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ABC Optimization Based Construction of Strong Substitution-Boxes

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Abstract

Most of the block ciphers contain substitution-boxes as their cornerstone primitive to add requisite nonlinearity. S-boxes are responsible to ensure strong confusion and resistance to linear and differential assaults. The security of such ciphers relies on the strength of S-boxes deployed during substitution stage. It is challenging to construct cryptographically strong S-boxes that satisfy several properties such as high nonlinearity, good avalanche effect, bit-independent criteria, low differential uniformity and linear probability, etc. In this paper, we proposed to construct an S-box based on artificial bee colony optimization and chaotic map. The algorithm is designed to optimize an initial S-box to satisfy many properties. The simulation outcomes and comparison with recent proposals show that the proposed ABC optimization based algorithm performs reasonably well and construct S-box that exhibits higher security strength.

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References

  1. Menezes, A. J., Oorschot, P. C. V., & Vanstone, S. A. (1997). Handbook of applied cryptography. Boca Raton: CRC Press.

    MATH  Google Scholar 

  2. Stinson, D. R. (2005). Cryptography: Theory and practice. Boca Raton: CRC Press.

    MATH  Google Scholar 

  3. Schneier, B. (1996). Applied cryptography: Protocols algorithms and source code in C. New York: Wiley.

    MATH  Google Scholar 

  4. Knudsen, L. R., & Robshaw, M. (2011). The block cipher companion. Berlin: Springer.

    Book  MATH  Google Scholar 

  5. Ozkaynak, F., & Sirma, Y. (2013). Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dynamics, 74(3), 551–557.

    Article  MathSciNet  MATH  Google Scholar 

  6. Cui, L., & Cao, Y. (2007). A new S-box structure named Affine-Power-Affine. International Journal of Innovative Computing, Information and Control, 3(3), 751–759.

    Google Scholar 

  7. Hussain, I., & Shah, T. (2013). Literature survey on nonlinear components and chaotic nonlinear components of block ciphers. Nonlinear Dynamics, 74(4), 869–904.

    Article  MathSciNet  MATH  Google Scholar 

  8. Farah, T., Rhouma, R., & Belghith, S. (2017). A novel method for designing S-box based on chaotic map and teaching–learning-based optimization. Nonlinear Dynamics, 88(2), 1059–1074.

    Article  Google Scholar 

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

    Article  Google Scholar 

  10. Guesmi, R., Farah, M. A. B., Kachouri, A., & Samet, M. (2014). A novel design of Chaos based S-boxes using genetic algorithm techniques. In IEEE/ACS 11th international conference on computer systems and applications (AICCSA) (pp. 678–684).

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

    Article  MATH  Google Scholar 

  12. Yong, W., & Peng, L. (2012). An Improved method to obtaining S-box based on chaos and genetic algorithm. HKIE Transactions, 19(4), 53–58.

    Article  Google Scholar 

  13. Clark, J. A., Jacob, J. L., & Stepney, S. (2005). The design of S-boxes by simulated annealing. New Generation Computing, 23(3), 219–231.

    Article  MATH  Google Scholar 

  14. Millan, W. (1998). How to improve the nonlinearity of bijective S-boxes. In Australasian conference on information security and privacy, lecture notes in computer science (Vol. 1438, pp. 181–192).

  15. Fuller, J., Millan, W., & Dawson, E. (2005). Multi-objective optimisation of bijective S-boxes. New Generation Computing, 23(3), 201–218.

    Article  MATH  Google Scholar 

  16. Laskari, E. C., Meletiou, G. C., & Vrahatis, M. N. (2006). Utilizing evolutionary computation methods for the design of S-boxes. In International conference on computational intelligence and security (pp. 1299–1302).

  17. May, R. M. (1976). Simple mathematical models with very complicated dynamics. Nature, 261(5560), 459–467.

    Article  MATH  Google Scholar 

  18. Karaboga, D. (2005). An idea based on honey bee swarm for numerical optimization (Vol. 200). Technical report-tr06, Erciyes University, Faculty of Engineering, Department of Computer Engineering.

  19. Tereshko, V. (2000). Reaction–diffusion model of a honeybee colony’s foraging behaviour. In M. Schoenauer (Ed.), Parallel problem solving from nature VI (Vol. 1917, pp. 807–816)., Lecture notes in computer science Berlin: Springer.

    Chapter  Google Scholar 

  20. Karaboga, D., & Akay, B. (2009). A comparative study of artificial bee colony algorithm. Applied Mathematics and Computation, 214(1), 108–132.

    Article  MathSciNet  MATH  Google Scholar 

  21. Karaboga, D., Gorkemli, B., Ozturk, C., & Karaboga, N. (2014). A comprehensive survey: Artificial bee colony (ABC) algorithm and applications. Artificial Intelligence Review, 42(1), 21–57.

    Article  Google Scholar 

  22. Dawson, M. H., & Tavares, S. E. (1991). An expanded set of S-box design criteria based on information theory and its relation to differential-like attacks. Advances in Cryptology, Lecture Notes in Computer Science, 547, 352–367.

    Article  MathSciNet  MATH  Google Scholar 

  23. Braeken, A. (2006). Cryptographic properties of Boolean functions and S-boxes. Ph.D. thesis available at http://homes.esat.kuleuven.be/abraeken/thesisAn.pdf. Accessed 21 May 2017.

  24. Burnett, L. (2005). Heuristic optimization of boolean functions and substitution boxes for cryptography. Doctoral dissertation, Queensland University of Technology.

  25. Isa, H., Jamil, N., & Zaba, M. R. (2015). Improved S-box construction from binomial power functions. Malaysian Journal of Mathematical Sciences, 9(S), 21–35.

