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Dynamic S-box construction based on a novel chaotic map and twitching approach

Authors

  • Muhammad Rehan Saleem

    School of Systems and Technology, University of Management and Technology, Lahore, 54000, Pakistan
    Author

  • Amjad Hussain Zahid

    School of Systems and Technology, University of Management and Technology, Lahore, 54000, Pakistan
    Author
    https://orcid.org/0000-0002-6123-6610

  • Ghulam Mustafa

    School of Systems and Technology, University of Management and Technology, Lahore, 54000, Pakistan
    Author

DOI:

https://doi.org/10.22581/muet1982.0354

Keywords:

Hyperchaotic Map, Substitution Box, Twitching Mechanism, Cryptanalysis, Cryptography, Key Space

Abstract

The increasing frequency of hacking and phishing assaults has made data encryption and information security as major solutions. Attackers are concentrating on breaking cryptosystems to obtain valuable data and information. Many ciphers have been created and put into use for the security of both data and information. A substitution box (S-Box), being an essential part of many symmetric-key block ciphers, provides much-needed confusion for the transmitted data. This research article offers an innovative method for creating key-dependent and dynamic S-Boxes using a new hyperchaotic map. Additionally, a dynamic twitching mechanism, that is presented first time, is applied to the initial S-Box for optimization purposes to ensure that the final S-Box adheres to the accepted cryptographic standards. Several tests, including the strict avalanche criterion, bit independence criterion, nonlinearity, fixed-point analysis, linear and differential probabilities, are performed to assess the cryptographic performance of the proposed S-Boxes. An example S-Box produced by the proposed approach is evaluated against these tests and compared with the contemporary S-Boxes. The comparative analysis reveals that the designed S-Box having average NL value of 112 and SAC value of 0.5 has the candid potential of adaptability in real-life security endeavors.

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Author Biographies

  • Muhammad Rehan Saleem, School of Systems and Technology, University of Management and Technology, Lahore, 54000, Pakistan

    School of Systems and Technology, Student

  • Amjad Hussain Zahid, School of Systems and Technology, University of Management and Technology, Lahore, 54000, Pakistan

    School of Systems and Technology, Associate Professor

  • Ghulam Mustafa, School of Systems and Technology, University of Management and Technology, Lahore, 54000, Pakistan

    School of Systems and Technology, Assistant Professor

References

[1]. E. Shannon, “Communication theory of secrecy systems,” Bell Labs Tech. J., vol. 28, no. 4, pp. 656–715, Oct. 1949.

[2]. C. Paar, J. Pelzl, and B. Preneel, Understanding Cryptography, 1st ed. Berlin, Germany: Springer, 2010.

[3]. A. Kadhim and S. Khalaf, “New approach for security chatting in real-time,” Int. J. Emerg. Trends Technol. Comput. Sci., vol. 4, no. 3, pp. 30–36, 2015.

[4]. X. Yan, S. Wang, A. A. A. El-Latif, and X. Niu, “Visual secret sharing based on random grids with abilities of AND and XOR lossless recovery,” Multimedia Tools Appl., vol. 74, no. 9, pp. 3231–3252, May 2015.

[5]. A. H. Zahid, M. Ahmad, A. Alkhayyat, M. T. Hassan, A. Manzoor, and A. K. Farhan, “Efficient dynamic S-box generation using linear trigonometric transformation for security applications,” IEEE Access, vol. 9, pp. 98460–98475, 2021.

[6]. A. Manzoor, A. H. Zahid, and M. T. Hassan, “A new dynamic substitution box for data security using an innovative chaotic map,” IEEE Access, vol. 10, pp. 74164–74174, 2022.

[7]. A. A. A. El-Latif, B. Abd-El-Atty, W. Mazurczyk, C. Fung, and S. E. Venegas-Andraca, “Secure data encryption based on quantum walks for 5G Internet of Things scenario,” IEEE Trans. Netw. Service Manage., vol. 17, no. 1, pp. 118–131, Mar. 2020.

