol. 91(C), pages 639-648.
    5. Xu, Shaochuan & Wang, Xingyuan & Ye, Xiaolin, 2022. "A new fractional-order chaos system of Hopfield neural network and its application in image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).
    6. Akhshani, A. & Behnia, S. & Akhavan, A. & Jafarizadeh, M.A. & Abu Hassan, H. & Hassan, Z., 2009. "Hash function based on hierarchy of 2D piecewise nonlinear chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2405-2412.
    7. Amin, Mohamed & Faragallah, Osama S. & Abd El-Latif, Ahmed A., 2009. "Chaos-based hash function (CBHF) for cryptographic applications," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 767-772.
    8. Xiao, Di & Liao, Xiaofeng & Deng, Shaojiang, 2005. "One-way Hash function construction based on the chaotic map with changeable-parameter," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 65-71.
    9. Asgari Chenaghlu, Meysam & Jamali, Shahram & Nikzad Khasmakhi, Narjes, 2016. "A novel keyed parallel hashing scheme based on a new chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 87(C), pages 216-225.
    10. Tutueva, Aleksandra V. & Karimov, Artur I. & Moysis, Lazaros & Volos, Christos & Butusov, Denis N., 2020. "Construction of one-way hash functions with increased key space using adaptive chaotic maps," Chaos, Solitons & Fractals, Elsevier, vol. 141(C).
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