Skip to main content

Advertisement

Springer Nature Link
Log in

Modified advanced encryption standard (MAES) based on non-associative inverse property loop

  • Published:
Multimedia Tools and Applications Aims and scope Submit manuscript

Abstract

In this paper, a cryptographic encryption standard is proposed whose model is same as presented in Rijndael Algorithm by Joan Daemen and Vincent Rijmen. The modification lies in the design of the Cipher, we have used inverse property (IP) loop instead of Extended Binary Galois Field (GF). The proposed mathematical structure is superior to GF in terms of complexity and has the ability to create arbitrary randomness due to a larger key space. Moreover, IP loop are non-isomorphic and have more than one Cayley table representation as compared to GF. This in result confirms the resistance against cryptanalytic attacks specifically on mathematical structures. The complete description of S-box, encryption and decryption of this cryptographic scheme is measured and evaluated critically to substantiate its multimedia applications.

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

Access this article

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

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

Data availability

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

References

  1. Abdullah A, Noor M, Majid K, Iqtadar H (2020) An encryption scheme based on discrete quantum map and continuous chaotic system. Int J Theor Phys 59(4):1227–1240

    Article  MathSciNet  MATH  Google Scholar 

  2. Adnan J, Tariq S, Attaullah (2020) A color image privacy scheme established on nonlinear system of coupled differential equations. Multimed Tools Appl 79:32487–32501

  3. Ahmad M, Doja MN, Beg SMM (2018) "Security analysis and enhancements of an image cryptosystem based on hyper chaotic system," Journal of King Saud University, Comput Inf Sci

  4. Ali A, Slaney J (2008) Counting loops with the inverse property. Quasigroups Related Struct 16:13–16

    MathSciNet  MATH  Google Scholar 

  5. Alligood KT, Sauer TD, Yorke JA (1996) Chaos an introduction to dynamical systems. Springer-verlag, New York

    Book  MATH  Google Scholar 

  6. Asif M, Shah T (2019) BCH codes with computational approach and its applications in image encryption. J Intell Fuzzy Syst 37(3):3925–3939

    Article  Google Scholar 

  7. Attaullah SJ, Shah T (2018) "A novel scheme for image encryption using substitution box and chaotic system.," Nonlinear Dyn, vol. 91

  8. Attaullah AJ, Shah T (2019) Cryptosystem techniques based on the improved Chebyshev map: an application in image encryption. Multimed Tools Appl 78:31467–31484

    Article  Google Scholar 

  9. Attaullah S, Jamal S, Shah T (2017) A novel construction of substitution box using a combination of chaotic maps with improved chaotic range. Nonlinear Dyn 88(4):2757–2769

    Article  Google Scholar 

  10. Attaullah S, Jamal S, Shah T (2018) A novel scheme for image encryption using substitution box and chaotic system. Nonlinear Dyn 91(1):359–370

  11. De Canniere, C (2005) "Triple-DES," Encyclopedia of cryptography and security, triple-DES. https://doi.org/10.1007/0-387-23483-7_437

  12. Chai X, Chen Y, Broyde L (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213

    Article  Google Scholar 

  13. Cui L, Cao Y (2007) A new S-box structure named affine power-affine. Int J Innov Comput Inf Control 3(3):45–53

    Google Scholar 

  14. Daemen J, Rijmen V (2002) The design of Rijndael-AES: the advanced encryption standard, Springer

  15. Hussain I, Shah T, Muhammad Asif G, Khan WA (2011) Costruction of cryptographically strong 8*8 S-boxes. World Appl Sci J 13(11):2389–2395

    Google Scholar 

  16. Hussain I, Shah T, Gondal MA, Mahmood H (2012) Generalized majority logic criterion to analyze the statistical strength of S-boxes. Z Naturforsch A 67a:282–288

    Article  Google Scholar 

  17. Hussain S, Jamal SS, Shah T, Hussain I (2020) A power associative loop structure for the construction of non-linear component of block cipher. IEEE Access, pp 123492–123506

  18. Jahangir S, Shah T (2020) "Designing S-boxes triplet over a finite chain ring and its application in RGB image encryption.," Multimed Tools Appl, no. 79, p. 26885–26911

  19. Jamal SS, Shah T, Attaullah (2017) "A group action method for construction of strong substituion box," 3D Research, vol. 8, no. 2

  20. Javeed A, Shah T, Attaullah (2020) Lightweight secure image encryption scheme based on chaotic differential equation. Chin J Phys. https://doi.org/10.1016/j.cjph.2020.04.008

  21. Javeed A, Shah T, Attaullah (2020) Design of an S-box using Rabinovich-Fabrikant system of differential equations perceiving third order nonlinearity. Multimed Tools Appl 79:6649–6660

