[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Novel Quasigroup Substitution Scheme for Chaos Based Image Encryption

Journal of Environmental Accounting and Management 7(4) (2018) 393--412 | DOI:10.5890/JAND.2018.12.007

Vinod Patidar, N. K. Pareek, G. Purohit

Department of Physics, Sir Padampat Singhania University, Bhatewar, Udaipur 313601, Rajasthan, India

Download Full Text PDF

 

Abstract

A During last two decades, there has been a prolific growth in the chaos based image encryption algorithms. Up to an extent these algorithms have been able to provide an alternative to exchange large media files (images and videos) over the networks in a secure way. However, there have been some issues with the implementation of chaos based image ciphers in practice. One of them is reduced/small key space due to the fact that chaotic behavior is only observed for certain range of system parameters/initial conditions of the chaotic system used in such algorithms. To overcome this difficulty, we propose a simple, efficient and robust image encryption algorithm based on combined applications of quasigroups and chaotic standard map. The proposed image cipher is based on the Shannon’s popular substitution-diffusion architecture where a quasigroup of order 256 and chaotic standard map have been used for the substitution and permutation of image pixels respectively. Due to the introduction of quasigroup as part of the secret key along with the parameter and initial conditions of the chaotic standard map, the key space has been increased significantly. The proposed image cipher is very fast due to the fact that the substitution based on the quasigroup operations is very simple and can be executed easily through the lookup table operations on Latin squares (which are Cayley operation tables of quasigroups) and the permutation is performed row-by-row as well as column-by-column using the pseudo random number sequences generated through the chaotic standard map. The security and performance have been analyzed through the histograms, correlation coefficients, information entropy, key sensitivity analysis, differential analysis, key space analysis etc. and the results prove the efficiency and robustness of the proposed image cipher against the possible security threats.