[8]. L. R. Knudsen and M. J. B. Robshaw, The Block Cipher Companion. Berlin, Germany: Springer-Verlag, 2011.

[9]. A. A. A. El-Latif, X. Niu, and M. Amin, “A new image cipher in time and frequency domains,” Opt. Commun., vol. 285, nos. 21–22, pp. 4241–4251, Oct. 2012.

[10]. A. Belazi, A. A. A. El-Latif, R. Rhouma, and S. Belghith, “Selective image encryption scheme based on DWT, AES S-box and chaotic permutation,” in Proc. Int. Wireless Commun. Mobile Comput. Conf. (IWCMC), Aug. 2015, Art. no. 606610.

[11]. A. K. Farhan, R. S. Ali, H. Natiq, and N. M. G. Al-Saidi, “A new Sbox generation algorithm based on multistability behaviour of a plasma perturbation model,” IEEE Access, vol. 7, pp. 124914–124924, 2019.

[12]. A. H. Zahid, A. M. Iliyasu, M. Ahmad, M. M. U. Shaban, M. J. Arshad, H. S. Alhadawi, and A. A. Abd El-Latif, “A novel construction of dynamic S-box with high nonlinearity using heuristic evolution,” IEEE Access, vol. 9, pp. 67797–67812, 2021.

[13]. A. Altaleb, M. S. Saeed, I. Hussain, and M. Aslam, “An algorithm for the construction of substitution box for block ciphers based on projective general linear group,” AIP Adv., vol. 7, no. 3, Mar. 2017, Art. no. 035116.

[14]. M. Sarfraz, I. Hussain, and F. Ali, “Construction of S-box based on Mobius transformation and increasing its confusion creating ability through invertible function,” Int. J. Comput. Sci. Inf. Secur., vol. 14, no. 2, pp. 187–199, 2016.

[15]. P. Agarwal, A. Singh, and A. Kilicman, “Development of key-dependent dynamic S-boxes with dynamic irreducible polynomial and affine constant,” Adv. Mech. Eng., vol. 10, no. 7, pp. 1–18, 2018.

[16]. S. Sahmoud, W. Elmasry, and S. Abudalfa, “Enhancement the security of AES against modern attacks by using variable key block cipher,” Int. Arab J. e-Tech., vol. 3, pp. 17–26, Jan. 2013.

[17]. M. S. M. Malik, M. A. Ali, M. A. Khan, M. Ehatisham-Ul-Haq, S. N. M. Shah, M. Rehman, and W. Ahmad, “Generation of highly nonlinear and dynamic AES substitution-boxes (S-boxes) using chaos-based rotational matrices,” IEEE Access, vol. 8, pp. 35682–35695, 2020.

[18]. E. M. Mahmoud, A. Abd, T. A. E. El Hafez, and T. A. El Hafez, “Dynamic AES-128 with key-dependent S-box,” Int. J. Eng. Res. Appl., vol. 3, no. 1, pp. 1662–1670, Jan./Feb. 2013.

[19]. J. Cui, L. Huang, H. Zhong, C. Chang, and W. Yang, “An improved AES S-box and its performance analysis,” Int. J. Innov. Comput., Inf. Control, vol. 7, no. 5, pp. 2291–2302, 2011.

[20]. A. H. Zahid, M. J. Arshad, and M. Ahmad, “A novel construction of efficient substitution-boxes using cubic fractional transformation,” Entropy, vol. 21, no. 3, p. 245, May 2019.

[21]. A. H. Zahid, E. Al-Solami, and M. Ahmad, “A novel modular approach based substitution-box design for image encryption,” IEEE Access, vol. 8, pp. 150326–150340, 2020.

[22]. A. H. Zahid and M. J. Arshad, “An innovative design of substitution-boxes using cubic polynomial mapping,” Symmetry, vol. 11, no. 3, p. 437, 2019.

[23]. Q. Lu, C. Zhu, and X. Deng, “An efficient image encryption scheme based on the LSS chaotic map and single S-box,” IEEE Access, vol. 8, pp. 25664–25678, 2020, doi: 10.1109/ACCESS.2020. 2970806.

