Image encryption based on modified Henon map using hybrid chaotic shift transform

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Abstract

In this paper, a new two dimensional modified Henon map (2D-MHM) which is derived from Henon map is proposed. Its chaotic performance is analyzed through bifurcation diagram, Lyapunov exponent spectrum and Lyapunov dimension. The map has broad chaotic regime over an extensive range of system parameters, maximum Lyapunov exponent and better chaotic performance when compared to existing chaotic maps. Further, a novel image cryptosystem is proposed based on 2D-MHM and sine map. The algorithm employs confusion and diffusion operations in consecutive manner which is different from traditional chaos based cryptosystems. Hybrid chaotic shift transform (HCST) is introduced to perform confusion operation which is controlled by 2D-MHM. The principle of diffusion is achieved by using chaotic matrix generated from sine map and exclusive or (XOR) operation. Extensive simulation results and performance analysis demonstrate that the proposed image cryptosystem is able to resist various cryptanalytic attacks. Furthermore, the comparison results reveal that the algorithm outperforms traditional and existing encryption schemes. The proposed algorithm is also applicable for speech signals and data encryption of other multimedia.

Keywords

Chaos Confusion Diffusion 2D-modified Henon map Hybrid chaotic shift transform 

List of abbreviations

2D-MHM

Two dimensional modified Henon map

HCST

Hybrid chaotic shift transform

XOR

Exclusive or

LFSR

Linear feedback shift register

AES

Advanced encryption standard

DES

Data encryption standard

T-DES

Triple DES

1D

One dimensional

HD

Higher dimension

HM

Henon map

SM

Sine map

LE

Lyapunov exponent

LD

Lyapunov dimension

NPCR

Number of pixels change rate;