References

  1. [1]  Fridrich, J. (1998), Symmetric ciphers based on two-dimensional chaotic maps, Int. J. Bifurc. Chaos, 8(6), 1259-1284.
  2. [2]  Baptista, M. (1998), Cryptography with chaos, Phys. Lett. A, 240(1-2) 50-54.
  3. [3]  Mao, Y., Chen, G., and Lian, S. (2004), A novel fast image encryption scheme based on 3D chaotic Baker maps, Int. J. Bifurc. Chaos, 14(10), 3613-3624.
  4. [4]  Chen, G., Mao, Y., and Chui, C. (2004), A symmetric image encryption scheme based on 3d chaotic cat maps, Chaos Solitons Fractals, 21, 749-761.
  5. [5]  Zhang, L., Liao, X., and Wang, X. (2005), An image encryption approach based on chaotic maps, Chaos, Solitons & Fractals, 24(3), 759-765.
  6. [6]  Pareek, N.K., Patidar, V., and Sud, K.K. (2006), Image encryption using chaotic logistic map, Image and Vision Computing, 24, 926-934.
  7. [7]  Pisarchik, A.N., and Zanin, M. (2008), Image encryption with chaotically coupled chaotic maps, Physica D, 237(20), 2638-2648.
  8. [8]  Patidar, V., Pareek, N.K., and Sud, K.K. (2009), A new substitution-diffusion based image cipher using chaotic standard and logistic maps, Comm. Nonl. Sc. Num. Sim., 14, 3056-3075.
  9. [9]  Alvarez, G. and Li, S. (2006), Some basic cryptographic requirements for chaos-based cryptosystems, Int. J. Bifurc. Chaos, 16(8), 2129-2151.
  10. [10]  Kelber, K. and Schwarz, W. (2007), Some design rules for chaos-based encryption systems, Int. J. Bifurc. Chaos, 17(10), 3703-3707.
  11. [11]  Rhouma, R., Solak, E., and Belghith, S. (2010), Cryptanalysis of a new substitutio-diffusion based image cipher, Commun. Nonlinear Sci. Numer. Simulat, 15(7), 1887-1892.
  12. [12]  Solak, E., Çokal, C., Yildiz, O.T., and Biyikoglu, T. (2010), Cryptanalysis of Fridrich's chaotic image encryption, Int. J. Bifurc. Chaos, 20(5), 1405-1413.
  13. [13]  Özkaynak, F. and Özer, A.B. (2016), Cryptanalysis of a new image encryption algorithm based on chaos, Optik - International Journal for Light and Electron Optics, 127(13), 5190-5192.
  14. [14]  Patidar, V., Pareek, N.K., Purohit, G., and Sud, K.K. (2011), A robust and secure chaotic standard map based pseudorandom permutation substitution scheme for image encryption, Optics Communications, 284, 4331-4339.
  15. [15]  Wang, X. and Xu, D. (2015), A novel image encryption scheme using chaos and Longton's ant cellular automaton, Nonlinear Dynamics, 79(4), 2449-2456.
  16. [16]  Wu, X., Wang, D., Kurths, J., and Kan, H. (2016), A novel lossless color image encryption scheme using 2D DWT and 6D hyperchaotic system, Information Sciences, 349-350, 137-153.
  17. [17]  Abd-El-Hafiz, S.K., Abd-El-Haleem, S.H., and Radwan, A.G. (2016), Novel permutation measures for image encryption algorithms, Optics and Lasers in Engineering, 85, 72-83.
  18. [18]  Farajallah, M. and Deforges, O. (2016), Fast and secure chaos-based cryptosystem for images, Int. J. Bifurc. Chaos, 26(2), 1650021.
  19. [19]  Schneier, B. (1996) Applied cryptography: protocols algorithms and source code in C, (Wiley New York)
  20. [20]  Dénes, J. and Keedwell, A.D. (1992), A new authentication scheme based on Latin squares, Discrete Mathematics, 106-107, 157-161.
  21. [21]  Keedwell, A.D. (1999), Crossed inverse quasigroups with long inverse cycles and applications to cryptography, Australasian Journal of Combinatorics, 20, 241-250.
  22. [22]  Kośielny, C. (1996), A method of constructing quasigroup-based stream-ciphers, Applied Mathematics and Computer Science, 6, 109-121.
  23. [23]  Kośielny, C. and Mullen G.L. (1999), A quasigroup-based public-key cryptosystem, International Journal of Applied Mathematics and Computer Science, 9(4), 955-963.
  24. [24]  Golomb, S., Welch, L., and Dénes, J. (2001), Encryption system based on crossed inverse quasigroups, (US Patent No. WO0191368)
  25. [25]  Gligoroski, D. (2004), Stream cipher based on quasigroup string transformations, arXiv: cs.CR/0403043.
  26. [26]  Gligoroski, D. (2005), Candidate One-Way Functions and One-Way Permutations Based on Quasigroup String Transformations, arXiv:cs.CR/0510018.
  27. [27]  Markovski, S., Gligoroski, D., and Kocarev, L.J. (2005), Unbiased random sequences from quasigroup string transformations, in H. Gilbert, and H. Handschuh, eds., Lecture Notes in Computer Science, 3557, pp.163-180 (Springer).
  28. [28]  Satti, M. and Kak, S. (2009), Multilevel Indexed Quasigroup Encryption for Data and Speech, IEEE Transactions on Broadcasting, 55, 270-281.
  29. [29]  Battey, M. and Parakh, A. (2013), An efficient quasigroup block cipher, Wireless Personal Communications, 73, 63-76.
  30. [30]  Dichtl, M. and Böffgen, P. (2012), Breaking Another Quasigroup-Based Cryptographic Scheme, Cryptology ePrint Archive Report 2012/661, available online at http://eprint.iacr.org/2012/661
  31. [31]  Shcherbacov, V.A. (2012), Quasigroup based crypto-algorithms, arXiv: math:GR/1201.3016v1.
  32. [32]  Mileva, A. (2014), New Developments in quasigroup-based cryptography, in Sattar, B., Sadkhan, A.M., Abbas, A.N. Eds. Multidisciplinary Perspectives in Cryptology and Information Security, pp. 286-317 (IGI Global)
  33. [33]  Pflugfelder, H.O. (1991) Quasigroups and Loops: Introduction, (Quasigroups and Loops: Introduction)
  34. [34]  Dénes, J. and Keedwell, A.D. (1991) Latin squares: New developments in the theory Annals of Discrete Mathematics, 46, (North-Holand: Elsevier)
  35. [35]  Lint, V. and Wilson, A. (1992) A Course in Combinatorics (Cambridge University Press)
  36. [36]  Jacobson, M.T. and Matthews, P. (1996), Generating uniformly distributed random Latin squares, J. Combinat. Desig., 4, 405-437.
  37. [37]  Shannon, C.E. (1949), Communication theory of secrecy systems, Bell System Technical Journal, 28, 656-715.
  38. [38]  Kośielny, C. (2002), Generating quasigroups for cryptographic applications, International Journal of Applied Mathematics and Computer Science, 12, 559-569.
  39. [39]  Mihajloska, H., Yalcin, T., and Gligoroski, D. (2013), How lightweight is the hardware Implementation of Quasigroup S-boxes, in S. Markovski and M. Gušev, eds., Advances in Intelligent Systems and Computing- ICT Innovations, pp 121-127 (Springer)

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates