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A new S-box design by applying Swarm Intelligence based technique

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Abstract

Substitution-boxes are important nonlinear components used for achieving strong confusion as well as cryptographic security in a majority of modern symmetric cryptosystems. Designing cryptographically strong S-boxes has been a major research domain for the designers of symmetric ciphers. In this research work, Firefly algorithm based technique is proposed for designing S-boxes. The proposed Swarm Intelligence (SI) based technique generates cryptographically strong S-boxes. Furthermore, authors analyze strength of the computed S-boxes by testing: nonlinearity, bijectivity, bit-independence criterion (BIC), linear probability and differential uniformity. For the S-box constructed by the proposed technique; average nonlinearity is 109.25 and average strict avalanche criteria (SAC) value is 0.504. The computed performance results for the S-box are compared with some recently reported S-boxes.

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References

  1. Stinson DR (2013) Cryptography: Theory and Practice. 3rd Edition, Chapman & Hall/CRC Publication, 593p

  2. Bogdanov A, Knudsen LR, Leander G, Paar C et al (2007) PRESENT-Ultra Lightweight Block Cipher. In Proc. Of the 9th Intl Workshop on Cryptographic Hardware and Embedded Systems, CHES ’07, Springer-Verlag, pp 450–466

  3. Biham E, Shamir A (1991) Differential cryptanalysis of DES-like cryptosystems. J of Cryptology 4(1):3–72

    Article  MathSciNet  MATH  Google Scholar 

  4. Jakimoski G, Kocarev L (2001) Chaos and cryptography: block encryption ciphers based on chaotic maps. IEEE Trans Circuits Systems 48:163

    Article  MathSciNet  MATH  Google Scholar 

  5. Tang G, Liao XF, Chen Y (2005) A novel method for designing S-boxes based on chaotic maps. Chaos Solitons Fractals 23:413–419

    Article  MATH  Google Scholar 

  6. Hussain I, Shah T, Gondal M (2012) A Novel approach for designing substitution boxes based on nonlinear chaotic algorithm. Nonlinear Dyn 70(3):1791–1794

    Article  MathSciNet  Google Scholar 

  7. Wang Y, Wong K-W, Li C, Li Y (2012) A novel method to design S-box based on chaotic map and genetic algorithm. Phy Letter A 376(6):827–833

    Article  MATH  Google Scholar 

  8. Ahmad M, Bhatia D, Hassan Y (2015) A novel ant colony optimization based scheme for substitution box design, Proc. Computer Science, 57,572–580

  9. 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

    Article  Google Scholar 

  10. Ahmed HA, Zolkipli MF, Ahmad M (2018) A novel efficient substitution-box design based on firefly algorithm and discrete chaotic map. Nat Comput Appl 31:7201–7210. https://doi.org/10.1007/s00521-018-3557-3

    Article  Google Scholar 

  11. Fister I, Fister I Jr, Yang X-S, Brest J (2013) A comprehensive review of firefly algorithm. Swarm Evol Computing 13:34–46

    Article  Google Scholar 

  12. Yang X-S (2010) Firefly algorithm, stochastic test functions and design optimization. Int J Bio-Inspired Computing 2(2):78–84

    Article  Google Scholar 

  13. Yang X-S, Hosseini SSS, Gandomi AH (2012) Firefly algorithm for solving non-convex economic dispatch problems with value loading effect. Appl Soft Computing 12(3):1180–1186

    Article  Google Scholar 

  14. Senthilnath J, Omkar S, Mani V (2011) Clustering using firefly algorithm; performance study. Swarm Evol Computing 1(3):164–171

    Article  Google Scholar 

  15. Yang X-S (2014) Cuckoo Search and firefly algorithm. Studies in computational intelligence, vol 516. Springer, Switzerland

    Google Scholar 

  16. Gandomi A, Yang X-S, Talatahari S et al (2013) Firefly algorithm with chaos, Common Nonlinear. Sci Numer Simul 18(1):89–98

    MathSciNet  MATH  Google Scholar 

  17. Yang X-S (2015) Analysis of firefly algorithm and automatic parameter tuning. Inemerging research on swarm intelligence and algorithm optimization, IGI Global,36–49

  18. Yang X-S (2009) Firefly algorithms for multimodal optimization. International Symposium on Stochastic Algorithms, 169-178p

  19. Yang XS, Cui Z, Xiao R, Gandomi AH (2013) Swarm Intelligence and Bio-Inspired Computations: Theory and Applications. Elsevier Publication, p 450