[24]. F. Riaz, “Design of an efficient cryptographic substitution box by using improved chaotic range with the golden ratio,” Int. J. Comput. Sci. Inf. Secur., vol. 18, no. 1, pp. 89–94, 2020.

[25]. J. Liu, X. Tong, M. Zhang, and Z. Wang, “The design of S-box based on combined chaotic map,” in Proc. 3rd Int. Conf. Adv. Electron. Mater., Comput. Softw. Eng. (AEMCSE), Apr. 2020, pp. 350–353, doi: 10.1109/AEMCSE50948.2020.00082.

[26]. A. Shafique, “A new algorithm for the construction of substitution box by using chaotic map,” Eur. Phys. J. Plus, vol. 135, no. 2, pp. 1–13, Feb. 2020, doi: 10.1140/epjp/s13360-020-00187-0.

[27]. S. Ibrahim, H. Alhumyani, M. Masud, S. S. Alshamrani, O. Cheikhrouhou, G. Muhammad, M. S. Hossain, and A. M. Abbas, “Framework for efficient medical image encryption using dynamic S-boxes and chaotic maps,” IEEE Access, vol. 8, pp. 160433–160449, 2020, doi: 10.1109/ACCESS.2020.3020746.

[28]. T. Farah, R. Rhouma, and S. Belghith, “A novel method for designing S-box based on chaotic map and teaching-learning-based optimization,” Nonlinear Dyn., vol. 88, no. 2, pp. 1059–1074, 2017, doi: 10.1007/s11071- 016-3295-y.

[29]. D. Lambić, “A novel method of S-box design based on discrete chaotic map,” Nonlinear Dyn., vol. 87, no. 4, pp. 2407–2413, 2017.

[30]. A. H. Zahid, L. Tawalbeh, M. Ahmad, A. Alkhayyat, M. T. Hassan, A. Manzoor, and A. K. Farhan, “Efficient dynamic S-box generation using linear trigonometric transformation for security applications,” IEEE Access, vol. 9, pp. 98460–98475, 2021, doi: 10.1109/ACCESS.2021.3095618.

[31]. D. Lambić, “S-box design method based on improved one-dimensional discrete chaotic map,” J. Inf. Telecommun., vol. 2, no. 2, pp. 181–191, Apr. 2018, doi: 10.1080/24751839.2018.1434723.

[32]. M. Long and L. Wang, “S-box design based on discrete chaotic map and improved artificial bee colony algorithm,” IEEE Access, vol. 9, pp. 86144–86154, 2021, doi: 10.1109/ACCESS.2021.3069965.

[33]. H. Zhu, X. Tong, Z. Wang, and J. Ma, “A novel method of dynamic S-box design based on combined chaotic map and fitness function,” Multimedia Tools Appl., vol. 79, nos. 17–18, pp. 12329–12347, May 2020, doi: 10.1007/s11042-019–08478-0.

[34]. Z. Jiang and Q. Ding, “Construction of an S-box based on chaotic and bent functions,” Symmetry, vol. 13, no. 4, p. 671, Apr. 2021, doi: 10.3390/sym13040671.

[35]. H. S. Alhadawi, M. A. Majid, D. Lambić, and M. Ahmad, “A novel method of S-box design based on discrete chaotic maps and cuckoo search algorithm,” Multimedia Tools Appl., vol. 80, no. 5, pp. 7333–7350, Feb. 2021, doi: 10.1007/s11042-020-10048-8.

[36]. D. Lambić, “A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design,” Nonlinear Dyn., vol. 100, no. 1, pp. 699–711, 2020, doi: 10.1007/s11071-020-05503-y.

[37]. Y.-Q. Zhang, J.-L. Hao, and X.-Y. Wang, “An efficient image encryption scheme based on S-boxes and fractional-order differential logistic map,” IEEE Access, vol. 8, pp. 54175–54188, 2020.