UACI

Unified average changing intensity

UIQ

Unified image quality index

SSIM

Structural similarity index measure

PSNR

Peak signal to noise ratio

References

  1. 1.
    Alligood KT, Sauer TD, Yorke JA (1997) Chaos: an introduction to dynamic systems. Textbooks in Mathematical Sciences Springer, New YorkCrossRefMATHGoogle Scholar
  2. 2.
    Alvarez G, Li S (2006) Some basic cryptographic requirements for chaos-based cryptosystems. Int J Bifurcat Chaos 16(8):2129–2151MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Bakhache B, Ghazal JM, El Assad S (2014) Improvement of the security of zigbee by a new chaotic algorithm. IEEE Syst J 8(4):1024–1033CrossRefGoogle Scholar
  4. 4.
    Boriga R, Dsclescu AC, Diaconu AV (2014) A new one-dimensional chaotic map and its use in a novel real-time image encryption scheme. Adv in Mult Article ID 409586Google Scholar
  5. 5.
    Chen JX, Zhu ZL, Fu C, Yu H, Zhang LB (2015) A fast chaos-based image encryption scheme with a dynamic state variables selection mechanism. Commun Nonlinear Sci Numer Simul 20(3):846–860CrossRefGoogle Scholar
  6. 6.
    El-Latif AAA, Li L, Zhang T et al (2012) Digital image encryption scheme based on multiple chaotic systems. Sens Imaging 13(2):67–88CrossRefGoogle Scholar
  7. 7.
    Elkamchouchi HM, Makar MA (2005) Measuring encryption quality for bitmap images encrypted with rijndael and kamkar block ciphers [C]. In: 2005 National conference on IEEE radio science (NRSC), pp 277–284Google Scholar
  8. 8.
    Enayatifar R, Sadaei HJ, Abdullah AH, Lee M, Isnin If (2015) A novel chaotic based image encryption using a hybrid model of deoxyribonucleic acid and cellular automata. Opt Laser Eng 71:33–41CrossRefGoogle Scholar
  9. 9.
    Faragallah OS (2011) Digital image encryption based on the RC5 block cipher algorithm. Sens Imaging 12(3):73–94CrossRefGoogle Scholar
  10. 10.
    Fridrich J (1998) Symmetric ciphers based on two-dimensional chaotic maps. Int J Bifurcation Chaos 8:1259–1284MathSciNetCrossRefMATHGoogle Scholar
  11. 11.
    Galizzi GE, Cuadrado-Laborde C (2015) Joint transform correlator optical encryption system: extensions of the recorded encrypted signal and its inverse Fourier transform. Opt Commun 353:76–82CrossRefGoogle Scholar
  12. 12.
    Gallas JA (1993) Structure of the parameter space of the Henon map. Phys Rev Lett 70(18):2714CrossRefGoogle Scholar
  13. 13.
    Habutsu T, Nishio Y, Sasase I, Mori S (1991) A secret key cryptosystem by iterating a chaotic map. In: Davies D (ed) Advances in cryptology - EUROCRYPT’91 lecture notes in computer science, vol 547. Springer, Berlin, pp 127–140Google Scholar
  14. 14.
    Hanchinamani G, Kulkarni L (2015) An efficient image encryption scheme based on a Peter De Jong chaotic map and a RC4 stream cipher. 3D Res 6(3):1–15CrossRefGoogle Scholar
  15. 15.
    Henon M (1976) A two-dimensional mapping with a strange attractor. In: The theory of chaotic attractors. Springer, New York, pp 94–102Google Scholar
  16. 16.
    Hu T, Liu Y, Gong LH et al (2017) Chaotic image cryptosystem using DNA deletion and DNA insertion. Signal Process 134:234–243CrossRefGoogle Scholar
  17. 17.
    Hua Z, Zhou Y, Chen CP (2013) A new series-wound framework for generating 1D chaotic maps [C]. In: 2013 International conference on IEEE digital signal processing and signal processing education meeting (DSP/SPE), pp 118–123Google Scholar
  18. 18.
    Huang CK, Liao CW, Hsu SL, Jeng YC (2013) Implementation of gray image encryption with pixel shuffling and gray-level encryption by single chaotic system. Telecommun Syst 52(2):1–9Google Scholar
  19. 19.
    Kanafchian M, Fathi-Vajargah B (2017) A novel image encryption scheme based on clifford attractor and noisy logistic map for secure transferring images in navy. Int J e-Navi Maritime Econ 6:53–63Google Scholar
  20. 20.
    Kocarev L (2001) Chaos-based cryptography: a brief overview. IEEE Circuits Syst Mag 1(3):6–21MathSciNetCrossRefGoogle Scholar
  21. 21.
    Kokkonis G, Psannis KE, Roumeliotis M, Schonfeld D (2017) Real-time wireless multisensory smart surveillance with 3D-HEVC streams for internet-of-things (IoT). J Supercomput 73(3):1044–1062CrossRefGoogle Scholar
  22. 22.
    Li C, Liu Y, Zhang LY, Chen MZ (2013) Breaking a chaotic image encryption algorithm based on modulo addition and XOR operation. Int J Bifurcat Chaos 23(4):1350075MathSciNetCrossRefMATHGoogle Scholar
  23. 23.
    Liu W, Sun K, Zhu C (2016) A fast image encryption algorithm based on chaotic map. Opt Lasers Eng 84:26–36CrossRefGoogle Scholar
  24. 24.
    Liu H, Kadir A, Sun X (2017) Chaos-based fast colour image encryption scheme with true random number keys from environmental noise. IET Image Process 11(5):324–332CrossRefGoogle Scholar
  25. 25.
    Machkour M, Saaidi A, Benmaati ML (2015) A novel image encryption algorithm based on the two-dimensional logistic map and the latin square image cipher. 3D Res 6(4):36CrossRefGoogle Scholar
