Skip to main content
SpringerLink
Log in

A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation

  • Original Article
  • Published:
Neural Computing and Applications Aims and scope Submit manuscript

Abstract

In this communication, we present a technique to synthesize resilient nonlinear mechanisms for the construction of substitution box. The proposed nonlinear component assists in transforming the intelligible message or plaintext into an enciphered format by the use of Gingerbreadman chaotic map and S8 permutations. The proposed substitution box is sensitive to the initial conditions provided to the chaotic system, which are subsequently used as parameters in creating an instance. The simulation results show that the use of the proposed substitution box to image encryption scheme provides an efficient and secure way for real-time communications.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Fig. 1
Fig. 2
Fig. 3
Fig. 4

Similar content being viewed by others

References

  1. Adams C, Tavares S (1989) Good S-boxes are easy to find In: Advances in cryptology: Proceedings of Crypto’89, Santa Barbara, USA. Lecture Notes in Computer Science 435:612–615

  2. Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurc Chaos Appl Sci Eng 16(8):2129–2153

    Article  MathSciNet  MATH  Google Scholar 

  3. Amigo JM, Kocarev L, Szczapanski J (2007) Theory and practice of chaotic cryptography. Phys Lett A 336:211–216

    Article  MATH  Google Scholar 

  4. Bard GV (2009) Algebraic Cryptanalysis. Springer, Berlin

    Book  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  6. Chen G (2008) A novel heuristic method for obtaining S-boxes. Chaos Solitons Fractals 36:1028–1036

    Article  MathSciNet  MATH  Google Scholar 

  7. Chen G, Chen Y, Liao X (2007) An extended method for obtaining S-boxes based on 3-dimensional chaotic baker maps. Chaos Solitons Fractals 31:571–579

    Article  MathSciNet  MATH  Google Scholar 

  8. Cusick TW, Stanica P (2009) Cryptographic boolean functions and applications. Elsevier, Amsterdam

    MATH  Google Scholar 

  9. Devaney RL (1984) A piecewise linear model for the zones of instability of an area preserving map. Phys D 10:387–393

    Article  MathSciNet  MATH  Google Scholar 

  10. Devaney RL (1992) The Gingerbreadman. Algorithm 3:15–16

    Google Scholar 

  11. Khan M (2015) A novel image encryption scheme based on multi-parameters chaotic S-boxes. Nonlinear Dyn 82:527–533

    Article  Google Scholar 

  12. Khan M (2015) An image encryption by using Fourier series. J Vib Control 21:3450–3455

    Article  MathSciNet  Google Scholar 

  13. Khan M, Shah T (2015) A novel construction of substitution box with Zaslavskii chaotic map and symmetric group. J Intell Fuzzy Syst 28:1509–1517

    MathSciNet  MATH  Google Scholar 

  14. Khan M, Shah T (2015) An image encryption technique. Neural Comput Applic 26:1137–1148

    Article  Google Scholar 

  15. Khan M, Shah T (2016) Construction and applications of chaotic S-boxes in image encryption. Neural Comput Applic 27:677–685

    Article  Google Scholar 

  16. Khan M, Shah T, Batool SI (2016) A new implementations of chaotic S-boxes in CAPTCHA. SIViP 10:293–300

    Article  Google Scholar 

  17. Ikeda K (1979) Multiple-valued stationary state and its instability of the transmitted light by a ring cavity system. Opt Commun 30:257–261

    Article  Google Scholar 

  18. Jakimoski G, Kocarev L (2001) Chaos and cryptography: block encryption ciphers. IEEE Trans Circuits Syst I Fundam Theory Appl 48(2):163–169

    Article  MATH  Google Scholar 

  19. Jing-mei L, Bao-dian W, Xiang-guo C et al (2005) Cryptanalysis of Rijndael S-box and improvement. Appl Math Comput 170(2):958–975

    MathSciNet  Google Scholar 

  20. Khan M, Shah T (2013) An efficient construction of substitution box with fractional chaotic system. Signal Image Video Process. doi:10.1007/s11760-013-0577-4