  20. Laskari EC, Meletiou GC, Stamatiou YC, Vrahatis MN (2007) Cryptography and cryptanalysis through computational intelligence, vol 57. Springer, Berlin, Heidelberg, pp 1–49. https://doi.org/10.1007/978-3-540-71078-3_1

    Book  Google Scholar 

  21. Din M, Pal SK, Muttoo SK (2018) A Review of Computational Swarm Intelligence Techniques for Solving Crypto Problems, Proceeding of International Conference SoCTA-2017, AISC, 742, 193–204, Springer Publication

  22. Din M, Pal SK, Muttoo SK (2019) Applying PSO based Technique for Analysis of Geffe Generator Cryptosystem, Proceeding of International Conference ICHSA-2018, AISC, 741, 741–749, Springer Publication

  23. Din M, Pal SK, Muttoo SK (2019) Analysis of RC4 Crypts using PSO based Swarm Technique, Proceeding of International Conference ICHSA-2018, AISC, 741, 1049–1056, Springer Publication

  24. Webster A, Tavares S (1986) On the design of S-boxes. In: Advances in cryptology: Proc of CRYPTO85. Lecture notes in computer science, 523 – 34

  25. Asim M, Jeoti V (2008) Efficient and simple method for designing chaotic S-boxes. ETRI J. x1, 170–172

  26. Ozkaynak F, Yavuz S (2013) Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn 74(3):551–557

    Article  MathSciNet  MATH  Google Scholar 

  27. Lambic D (2014) A novel method of S-box design based on chaotic map and composition method. Chaos Solitons and Fractals 58:16–21

    Article  MATH  Google Scholar 

  28. Ahmad M, Ahmad F, Nasim Z, Bano Z, Zafar S (2015) Designing chaos based strong substitution box. Proc. of eighth international conference on contemporary computing (IC3).

  29. Ahmad M, Seeru F, Siddiqi AM, Masood S (2018) Dynamic 9 × 9 substitution-boxes using Chaos-based heuristic search. : soft computing: theories and applications. Springer, pp 839–851

  30. Alhadawi HS, Majid MA, Lambic D, Ahmad M (2020) A novel method of S-box design based on discrete chaotic maps and Cuckoo search algorithm, Multimedia Tools and Applications, part of Springer Nature-2020. https://doi.org/10.1007/s11042-020-10048-8

  31. Al Solami E, Ahmad M, Volos C, Doja M, Beg M (2018) A new hyper chaotic system-based design for efficient Bijective substitution-boxes. Entropy 20(7):525

    Article  Google Scholar 

  32. Matsui M (1993) Linear cryptanalysis method for DES cipher,Workshop on the theory and application of cryptographic techniques,386–397

  33. Dawson M, Tavares SE (1991) An expanded set of S-box design criteria based on information theory and its relation to differential-like attacks,Workshop on the theory and application of cryptographic techniques,352–367

  34. Wang Y, Xie Q, Wu Y, Du B (2009) A software for S-box performance analysis and test, Proc. International Conference on Electronic commerce and business intelligence, 125–128

  35. Bennis F, Bhattacharjya RK (eds) (2020) Nature-Inspired Methods for Meta-heuristics Optimization – Modeling and Optimization in Science and Technology. Springer Nature Switzerland AG, p 488

  36. 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

    Article  MathSciNet  MATH  Google Scholar 

  37. Cavuoglu Unal Z, Ahmet PI, Kacar Sezgin (2017) A novel approach for strong S-box generation algorithm design based on chaotic scaled Zhongtang system. Nonlinear Dyn 87(2):1081–1094

    Article  Google Scholar 

  38. Lambic D (2017) A novel method of S-box design based on discrete chaotic map. Nonlinear Dyn 87(4):2407–2413

    Article  MathSciNet  Google Scholar 

  39. Ozkaynak F (2019) Construction of robust substitution boxes based on chaotic systems. Neural Comput Appl 31(3):1–10. DOI: https://doi.org/10.1007/s00521-017-3287-y

    Article  Google Scholar 

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Acknowledgements

My sincere thanks to the co-authors/ PhD supervisor(s) for valuable technical guidance and support in carrying out the proposed research work in this paper.

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Correspondence to Maiya Din.

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Din, M., Pal, S.K., Muttoo, S.K. et al. A new S-box design by applying Swarm Intelligence based technique. Int J Syst Assur Eng Manag 13, 2963–2970 (2022). https://doi.org/10.1007/s13198-022-01766-3

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  • DOI: https://doi.org/10.1007/s13198-022-01766-3

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