[38]. K. M. Ali and M. Khan, “A new construction of confusion component of block ciphers,” Multimedia Tools Appl., vol. 78, no. 22, pp. 32585–32604, Nov. 2019, doi: 10.1007/s11042-019-07866-w.

[39]. S. Beg, N. Ahmad, A. Anjum, M. Ahmad, A. Khan, F. Baig, and A. Khan, “S-box design based on optimize LFT parameter selection: A practical approach in recommendation system domain,” Multimedia Tools Appl., vol. 79, nos. 17–18, pp. 11667–11684, May 2020.

[40]. T. S. Ali and R. Ali, “A novel color image encryption scheme based on a new dynamic compound chaotic map and S-box,” Multimedia Tools and Applications, vol. 81, no. 1, pp. 20585–20609, 2022.

[41]. Z. Liu, J. Li and X. Di, “A new hyperchaotic 4D-FDHNN system with four positive Lyapunov exponents and its application in image encryption,” Entropy, vol. 24, no. 7, pp. 1–28, 2022.

[42]. H. M. Heys, “A tutorial on linear and differential cryptanalysis,” Cryptologia, vol. 26, no. 3, pp. 189–221, Jul. 2002, doi: 10.1080/0161- 110291890885.

[43]. M. M. Lauridsen, C. Rechberger, and L. R. Knudsen, “Design and analysis of symmetric primitive,” Tech. Univ. Denmark, Lyngby, Denmark, Tech. Rep. 382, 2016.

[44]. L. Li, B. Abd-El-Atty, A. A. El-Latif, and A. Ghoneim, “Quantum color image encryption based on multiple discrete chaotic systems,” in Proc. Federated Conf. Comput. Sci. Inf. Syst., Sep. 2017, pp. 555–559.

[45]. A. K. Farhan, R. S. Ali, H. R. Yassein, N. M. G. Al-Saidi, and G. H. Abdul-Majeed, “A new approach to generate multi S-boxes based on RNA computing,” Int. J. Innov. Comput., Inf. Control, vol. 16, pp. 331–348, Oct. 2020.

[46]. U. Hayat, N. A. Azam, H. R. Gallegos-Ruiz, S. Naz, and L. Batool, “A truly dynamic substitution box generator for block ciphers based on elliptic curves over finite rings,” Arabian J. Sci. Eng., pp. 1–13, May 2021, doi: 10.1007/s13369-021-05666-9.

[47]. N. A. Azam, U. Hayat, and M. Ayub, “A substitution box generator, its analysis, and applications in image encryption,” Signal Process., vol. 187, Oct. 2021, Art. no. 108144, doi: 10.1016/j.sigpro.2021.108144.

[48]. K. Mohamed, M. Nazran, M. Pauzi, F. Hani, H. M. Ali, S. Ariffin, N. Huda, and N. Zulkipli, “Study of S-box properties in block cipher,” in Proc. Int. Conf. Comput. Commun. Control Technol., Langkawi, Malaysia, Sep. 2014, pp. 2–4.

[49]. A. H. Zahid, M. J. Arshad, M. Ahmad, N. F. Soliman, and W. El-Shafai, “Dynamic S-Box Generation Using Novel Chaotic Map with Nonlinearity Tweaking,” Computers, Materials & Continua, vol. 75, no. 2, 2023.

[50]. K. U. Shahna, “Novel chaos-based cryptosystem using four-dimensional hyperchaotic map with efficient permutation and substitution techniques,” Chaos, Solitons & Fractals, vol. 170, p. 113383, 2023.

[51]. I. Hussain, A. Anees, T. Al-Maadeed, and M. Mustafa, “Construction of S-box based on chaotic map and algebraic structures,” Symmetry, vol. 11, no. 3, p. 351, Mar. 2019.

[52]. B. Idrees, S. Zafar, T. Rashid, and W. Gao, “Image encryption algorithm using S-box and dynamic Hénon bit-level permutation,” Multimedia Tools Appl., vol. 79, nos. 9–10, pp. 6135–6162, Mar. 2020.