    MathSciNet  Google Scholar 

  26. Cusick, T. W., & Stanica, P. (2009). Cryptographic Boolean functions and applications. Amsterdam: Elsevier.

    MATH  Google Scholar 

  27. Ding, C., Xiao, G., & Shan, W. (1991). The stability theory of stream ciphers (Vol. 561)., LNCS Berlin: Springer.

    MATH  Google Scholar 

  28. Matsui, M. (1994). Linear cryptanalysis method for DES cipher. In Proceedings of EUROCRYPT’93, lecture notes in computer science (Vol. 765, pp. 386–397).

  29. Webster, A. F., & Tavares, S. E. (1986). On the design of S-boxes. Advances in Cryptology, Lecture Notes in Computer Science, 218, 523–534.

    Article  Google Scholar 

  30. Adams, C., & Tavares, S. (1990). The structured design of cryptographically good S-boxes. Journal of Cryptology, 3(1), 27–41.

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  32. Sarfraz, M., Hussain, I., & Ali, F. (2016). Construction of S-Box based on Mobius transformation and increasing its confusion creating ability through invertible function. International Journal of Computer Science and Information Security, 14(2), 187–18x.

    Google Scholar 

  33. Ahmad, M., Mittal, N., Garg, P., & Khan, M. M. (2016). Efficient cryptographic substitution box design using travelling salesman problem and chaos. Perspectives in Science, 8, 465–468.

    Article  Google Scholar 

  34. Bhattacharya, D., Bansal, N., Banaerji, A., & Chowdhury, D. R. (2007). A near optimal S-box design. In P. McDaniel & S. K. Gupta (Eds.) ICISS 2007, LNCS (Vol. 4812, pp. 77–90).

  35. Jamal, S. S., Shah, T., & Attaullah, A. (2017). A group action method for construction of strong substitution box. 3D Research, 8(2), 1–12.

    Article  Google Scholar 

  36. Khan, M., & Asghar, Z. (2017). A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation. Neural Computing and Applications. https://doi.org/10.1007/s00521-016-2511-5.

    Google Scholar 

  37. Khan, M., Shah, T., & Batool, S. I. (2016). Construction of S-box based on chaotic Boolean functions and its application in image encryption. Neural Computing and Applications, 27(3), 677–685.

    Article  Google Scholar 

  38. Khan, M., & Shah, T. (2015). A novel construction of substitution box with Zaslavskii chaotic map and symmetric group. Journal of Intelligent and Fuzzy Systems, 28(4), 1509–1517.

    MathSciNet  MATH  Google Scholar 

  39. Islam, F., & Liu, G. (2017). Designing S-box based on 4D-4wing hyperchaotic system. 3D Research, 8(1), 1–9.

    Article  Google Scholar 

  40. Belazi, A., & El-Latif, A. A. A. (2017). A simple yet efficient S-box method based on chaotic sine map. Optik-International Journal for Light and Electron Optics, 130, 1438–1444.

    Article  Google Scholar 

  41. Özkaynak, F., Çelik, V., & Özer, A. B. (2017). A new S-box construction method based on the fractional-order chaotic Chen system. Signal, Image and Video Processing, 11(4), 59–64.

    Article  Google Scholar 

  42. Lambić, D. (2017). A novel method of S-box design based on discrete chaotic map. Nonlinear Dynamics, 87(4), 2407–2413.

    Article  MathSciNet  Google Scholar 

  43. 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 Dynamics, 87(2), 1081–1094.

    Article  MATH  Google Scholar 

  44. Anees, A., & Ahmed, Z. (2015). A technique for designing substitution box based on van der pol oscillator. Wireless Personal Communications, 82(3), 1497–1503.

    Article  Google Scholar 

  45. Kazlauskas, K., Vaicekauskas, G., & Smaliukas, R. (2015). An algorithm for key-dependent S-box generation in block cipher system. Informatica, 26(1), 51–65.

    Article  Google Scholar 

  46. Majid, K., & Tariq, S. (2015). An efficient construction of substitution box with fractional chaotic system. Signal Image Video Processing, 9(6), 1335–1338.

    Article  Google Scholar 

  47. Liu, G., Yang, W., Liu, W., & Dai, Y. (2015). Designing S-boxes based on 3-D four-wing autonomous chaotic system. Nonlinear Dynamics, 82(4), 1867–1877.

    Article  MathSciNet  Google Scholar 

  48. Hongjun, L., Abdurahman, K., & Yujun, N. (2014). Chaos-based color image block encryption scheme using S-box. AEU-International Journal of Electronics and Communications, 68(7), 676–686.

    Article  Google Scholar 

  49. Gondal, M. A., Raheem, A., & Hussain, I. (2014). A scheme for obtaining secure S-boxes based on Chaotic Baker’s Map. 3D Research, 5(3), 1–8.

    Article  Google Scholar 

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Authors and Affiliations

  1. Department of Computer Engineering, Jamia Millia Islamia, New Delhi, 110025, India

    Musheer Ahmad & M. N. Doja

  2. Department of Computer Engineering, Aligarh Muslim University, Aligarh, 202002, India

    M. M. Sufyan Beg

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  1. Musheer Ahmad
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  2. M. N. Doja
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  3. M. M. Sufyan Beg
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Correspondence to Musheer Ahmad.

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Ahmad, M., Doja, M.N. & Beg, M.M.S. ABC Optimization Based Construction of Strong Substitution-Boxes. Wireless Pers Commun 101, 1715–1729 (2018). https://doi.org/10.1007/s11277-018-5787-1

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