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Logistic chaotic maps for binary numbers generations

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  • Kanso, Ali
  • Smaoui, Nejib

Abstract

Two pseudorandom binary sequence generators, based on logistic chaotic maps intended for stream cipher applications, are proposed. The first is based on a single one-dimensional logistic map which exhibits random, noise-like properties at given certain parameter values, and the second is based on a combination of two logistic maps. The encryption step proposed in both algorithms consists of a simple bitwise XOR operation of the plaintext binary sequence with the keystream binary sequence to produce the ciphertext binary sequence. A threshold function is applied to convert the floating-point iterates into binary form. Experimental results show that the produced sequences possess high linear complexity and very good statistical properties. The systems are put forward for security evaluation by the cryptographic committees.

Suggested Citation

  • Kanso, Ali & Smaoui, Nejib, 2009. "Logistic chaotic maps for binary numbers generations," Chaos, Solitons & Fractals, Elsevier, vol. 40(5), pages 2557-2568.
    • Handle: RePEc:eee:chsofr:v:40:y:2009:i:5:p:2557-2568
    DOI: 10.1016/j.chaos.2007.10.049
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    References listed on IDEAS

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    1. Ali-Pacha, Adda & Hadj-Said, Naima & M’Hamed, A. & Belgoraf, A., 2007. "Lorenz’s attractor applied to the stream cipher (Ali-Pacha generator)," Chaos, Solitons & Fractals, Elsevier, vol. 33(5), pages 1762-1766.
    2. Xiao, Di & Liao, Xiaofeng & Wong, K.W., 2005. "An efficient entire chaos-based scheme for deniable authentication," Chaos, Solitons & Fractals, Elsevier, vol. 23(4), pages 1327-1331.
    3. Gao, Haojiang & Zhang, Yisheng & Liang, Shuyun & Li, Dequn, 2006. "A new chaotic algorithm for image encryption," Chaos, Solitons & Fractals, Elsevier, vol. 29(2), pages 393-399.
    4. Li, Ping & Li, Zhong & Halang, Wolfgang A. & Chen, Guanrong, 2007. "A stream cipher based on a spatiotemporal chaotic system," Chaos, Solitons & Fractals, Elsevier, vol. 32(5), pages 1867-1876.
    5. Huang, Fangjun & Guan, Zhi-Hong, 2005. "A modified method of a class of recently presented cryptosystems," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1893-1899.
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    Cited by:

    1. Tutueva, Aleksandra V. & Nepomuceno, Erivelton G. & Karimov, Artur I. & Andreev, Valery S. & Butusov, Denis N., 2020. "Adaptive chaotic maps and their application to pseudo-random numbers generation," Chaos, Solitons & Fractals, Elsevier, vol. 133(C).
    2. Sukegawa, Noriyoshi & Ikeguchi, Tohru, 2022. "How to perturb Bernoulli shift map," Chaos, Solitons & Fractals, Elsevier, vol. 165(P1).
    3. Padmapriya Praveenkumar & Rengarajan Amirtharajan & Karuppuswamy Thenmozhi & John Bosco Balaguru Rayappan, 2017. "Fusion of confusion and diffusion: a novel image encryption approach," Telecommunication Systems: Modelling, Analysis, Design and Management, Springer, vol. 65(1), pages 65-78, May.
    4. Smaoui, Nejib & Kanso, Ali, 2009. "Cryptography with chaos and shadowing," Chaos, Solitons & Fractals, Elsevier, vol. 42(4), pages 2312-2321.
    5. Elmanfaloty, Rania A. & Abou-Bakr, Ehab, 2019. "Random property enhancement of a 1D chaotic PRNG with finite precision implementation," Chaos, Solitons & Fractals, Elsevier, vol. 118(C), pages 134-144.
    6. Pengchao Zhang & Xiang Liu & Zebang Yi & Qiuzhi He, 2024. "Improved Multi-Objective Beluga Whale Optimization Algorithm for Truck Scheduling in Open-Pit Mines," Sustainability, MDPI, vol. 16(16), pages 1-21, August.
    7. Wafaa S. Sayed & Ahmed G. Radwan & Ahmed A. Rezk & Hossam A. H. Fahmy, 2017. "Finite Precision Logistic Map between Computational Efficiency and Accuracy with Encryption Applications," Complexity, Hindawi, vol. 2017, pages 1-21, February.
    8. 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.
    9. Yanfen Tong & Xianbao Cheng, 2022. "Location of Logistics Distribution Center Based on Improved Bald Eagle Algorithm," Sustainability, MDPI, vol. 14(15), pages 1-14, July.
    10. Darani, A. Yousefian & Yengejeh, Y. Khedmati & Pakmanesh, H. & Navarro, G., 2024. "Image encryption algorithm based on a new 3D chaotic system using cellular automata," Chaos, Solitons & Fractals, Elsevier, vol. 179(C).
    11. Zribi, Mohamed & Smaoui, Nejib & Salim, Haitham, 2009. "Synchronization of the unified chaotic systems using a sliding mode controller," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 3197-3209.

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