Skip to main content
SpringerLink
Log in

On security of image ciphers based on logic circuits and chaotic permutations

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

Abstract

This paper introduces a cryptanalysis of image encryption techniques that are using chaotic scrambling and logic gates/circuits. Chaotic scrambling, as well as general permutations are considered together with reversible and irreversible gates, including XOR, Toffoli and Fredkin gates. We also investigate ciphers based on chaotic permutations and balanced logic circuits. Except for the implementation of Fredkin’s gate, these ciphers are insecure against chosen-plaintext attacks, no matter whether a permutation is applied globally on the image or via a block-by-block basis. We introduce a new cipher based on chaotic permutations, logic circuits and randomized Fourier-type transforms. The strength of the new cipher is statistically verified with standard statistical encryption measures.

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
Fig. 5
Fig. 6
Fig. 7
Fig. 8

Similar content being viewed by others

References

  1. Amigó J, Kocarev L, Szczepanski J (2007) Theory and practice of chaotic cryptography. Phys Lett A 366(3):211–216

    Article  MATH  Google Scholar 

  2. Annaby M, Rushdi M, Nehary E (2016) Image encryption via discrete fractional Fourier-type transforms generated by random matrices. Signal Process: Image Commun 49:25–46

    Google Scholar 

  3. Benjamini I, Schramm O, Wilson DB (2005) Balanced boolean functions that can be evaluated so that every input bit is unlikely to be read. In: Proceedings of the thirty-seventh annual ACM symposium on Theory of computing. ACM, pp 244–250

  4. Candan C, Kutay M, Ozaktas H (2000) The discrete fractional Fourier transform. IEEE Trans Signal Process 48(5):1329–1337

    Article  MathSciNet  MATH  Google Scholar 

  5. De Vos A (2011) Reversible computing: fundamentals, quantum computing, and applications. Wiley, Weinheim

    MATH  Google Scholar 

  6. Devaney R (2003) An introduction to chaotic dynamical systems. Westview Press, Cambridge

    MATH  Google Scholar 

  7. Gupta P, Agrawal A, Jha NK (2006) An algorithm for synthesis of reversible logic circuits. IEEE Trans Comput-Aided Des Integr Circ Syst 25(11):2317–2330

    Article  Google Scholar 

  8. Hennelly B, Sheridan JT (2003) Optical image encryption by random shifting in fractional Fourier domains. Opt Lett 28(4):269–271

    Article  Google Scholar 

  9. Hsue WL, Chang WC (2015) Real discrete fractional Fourier, Hartley, generalized Fourier and generalized Hsartley transforms with many parameters. IEEE Trans Circ Syst I: Reg Pap 62(10):2594–2605

    Google Scholar 

  10. Jolfaei A, Wu XW, Muthukkumarasamy V (2016) On the security of permutation-only image encryption schemes. IEEE Trans Inf Forensic Secur 11 (2):235–246

    Article  Google Scholar 

  11. Kanso A, Smaoui N (2009) Logistic chaotic maps for binary numbers generations. Chaos, Solitons Fractals 40(5):2557–2568

    Article  MATH  Google Scholar 

  12. Kocarev L (2001) Chaos-based cryptography: a brief overview. IEEE Circ Syst Mag 1(3):6–21

    Article  Google Scholar 

  13. Li C, Li S, Alvarez G, Chen G, Lo KT (2007) Cryptanalysis of two chaotic encryption schemes based on circular bit shift and XOR operations. Phys Lett A 369(1):23–30

    Article  MATH  Google Scholar 

  14. Li S, Li C, Chen G, Bourbakis NG, Lo KT (2008) A general quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal Process: Image Commun 23(3):212–223

    Google Scholar 

  15. Li C, Lo KT (2011) Optimal quantitative cryptanalysis of permutation-only multimedia ciphers against plaintext attacks. Signal process 91(4):949–954

    Article  MATH  Google Scholar 

  16. Mao Y, Chen G, Lian S (2004) A novel fast image encryption scheme based on 3D chaotic baker maps. Int J Bifurcation Chaos 14(10):3613–3624