    Google Scholar 

  21. Khan M, Shah T (2014) A construction of novel chaos base nonlinear component of block cipher. Nonlinear Dyn 76:377–382

    Article  MathSciNet  MATH  Google Scholar 

  22. Khan M, Shah T, Mahmood H et al (2012) A novel technique for the construction of strong S-boxes based on chaotic Lorenz systems. Nonlinear Dyn 70:2303–2311

    Article  MathSciNet  Google Scholar 

  23. Khan M, Shah T, Mahmood H, Gondal MA (2013) An efficient method for the construction of block cipher with multi-chaotic systems. Nonlinear Dyn 71(3):489–492

    Article  MathSciNet  Google Scholar 

  24. Khan M, Shah T, Mahmood H (2013) Gondal MA (2013b) An efficient technique for the construction of substitution box with chaotic partial differential equation. Nonlinear Dyn 73(2013):1795–1801

    Article  Google Scholar 

  25. Kuang Y (1993) Delay differential equations with applications in population dynamics. Academic, London

    MATH  Google Scholar 

  26. Özkaynak F, Özer AB (2010) A method for designing strong S-boxes based on chaotic Lorenz system. Phys Lett A 374:3733–3738

    Article  MATH  Google Scholar 

  27. Özkaynak F, Sırma Y (2013) Designing chaotic S-boxes based on time-delay chaotic system. Nonlinear Dyn. doi:10.1007/s11071-013-0987-4

    MathSciNet  MATH  Google Scholar 

  28. Prokhorow MD, Ponomarenko VI (2008) Encryption and de-cryption of information in chaotic communication systems governed by delay-differential equations. Chaos Solitons Fractals 35:871–877

    Article  Google Scholar 

  29. Sprott JC (2003) Chaos and time-series analysis. Oxford University Press, London

    MATH  Google Scholar 

  30. Sprott JC (2007) A simple chaotic delay differential equation. Phys Lett A 366:397–402

    Article  MathSciNet  MATH  Google Scholar 

  31. Sprott JC (2010) Elegant chaos algebraically simple chaotic flow. World Scientific, Singapore

    Book  MATH  Google Scholar 

  32. Tang G, Liao X (2005) A method for designing dynamical S-boxes based on discretized chaotic map. Chaos Solitons Fractals 23(5):1901–1909

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MATH  Google Scholar 

  34. Tang Y, Wang Z, Fang J (2010) Image encryption using chaotic coupled map lattices with time-varying delays. Commun Nonlinear Sci Numer Simul 15:2456–2468

    Article  MathSciNet  MATH  Google Scholar 

  35. Verhulst PF (1838) Notice sur la loi que la population poursuit dans son accroissement. Corresp Math Phys 10:113–121

    Google Scholar 

  36. Wang Y, Xie Q, Wu Y, et al. (2009) A software for S-box performance analysis and test. In: 2009 international conference on electronic commerce and business intelligence, Beijing, China, pp 125–128

  37. Webster A, Tavares S (1986) On the design of S-boxes. In: Advances in cryptology: proceedings of Crypto’85, Santa Barbara, USA. Lecture Notes in Computer Science 218:523–534

  38. Youssef AM, Tavares SE (2005) Affine equivalence in the AES round function. Discrete Appl Math 148(2):161–170

    Article  MathSciNet  MATH  Google Scholar 

  39. Youssef AM, Tavares SE, Gong G (2006) On some probabilistic approximations for AES-like S-boxes. Discrete Math 306(16):2016–2020

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Institute of Space Technology, Islamabad, 44000, Pakistan

    Majid Khan & Zeeshan Asghar

Authors
  1. Majid Khan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Zeeshan Asghar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Zeeshan Asghar.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Khan, M., Asghar, Z. A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation. Neural Comput & Applic 29, 993–999 (2018). https://doi.org/10.1007/s00521-016-2511-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00521-016-2511-5

Keywords

Search

Navigation