[53]. A. A. A. El-Latif, B. Abd-El-Atty, M. Amin, and A. M. Iliyasu, “Quantum inspired cascaded discrete-time quantum walks with induced chaotic dynamics and cryptographic applications,” Sci. Rep., vol. 10, no. 1, pp. 1–16, Feb. 2020.

[54]. N. A. Khan, M. Altaf, and F. A. Khan, “Selective encryption of jpeg images with chaotic based novel S-box,” Multimedia Tools Appl., vol. 80, pp. 9639–9656, Jan. 2021.

[55]. A. H. Brahim, A. A. Pacha, and N. H. Said, “A new image encryption scheme based on a hyperchaotic system & multi specific S-boxes,” Inf. Secur. J., A Global Perspective, vol. 32, no. 2, pp. 59–75, Mar. 2023.

[56]. A. Razaq, G. Alhamzi, S. Abbas, M. Ahmad, and A. Razzaque, “Secure communication through reliable S-box design: A proposed approach using coset graphs and matrix operations,” Heliyon, vol. 9, no. 5, May 2023, Art. no. e15902.

[57]. R. Anjum, M. Abbas, “Fixed point property of a nonempty set relative to the class of friendly mappings.” RACSAM, vol. 116, no. 32, pp. 1–10, 2022.

[58]. Artuğer F., (2024) “A new S-box generator algorithm based on chaos and cellular automata,” Signal, Image and Video Processing, vol. 18, pp. 4731–4740, 2024.

[59]. Vijayakumar M, Ahilan A, (2024) “An optimized chaotic S-box for real-time image encryption scheme based on 4-dimensional memristive hyperchaotic map,” Ain Shams Engineering J, vol. 15:102620, 2024.

[60]. Artuğer F., (2023) “A new S‑box generator algorithm based on 3d chaotic maps and whale optimization algorithm,” Wireless Personal Comm, vol. 131, pp. 835–853, 2023.

[61]. Wang M, Liu H, Zhao M., (2023) “Construction of a non-degeneracy 3D chaotic map and application to image encryption with keyed S-box,” Multimedia Tools and Appl. Vol. 82, pp. 34541–34563, 2023.

[62]. Zhao M, Yuan Z, Li L, Chen X., (2024) “A novel efficient S-box design algorithm based on a new chaotic map and permutation,” Multimedia Tools and Appl. Vol. 83, pp. 64899–64918, 2024.

[63]. Liu H, Liu J, Ma C., (2023) “Constructing dynamic strong S-box using 3D chaotic map and application to image encryption,” Multimedia Tools and Appl. Vol. 82, pp. 23899–23914, 2023.

[64]. Khadem B, Zade S. R., (2022) “Construction of side channel attack resistant S-boxes using genetic algorithms based on coordinate functions,” J Electr Comput Eng Innovations, vol. 10, pp. 143–152, 2022.

[65]. A. F. Webster, and S. E. Tavares, “On the Design of S-Boxes,” in Proc. Conf. Theory Appl. Crypto. Tech.,” pp. 523–534, Santa Barbara, CA, USA, August 1986.

[66]. M. Matsui, “Linear Cryptanalysis Method for DES Cipher,” in Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 1994, vol. 765 LNCS, pp. 386–397.

[67]. E. Biham and A. Shamir, “Differential Cryptanalysis of DES-like Cryptosystems,” J. Cryptology, vol. 4, no. 1, pp. 3–72, 1991.

[68]. A. H. Zahid, H. A. M. Elahi, M. Ahmad, L. A. Maghrabi, and R. S. A. Said, “Secure Key-Based Substitution-Boxes Design Using Systematic Search for High Nonlinearity,” IEEE Access, vol. 11, pp. 139745–139758, 2023.

Published

2025-10-28

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Vol. 44 No. 4 (2025): October Issue

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How to Cite

Dynamic S-box construction based on a novel chaotic map and twitching approach. (2025). Mehran University Research Journal of Engineering and Technology, 44(4), 101-119. https://doi.org/10.22581/muet1982.0354

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