Skip to main content
SpringerLink
Log in

An asymmetric hybrid cryptosystem using hyperchaotic system and random decomposition in hybrid multi resolution wavelet domain

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

Abstract

In this paper, an asymmetric hybrid cryptosystem utilizing four-dimensional (4D) hyperchaotic framework by means of coherent superposition and random decomposition in hybrid multi-resolution wavelet domain is put forward. The 4D hyperchaotic framework is utilized for creating permutation keystream for a pixel swapping procedure. The hybrid multi-resolution wavelet is formed by combining Walsh transform and fractional Fourier transform of various orders. The 4D hyperchaotic framework’s parameters and preliminary conditions alongside the fractional orders extend the key-space and consequently give additional strength to the proposed cryptosystem. The proposed cryptosystem has an extended key-space to avoid any brute-force attack and is nonlinear in nature. The scheme is validated on greyscale images. Computer-based simulations have been executed to validate the robustness of the proposed scheme against different types of attacks. Results demonstrate that the proposed cryptosystem along with offering higher protection against noise and occlusion attacks is also unassailable to special attack.

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
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21

Similar content being viewed by others

References

  1. Abuturab MR (2015) Group multiple-image encoding and watermarking using coupled logistic maps and gyrator wavelet transform. J Opt Soc Am A, JOSAA 32:1811–1820. https://doi.org/10.1364/JOSAA.32.001811

    Article  Google Scholar 

  2. Barfungpa SP, Abuturab MR (2016) Asymmetric cryptosystem using coherent superposition and equal modulus decomposition of fractional Fourier spectrum. Opt Quant Electron 48:520. https://doi.org/10.1007/s11082-016-0786-5

    Article  Google Scholar 

  3. Biryukov A (2011) Known plaintext attack. In: Encyclopedia of cryptography and security. Springer, Boston, MA: 704–705

  4. Biryukov A (2011) Chosen Ciphertext attack. In: Encyclopedia of cryptography and security. Springer, Boston, MA: 205–205

  5. Cai J, Shen X (2017) Modified optical asymmetric image cryptosystem based on coherent superposition and equal modulus decomposition. Opt Laser Technol Complete:105–112. doi:https://doi.org/10.1016/j.optlastec.2017.04.018

  6. Cai J, Shen X, Lei M et al (2015) Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition. Opt Lett, OL 40:475–478. https://doi.org/10.1364/OL.40.000475

    Article  Google Scholar 

  7. Chai X, Chen Y, Broyde L (2017) A novel chaos-based image encryption algorithm using DNA sequence operations. Opt Lasers Eng 88:197–213. https://doi.org/10.1016/j.optlaseng.2016.08.009

    Article  Google Scholar 

  8. Chen L, Zhao D (2006) Optical image encryption with Hartley transforms. Opt Lett, OL 31:3438–3440. https://doi.org/10.1364/OL.31.003438

    Article  Google Scholar 

  9. Chen A, Lu J, Lü J, Yu S (2006) Generating hyperchaotic Lü attractor via state feedback control. Physica A: Stat Mech Applic 364:103–110. https://doi.org/10.1016/j.physa.2005.09.039

    Article  Google Scholar 

  10. Chen W, Chen X, Sheppard CJR (2010) Optical image encryption based on diffractive imaging. Opt Lett, OL 35:3817–3819. https://doi.org/10.1364/OL.35.003817

    Article  Google Scholar 

  11. Chen J-X, Zhu Z-L, Fu C et al (2014) Cryptanalysis and improvement of an optical image encryption scheme using a chaotic baker map and double random phase encoding. J Opt 16:125403. https://doi.org/10.1088/2040-8978/16/12/125403

    Article  Google Scholar 

  12. Chen H, Tanougast C, Liu Z, Sieler L (2017) Asymmetric optical cryptosystem for color image based on equal modulus decomposition in gyrator transform domains. Opt Lasers Eng 93:1–8. https://doi.org/10.1016/j.optlaseng.2017.01.005

    Article  Google Scholar 

  13. Cheng XC, Cai LZ, Wang YR et al (2008) Security enhancement of double-random phase encryption by amplitude modulation. Opt Lett, OL 33:1575–1577. https://doi.org/10.1364/OL.33.001575

    Article  Google Scholar 

  14. Cho M, Javidi B (2013) Three-dimensional photon counting double-random-phase encryption. Opt Lett, OL 38:3198–3201. https://doi.org/10.1364/OL.38.003198

    Article  Google Scholar 

  15. Deng X (2015) Asymmetric optical cryptosystem based on coherent superposition and equal modulus decomposition: comment. Opt Lett, OL 40:3913–3913. https://doi.org/10.1364/OL.40.003913

    Article  Google Scholar 

  16. Deng X, Zhao D (2012) Multiple-image encryption using phase retrieve algorithm and intermodulation in Fourier domain. Opt Laser Technol 44:374–377. https://doi.org/10.1016/j.optlastec.2011.07.019

    Article  Google Scholar 

  17. Elshamy AM, Rashed ANZ, Mohamed AENA et al (2013) Optical image encryption based on chaotic baker map and double random phase encoding. J Lightwave Technol 31:2533–2539. https://doi.org/10.1109/JLT.2013.2267891