    Article  Google Scholar 

  22. Javeed A, Shah T, Attaullah (2020) "Construction of non-linear component of block cipher by means of chaotic dynamical system and symmetric group," Wireless Personal Commun, pp. 1–14

  23. Kaur M, Singh D, Kumar V, Gupta BB, El-Latif AAA (2021) Secure and energy efficient-based E-health care framework for green internet of things. IEEE Trans Green Commun Netw 5(3):1223–1231

  24. Khan M, Shah T (2014) A novel image encryption technique based on Henon chaotic map and S8 symmetric group. Neural Comput 25:1717–1722

  25. Kocarev L (2001) Chaos-based cryptography: a brief overview. IEEE Circut Syst 1:6–21

    Article  Google Scholar 

  26. Lambic D (2020) A new discrete-space chaotic map based on the multiplication of integer numbers and its application in S-box design. Nonlinear Dyn. https://doi.org/10.1007/s11071-020-05503-y

  27. Li X, Wang L, Yan Y, Liu P (2016) An improvement color image encryption algorithm based on DNA operations and real and complex chaotic systems. Opt-Int J Light Electron 127(5):2558–2565

    Article  Google Scholar 

  28. Liu H, Kadir A, Xu C (2020) Cryptanalysis and constructing S-Box based on chaotic map and backtracking, vol. 376

  29. Majid K, Zeeshan A (2018) A novel construction of substitution box for image encryption applications with Gingerbreadman chaotic map and S8 permutation. Neural Comput & Applic 29:993–999

    Article  Google Scholar 

  30. Meshram C, Obaidat M, Meshram S (2018) "Chebyshev chaotic map-based ID-based cryptographic model using subtree and fuzzy-entity data sharing for public key cryptography,," Secur Priv, p. 1:e12

  31. Naseer Y, Shah T, Attaullah, Javeed A (2020) Advance image encryption technique utilizing compression, dynamical system and S-boxes. Math Comput Simul178:207–217

  32. Naseer Y, Shah D, Shah T (2018) A Novel Approach to improve multimedia security utilizing 3D Mixed Chaotic map. Microprocess Microsyst 65. https://doi.org/10.1016/j.micpro.2018.12.003

  33. Naseer Y, Shah T, Sadam H, Asif A (2019) Steps towards redesigning cryptosystems by a non-associative algebra of IP-loops. Wirel Pers Commun 108:1379–1392

  34. Paar C, Pelzl J (2010) Understanding cryptography: a textbook for students and practitioners. Springer-Verlag, New York

    Book  MATH  Google Scholar 

  35. Schneier B (1994) The blowfish encryption algorithm. Dr Dobb’s J 19(4):38–40

    Google Scholar 

  36. Shah T, Qamar A, Hussain I (2013) Substitution box on a maximal cyclic subgroup of units of a Galois ring. Zeitschrift fur Natureforschung A 68:567–572

    Article  Google Scholar 

  37. Shah T, Ali A, Khan M et al (2020) Galois Ring GR(23,8) Dependent 24×24 S-Box Design: An RGB Image Encryption Application. Wireless Pers Commun 113:1201–1224

    Article  Google Scholar 

  38. Shannon CE (1948) A mathematical theory of communication. In the Bell Syst Tech J 27(3):379–423

    Article  MathSciNet  MATH  Google Scholar 

  39. Si Y, Liu H, Chen Y (2021) "Constructing keyed strong S-Box using an enhanced quadratic map.," Int J Bifurcation Chaos, vol. 31, no. 10

  40. Tian Y, Lu Z (2017) "Chaotic S-box: intertwining logistic map and bacterial foraging optimization," Math Problems Eng 2017

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Quaid-i-Azam University, Islamabad, Pakistan

    Sadam Hussain, Tariq Shah & Adnan Javeed

  2. Government Associate College Daultala, Rawalpindi, Pakistan

    Adnan Javeed

Authors
  1. Sadam Hussain
    View author publications

    You can also search for this author inPubMed Google Scholar

  2. Tariq Shah
    View author publications

    You can also search for this author inPubMed Google Scholar

  3. Adnan Javeed
    View author publications

    You can also search for this author inPubMed Google Scholar

Corresponding author

Correspondence to Adnan Javeed.

Ethics declarations

Conflict of interests

The authors declare that they have no conflict of interest.

Additional information

Publisher’s note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Hussain, S., Shah, T. & Javeed, A. Modified advanced encryption standard (MAES) based on non-associative inverse property loop. Multimed Tools Appl 82, 16237–16256 (2023). https://doi.org/10.1007/s11042-022-14064-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-022-14064-8

Keywords