  26. 26.
    Mandal MK, Banik GD, Chattopadhyay D, Nandi D (2012) An image encryption process based on chaotic logistic map. IETE Tech Rev 29(5):395–404CrossRefGoogle Scholar
  27. 27.
    Matthews R (1989) On the derivation of a chaotic encryption algorithm. Cryptologia 13(1):29–42MathSciNetCrossRefGoogle Scholar
  28. 28.
    Mehra I, Nishchal NK (2015) Optical asymmetric image encryption using gyrator wavelet transform. Opt Commun 354:344–352CrossRefGoogle Scholar
  29. 29.
    Memos VA, Psannis KE, Ishibashi Y, Kim BG, Gupta BB (2017) An efficient algorithm for media-based surveillance system (EAMSuS) in IoT smart city framework. Future Gener Comput SystGoogle Scholar
  30. 30.
    Pareek NK (2012) Design and analysis of a novel digital image encryption scheme. Int J Netw Secur Appl 4(2):95–108Google Scholar
  31. 31.
    Schneier B (1996) Applied cryptography, protocols, algorithms and source code in C. Wiley, New YorkMATHGoogle Scholar
  32. 32.
    Shannon CE (1949) Communication theory of secrecy systems. Bell Labs Techn J 28(4):656–715MathSciNetCrossRefMATHGoogle Scholar
  33. 33.
    Sheela SJ, Suresh KV, Tandur D (2016) Performance evaluation of modified Henon map in image encryption. In: Ray I, Gaur M, Conti M, Sanghi D, Kamakoti V (eds) Information systems security (ICISS) lecture notes in computer science, vol 10063. Springer, pp 225–240Google Scholar
  34. 34.
    Sheela SJ, Suresh KV, Tandur D (2017) A novel audio cryptosystem using chaotic maps and DNA encoding. J Comput Netw Comm, Article ID 2721910Google Scholar
  35. 35.
    Sun F, Liu S, Li Z, Lu Z (2008) A novel image encryption scheme based on spatial chaos map. Chaos, Solitons and Fractals 38(3):631–640MathSciNetCrossRefMATHGoogle Scholar
  36. 36.
    Tong XJ, Zhang M, Wang Z, Liu Y, Ma J (2015) An image encryption scheme based on a new hyper-chaotic finance system. Optik-Int J Light Electron Opt 126(20):2445–2452CrossRefGoogle Scholar
  37. 37.
    Wang Z, Bovik AC (2002) A universal image quality index. IEEE Signal Process Lett 9(3):81–84CrossRefGoogle Scholar
  38. 38.
    Wang XY, Wang Q (2014) A fast image encryption algorithm based on only blocks in cipher text. Chin Phys B 23(3):030503CrossRefGoogle Scholar
  39. 39.
    Wang Z, Bovik AC, Sheikh HR, Simoncelli EP (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13 (4):600–612CrossRefGoogle Scholar
  40. 40.
    Wang X, Wang Q, Zhang Y (2015) A fast image algorithm based on rows and columns switch. Nonlinear Dyn 79(2):1141–1149MathSciNetCrossRefGoogle Scholar
  41. 41.
    Wu Y, Yang G, Jin H, Noonan JP (2012) Image encryption using the two-dimensional logistic chaotic map. J Electron Imaging 21(1):013014–1CrossRefGoogle Scholar
  42. 42.
    Xie J, Yang C, Xie Q, Tian L (2009) An encryption algorithm based on transformed logistic map [C]. In: 2009 International conference on IEEE networks security wireless communications and trusted computing (NSWCTC), pp 111–114Google Scholar
  43. 43.
    Xu L, Li Z, Li J, Hua W (2016) A novel bit-level image encryption algorithm based on chaotic maps. Opt Lasers Eng 78:17–25CrossRefGoogle Scholar
  44. 44.
    Xue X, Zhang Q, Wei X et al (2010) A digital image encryption algorithm based on DNA sequence and multi-chaotic maps. Neural Netw World 20(3):285Google Scholar
  45. 45.
    Ye G (2010) Image scrambling encryption algorithm of pixel bit based on chaos map. Pattern Recogn Lett 31(5):347–354CrossRefGoogle Scholar
  46. 46.
    Yuan HM, Liu Y, Gong LH, Wang J (2017) A new image cryptosystem based on 2D hyper-chaotic system. Multimed Tools Appl 76(6):8087–8108CrossRefGoogle Scholar
  47. 47.
    Zhang XP, Zhao ZM (2014) Chaos-based image encryption with total shuffling and bidirectional diffusion. Nonlinear Dyn 75(1–2):319–330CrossRefGoogle Scholar
  48. 48.
    Zhang LY, Hu X, Liu Y, Wong KW, Gan J (2014) A chaotic image encryption scheme owning temp-value feedback. Commun Nonlinear Sci Numer Simul 19(10):3653–3659MathSciNetCrossRefGoogle Scholar
  49. 49.
    Zhang Q, Liu L, Wei XP (2014) Improved algorithm for image encryption based on DNA encoding and multi-chaotic maps. AEU Int J Electron Commun 68(3):186–192CrossRefGoogle Scholar
  50. 50.
    Zhang X, Mao Y, Zhao Z (2014) An efficient chaotic image encryption based on alternate circular S-boxes. Nonlinear Dyn 78(1):359–369CrossRefGoogle Scholar
  51. 51.
    Zhou Y, Bao L, Chen CP (2013) Image encryption using a new parametric switching chaotic system. Signal Process 93(11):3039–3052CrossRefGoogle Scholar
  52. 52.
    Ziedan IE, Fouad MM, Salem DH (2003) Application of data encryption standard to bitmap and JPEG images [C]. In: 2003 National conference on IEEE radio science (NRSC), pp 16–1Google Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Siddaganga Institute of TechnologyTumakuruIndia
  2. 2.Corporate Research India, ABBBengaluruIndia

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