    Article  MathSciNet  MATH  Google Scholar 

  17. Mao Y, Chen G (2005) Chaos-based image encryption. In: Handbook of geometric computing. Springer, Berlin, pp 231–265

  18. Morrison M (2014) Theory, synthesis, and application of adiabatic and reversible logic circuits for security applications. In: 2014 IEEE Computer Society Annual Symposium on VLSI. IEEE, pp 252–255

  19. Pei SC, Yeh MH (1997) Improved discrete fractional Fourier transform. Opt Lett 22(14):1047–1049

    Article  Google Scholar 

  20. Pei SC, Hsue WL (2006) The multiple-parameter discrete fractional Fourier transform. IEEE Signal Process Lett 13(6):329–332

    Article  Google Scholar 

  21. Sam IS, Devaraj P, Bhuvaneswaran RS (2011) Chaos based image encryption scheme based on enhanced logistic map. In: International Conference on Distributed Computing and Internet Technology. Springer, pp 290–300

  22. Shannon CE (2001) A mathematical theory of communication. ACM SIGMOBILE Mob Comput Commun Rev 5(1):3–55

    Article  MathSciNet  Google Scholar 

  23. Shende VV, Prasad AK, Markov IL, Hayes JP (2003) Synthesis of reversible logic circuits. IEEE Trans Comput-Aided Des Integr Circ Syst 22(6):710–722

    Article  Google Scholar 

  24. Tang Z, Wang F, Zhang X (2017) Image encryption based on random projection partition and chaotic system. Multimed Tools Appl 76(6):82578283

    Article  Google Scholar 

  25. Thapliyal H, Zwolinski M (2006) Reversible logic to cryptographic hardware: A new paradigm. In: 2006 49th IEEE International Midwest Symposium on Circuits and Systems, vol 1. IEEE, pp 342–346

  26. Wang Y, Liao X, Xiang T, Wong KW, Yang D (2007) Cryptanalysis and improvement on a block cryptosystem based on iteration a chaotic map. Phys Lett A 363(4):277–281

    Article  MATH  Google Scholar 

  27. Wong KW (2009) Image encryption using chaotic maps. In: Intelligent computing based on chaos. Springer, Berlin, pp 333–354

  28. Wu Y, Noonan JP, Agaian S (2011) NPCR and UACI color image encryption using randomness tests for image encryption. Cyber journals: multidisciplinary journals in science and technology. J Select Areas Telecommun (JSAT), April Edition:31–38

  29. Xiang T, Liao X, Tang G, Chen Y, Wong Kw (2006) A novel block cryptosystem based on iterating a chaotic map. Phys Lett A 349(1):109–115

    Article  MATH  Google Scholar 

  30. Xu L, Gou X, Li Z, Li J (2017) A novel chaotic image encryption algorithm using block scrambling and dynamic index based diffusion. Opt Lasers Eng 91:41–52

    Article  Google Scholar 

  31. Ye G (2010) Image scrambling encryption algorithm of pixel bit based on chaos map. Pattern Recogn Lett 31(5):347–354

    Article  Google Scholar 

  32. Yuan HM, Gong LH, Wang J (2017) A new image cryptosystem based on 2D hyper-chaotic system. Multimedia Tools and Applications 76(6):80878108

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, Cairo University, Giza, 12613, Egypt

    Mahmoud H. Annaby & Hassan Ayad

  2. Department of Biomedical Engineering and Systems, Faculty of Engineering, Cairo University, Giza, 12613, Egypt

    Muhammad A. Rushdi

Authors
  1. Mahmoud H. Annaby
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Hassan Ayad
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Muhammad A. Rushdi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mahmoud H. Annaby.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Annaby, M.H., Ayad, H. & Rushdi, M.A. On security of image ciphers based on logic circuits and chaotic permutations. Multimed Tools Appl 77, 20455–20476 (2018). https://doi.org/10.1007/s11042-017-5439-6

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-017-5439-6

Keywords

Search

Navigation