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Utilizing the roulette wheel based social network search algorithm for substitution box construction and optimization

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Abstract

This paper introduces a new variant of a recent metaheuristic algorithm based on the Social Network Search algorithm (SNS), which is called the Roulette Wheel Social Network Search algorithm (SNS). As the name indicates, the main feature of RWSNS is the fact that the algorithm allows proportionate selection of its search operators (i.e., from imitation, conversation, disputation and innovation) through exploiting the roulette wheel. Additionally, RWSNS also incorporates the Piecewise map as replacement for the pseudo random generator during the population initialisation to ensure high nonlinearity and allow further solution diversification. Finally, unlike its predecessor, RWSNS also permits the systematic manipulation of candidate solutions around the global best agent through the swap operator to boost its search intensification process, as the global best candidate solution is often clustered and always lurking around the current local best. Results based on the construction of 8 × 8 substitution-box demonstrate that the proposed RWSNS exceeds other competing metaheuristic algorithms in two main S-box criteria, namely, the average nonlinearity score and strict avalanche criteria (i.e., SAC offset), whilst maintaining a commendable performance on bits independence criteria, differential approximation probability and linear approximation probability.

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References

  1. Farah MAB, Farah A, Farah T (2020) An image encryption scheme based on a new hybrid chaotic map and optimized substitution box. Nonlinear Dyn 99:3041–3064. https://doi.org/10.1007/s11071-019-05413-8

    Article  Google Scholar 

  2. Alhadawi HS, Lambić D, Zolkipli MF, Ahmad M (2020) Globalized firefly algorithm and chaos for designing substitution box. J Inf Secur Appl 55:1–13. https://doi.org/10.1016/j.jisa.2020.102671

    Article  Google Scholar 

  3. Alhadawi HS, Majid MA, Lambić D, Ahmad M (2020) A novel method of s-box design based on discrete chaotic maps and cuckoo search algorithm. Multimedia Tools Appl. https://doi.org/10.1007/s11042-020-10048-8

    Article  Google Scholar 

  4. Zamli KZ (2021) Optimizing s-box generation based on the adaptive agent heroes and cowards algorithm. Expert Syst Appl. https://doi.org/10.1016/j.eswa.2021.115305

    Article  Google Scholar 

  5. Tian Y, Lu Z (2016) S-box: Six-dimensional compound hyperchaotic map and artificial bee colony algorithm. J Syst Eng Electron 27(1):232–241. https://doi.org/10.1109/JSEE.2016.00023

    Article  Google Scholar 

  6. Talatahari S, Bayzidi H, Saraee M (2021) Social network search for global optimization. IEEE Access 9:92815–92863. https://doi.org/10.1109/ACCESS.2021.3091495

    Article  Google Scholar 

  7. Daemen J, Rijmen V (2020) The design of rijndael. In: Information security and cryptography, 2 edn. Springer-Verlag Berlin Heidelberg.

  8. Nyberg K (1993) Differentially uniform mappings for cryptography. In: Proceedings of the Theory and Application of Cryptographic Techniques. pp 55–64

  9. Qu L, Tan Y, Li C, Gong G (2016) More constructions of differentially 4-uniform permutations on f(2^2k). Des Codes Crypt 78(2):391–408. https://doi.org/10.1007/s10623-014-0006-x

    Article  MATH  Google Scholar 

  10. Liu G, Yang W, Liu W, Dai Y (2015) Designing s-boxes based on 3-d four-wing autonomous chaotic system. Nonlinear Dyn 82(4):1867–1877. https://doi.org/10.1007/s11071-015-2283-y

    Article  MATH  Google Scholar 

  11. Khan M, Asghar Z (2018) A novel construction of substitution box for image encryption applications with gingerbreadman chaotic map and s8 permutation. Neural Comput Appl 29(4):993–999. https://doi.org/10.1007/s00521-016-2511-5

    Article  Google Scholar 

  12. Abd El-Latif AA, Li L, Wang N, Li Q, Niu X (2012) A new image encryption based on chaotic systems and singular value decomposition. In: Proceedings of the Fourth International Conference on Digital Image Processing (ICDIP 2012). pp 83343F

  13. Zaghloul A, Zhang T, Hou H, Amin M, Abd El-Latif AA, Abd El-Wahab MS (2014) A block encryption scheme for secure still visual data based on one-way coupled map lattice. Int J Secur Appl 8(4):89–100. https://doi.org/10.14257/ijsia.2014.8.4.09

    Article  Google Scholar 

  14. Belazi A, Abd El-Latif AA, Rhouma R, BelghithS (2015) Selective image encryption scheme based on DWT, AES s-box and chaotic permutation. In: Proceedings of the 2015 International wireless communications and mobile computing conference (IWCMC). pp 606–610

  15. Mohamed NA, El-Azeim MA, Zaghloul A, Abd El-Latif AA (2015) Image encryption scheme for secure digital images based on 3d cat map and turing machine. In: Proceedings of the 2015 7th international conference of soft computing and pattern recognition (SoCPaR). pp 230–234

  16. Belazi A, Abd El-Latif AA, Belghith S (2016) A novel image encryption scheme based on substitution-permutation network and chaos. Signal Process 128:155–170. https://doi.org/10.1016/j.sigpro.2016.03.021

    Article  Google Scholar 

  17. Çavuşoğlu Ü, Kaçar S, Pehlivan I, Zengin A (2017) Secure image encryption algorithm design using a novel chaos based s-box. Chaos Solitons Fractals 95:92–101. https://doi.org/10.1016/j.chaos.2016.12.018

    Article  MATH  Google Scholar 

  18. Ali TS, Ali R (2022) A novel color image encryption scheme based on a new dynamic compound chaotic map and s-box. Multimedia Tools Appl. https://doi.org/10.1007/s11042-022-12268-6

    Article  Google Scholar 

  19. Lambić D (2014) A novel method of s-box design based on chaotic map and composition method. Chaos Solitons Fractals 58:16–21. https://doi.org/10.1016/j.chaos.2013.11.001

    Article  MATH  Google Scholar 

  20. Lambić D (2017) A novel method of s-box design based on discrete chaotic map. Nonlinear Dyn 87(4):2407–2413. https://doi.org/10.1007/s11071-016-3199-x

    Article  Google Scholar 

  21. Çavuşoğlu Ü, Zengin A, Pehlivan I, Kaçar S (2017) A novel approach for strong s-box generation algorithm design based on chaotic scaled zhongtang system. Nonlinear Dyn 87(2):1081–1094. https://doi.org/10.1007/s11071-016-3099-0

    Article  MATH  Google Scholar 

  22. Alshekly TK, Albahrani EA, Lafta SH (2022) 4d chaotic system as random substitution-box. Multimedia Tools Appl 81(11):15793–15814. https://doi.org/10.1007/s11042-022-11928-x

    Article  Google Scholar 

  23. Zhou P, Du J, Zhou K, Wei S (2021) 2d mixed pseudo-random coupling ps map lattice and its application in s-box generation. Nonlinear Dyn 103(1):1151–1166. https://doi.org/10.1007/s11071-020-06098-0

    Article  Google Scholar 

  24. Tang G, Liao X, Chen Y (2005) A novel method for designing s-boxes based on chaotic maps. Chaos Solitons Fractals 23(2):413–419. https://doi.org/10.1016/j.chaos.2004.04.023

    Article  MATH  Google Scholar 

  25. Jakimoski G, Kocarev L (2001) Chaos and cryptography: Block encryption ciphers based on chaotic maps. IEEE Trans Circuits Syst I Fundam Theory Appl 48(2):163–169. https://doi.org/10.1109/81.904880

    Article  MATH  Google Scholar 

  26. Özkaynak F, Özer AB (2010) A method for designing strong s-boxes based on chaotic lorenz system. Phys Lett A 374(36):3733–3738. https://doi.org/10.1016/j.physleta.2010.07.019

    Article  MATH  Google Scholar 

  27. Khan M, Shah T, Mahmood H, Gondal MA, Hussain I (2012) A novel technique for the construction of strong s-boxes based on chaotic lorenz systems. Nonlinear Dyn 70(3):2303–2311. https://doi.org/10.1007/s11071-012-0621-x

    Article  Google Scholar 

  28. Belazi A, El-Latif AAA (2017) A simple yet efficient s-box method based on chaotic sine map. Optik 130:1438–1444. https://doi.org/10.1016/j.ijleo.2016.11.152

    Article  Google Scholar 

  29. Chen G (2008) A novel heuristic method for obtaining s-boxes. Chaos Solitons Fractals 36(4):1028–1036. https://doi.org/10.1016/j.chaos.2006.08.003

    Article  MATH  Google Scholar 

  30. Farah T, Rhouma R, Belghith S (2017) A novel method for designing s-box based on chaotic map and teaching–learning-based optimization. Nonlinear Dyn 88(2):1059–1074. https://doi.org/10.1007/s11071-016-3295-y

    Article  Google Scholar 

  31. Ahmad M, Bhatia D, Hassan Y (2015) A novel ant colony optimization based scheme for substitution box design. Procedia Comput Sci 57:572–580. https://doi.org/10.1016/j.procs.2015.07.394

    Article  Google Scholar 

  32. Alhadawi HS, Zolkipli MF, Ahmad M (2019) A novel efficient substitution-box design based on firefly algorithm and discrete chaotic map. Neural Comput Appl 31(11):7201–7210. https://doi.org/10.1007/s00521-018-3557-3

    Article  Google Scholar 

  33. Soto R, Crawford B, Molina FG, Olivares R (2021) Human behaviour based optimization supported with self-organizing maps for solving the s-box design problem. IEEE Access 9:84605–84618. https://doi.org/10.1109/ACCESS.2021.3087139

    Article  Google Scholar 

  34. Hematpour N, Ahadpour S (2021) Execution examination of chaotic s-box dependent on improved pso algorithm. Neural Comput Appl 33(10):5111–5133. https://doi.org/10.1007/s00521-020-05304-9

    Article  Google Scholar 

  35. Alhadawi HS, Salih SQ, SalmanYD (2021) Chaotic particle swarm optimization based on meeting room approach for designing bijective s-boxes. In: Proceedings of International Conference on Emerging Technologies and Intelligent Systems. pp 331–341

  36. Long M, Wang L (2021) S-box design based on discrete chaotic map and improved artificial bee colony algorithm. IEEE Access 9:86144–86154. https://doi.org/10.1109/ACCESS.2021.3069965

    Article  Google Scholar 

  37. Isa H, Jamil N, Z’aba MR (2016) Construction of cryptographically strong s-boxes inspired by bee waggle dance. N Gener Comput 34(3):221–238. https://doi.org/10.1007/s00354-016-0302-2

    Article  Google Scholar 

  38. Tian Y, Lu Z (2017) Chaotic s-box: Intertwining logistic map and bacterial foraging optimization. Math Probl Eng 2017:1–12. https://doi.org/10.1155/2017/6969312

    Article  MATH  Google Scholar 

  39. Wang Y, Wong K-W, Li C, Li Y (2012) A novel method to design s-box based on chaotic map and genetic algorithm. Phys Lett A 376(6–7):827–833. https://doi.org/10.1016/j.physleta.2012.01.009s

    Article  MATH  Google Scholar 

  40. Zamli KZ, Kader A, Din F, Alhadawi HS (2021) Selective chaotic maps tiki-taka algorithm for the s-box generation and optimization. Neural Comput Appl. https://doi.org/10.1007/s00521-021-06260-8

    Article  Google Scholar 

  41. Holland JH (1992) Adaptation in natural and artificial systems. 1975, University of Michigan Press, Ann Arbor, Michigan; re-issued by MIT Press.

  42. Hussain I, Gondal MA, Hussain A (2015) Construction of substitution box based on piecewise linear chaotic map and s8 group. 3D Res 6(1):3. https://doi.org/10.1007/s13319-014-0032-5

    Article  Google Scholar 

  43. Yoshioka D, Tsuneda A (2014) The design of low complexity s-boxes based on a discretized piecewise linear chaotic map. IEICE Trans Fundam Electron Commun Comput Sci E97.A(6):1396–1404. https://doi.org/10.1587/transfun.E97.A.1396

    Article  Google Scholar 

  44. Asim M, Jeoti V (2008) The design of low complexity s-boxes based on a discretized piecewise linear chaotic map. ETRI J 30(1):170–172. https://doi.org/10.4218/etrij.08.0207.0188

    Article  Google Scholar 

  45. Webster AF, Tavares SE (1986) On the design of s-boxes. In: Proceedings of the advances in cryptology. Berlin, Heidelberg, pp 523–534

  46. Matsui M (1994) Linear cryptanalysis method for des cipher. In: Proceedings of the Advances in Cryptology. Berlin, Heidelberg, pp 386–397

  47. Alzaidi AA, Ahmad M, Ahmed HS, Solami EA (2018) Sine cosine optimization-based bijective substitution-boxes construction using enhanced dynamics of chaotic map. Complexity 2018:1–16. https://doi.org/10.1155/2018/9389065

    Article  Google Scholar 

  48. Zamli KZ, Kader A, Azad S, Ahmed BS (2021) Hybrid henry gas solubility optimization algorithm with dynamic cluster-to-algorithm mapping. Neural Comput Appl 33:8389–8416. https://doi.org/10.1007/s00521-020-05594-z

    Article  Google Scholar 

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Acknowledgements

The work reported in this paper is funded by the Malaysian Technical University Network (MTUN) Research Grant from the Ministry of Higher Education Malaysia titled: The Development of T-Way Test Generation Tool for Combinatorial Testing (Grant No: UIC19102).

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Authors and Affiliations

  1. Faculty of Computing, College of Computing and Applied Sciences, Universiti Malaysia Pahang, 26600, Pekan, Pahang, Malaysia

    Kamal Z. Zamli

  2. Faculty of Science and Technology, Universitas Airlangga–C Campus, JI. Dr. H. Soekamo, Mulyorejo, Surabaya, 60115, Indonesia

    Kamal Z. Zamli

  3. Department of Computer Techniques Engineering, Dijlah University College, Baghdad, Iraq

    Hussam S. Alhadawi

  4. College of Engineering, University of Warith Al-Anbiyaa, Karbala, Iraq

    Hussam S. Alhadawi

  5. Department of Computer Science and IT, Faculty of Information Technology, University of Malakand, Chakdara, Khyber Pakhtunkhwa, Pakistan

    Fakhrud Din

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  1. Kamal Z. Zamli
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Correspondence to Kamal Z. Zamli.

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Zamli, K.Z., Alhadawi, H.S. & Din, F. Utilizing the roulette wheel based social network search algorithm for substitution box construction and optimization. Neural Comput & Applic 35, 4051–4071 (2023). https://doi.org/10.1007/s00521-022-07899-7

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