    Article  Google Scholar 

  18. Fatima A, Mehra I, Nishchal NK (2016) Optical image encryption using equal modulus decomposition and multiple diffractive imaging. J Opt 18:085701. https://doi.org/10.1088/2040-8978/18/8/085701

    Article  Google Scholar 

  19. Frauel Y, Castro A, Naughton TJ, Javidi B (2007) Resistance of the double random phase encryption against various attacks. Opt Express, OE 15:10253–10265. https://doi.org/10.1364/OE.15.010253

    Article  Google Scholar 

  20. Fu C, Zhang G, Zhu M et al (2018) A new chaos-based color image encryption scheme with an efficient substitution keystream generation strategy. Sec Commun Netw. https://doi.org/10.1155/2018/2708532

  21. Ge M, Ye R (2018) A novel image encryption scheme based on 3D bit matrix and chaotic map with Markov properties. Egypt Inform J. https://doi.org/10.1016/j.eij.2018.10.001

  22. Gopinathan U, Monaghan DS, Naughton TJ, Sheridan JT (2006) A known-plaintext heuristic attack on the Fourier plane encryption algorithm. Opt Express, OE 14:3181–3186. https://doi.org/10.1364/OE.14.003181

    Article  Google Scholar 

  23. Hennelly B, Sheridan JT (2003) Optical image encryption by random shifting in fractional Fourier domains. Opt Lett, OL 28:269–271. https://doi.org/10.1364/OL.28.000269

    Article  Google Scholar 

  24. Huang J-J, Hwang H-E, Chen C-Y, Chen C-M (2012) Lensless multiple-image optical encryption based on improved phase retrieval algorithm. Appl Opt, AO 51:2388–2394. https://doi.org/10.1364/AO.51.002388

    Article  Google Scholar 

  25. Javidi B, Nomura T (2000) Securing information by use of digital holography. Opt Lett, OL 25:28–30. https://doi.org/10.1364/OL.25.000028

    Article  Google Scholar 

  26. Kekre HB, Sarode TK, Vig R (2015) A new multi-resolution hybrid wavelet for analysis and image compression. Int J Electron 102:2108–2126. https://doi.org/10.1080/00207217.2015.1020882

    Article  Google Scholar 

  27. Kumar R, Bhaduri B (2017) Optical image encryption using Kronecker product and hybrid phase masks. Opt Laser Technol 95:51–55. https://doi.org/10.1016/j.optlastec.2017.03.041

    Article  Google Scholar 

  28. Kumar R, Bhaduri B, Nishchal NK (2017) Nonlinear QR code based optical image encryption using spiral phase transform, equal modulus decomposition and singular value decomposition. J Opt 20(1):015701. https://doi.org/10.1088/2040-8986/aa9943

    Article  Google Scholar 

  29. Li T, Shi Y (2015) Security risk of diffractive-imaging-based optical cryptosystem. Opt Express, OE 23:21384–21391. https://doi.org/10.1364/OE.23.021384

    Article  Google Scholar 

  30. Liu S, Mi Q, Zhu B (2001) Optical image encryption with multistage and multichannel fractional Fourier-domain filtering. Opt Lett, OL 26:1242–1244. https://doi.org/10.1364/OL.26.001242

    Article  Google Scholar 

  31. Liu Z, Chen H, Liu T et al (2011) Image encryption by using gyrator transform and Arnold transform. JEI. JEIME5 20:013020. https://doi.org/10.1117/1.3557790

    Google Scholar 

  32. Liu W, Liu Z, Liu S (2013) Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang-Gu algorithm. Opt Lett, OL 38:1651–1653. https://doi.org/10.1364/OL.38.001651

    Article  Google Scholar 

  33. Maluenda D, Carnicer A, Martínez-Herrero R et al (2015) Optical encryption using photon-counting polarimetric imaging. Opt Express, OE 23:655–666. https://doi.org/10.1364/OE.23.000655

    Article  Google Scholar 

  34. Mehra I, Nishchal NK (2014) Image fusion using wavelet transform and its application to asymmetric cryptosystem and hiding. Opt Express, OE 22:5474–5482. https://doi.org/10.1364/OE.22.005474

    Article  Google Scholar 

  35. Nishchal K, Joseph J, Singh K, Naveen (2004) Securing information using fractional Fourier transform in digital holography. Opt Commun 235:253–259. https://doi.org/10.1016/j.optcom.2004.02.052

    Article  Google Scholar 

  36. Nomura T, Javidi B (2000) Optical encryption using a joint transform correlator architecture. OE, OPEGAR 39:2031–2036. https://doi.org/10.1117/1.1304844

    Article  Google Scholar 

  37. Peng X, Zhang P, Wei H, Yu B (2006) Known-plaintext attack on optical encryption based on double random phase keys. Opt Lett, OL 31:1044–1046. https://doi.org/10.1364/OL.31.001044

    Article  Google Scholar 

  38. Qin W (2011) Universal and special keys based on phase-truncated Fourier transform. Opt Eng 50:080501. https://doi.org/10.1117/1.3607421

    Article  Google Scholar 

  39. Qin W, Peng X (2010) Asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt Lett, OL 35:118–120. https://doi.org/10.1364/OL.35.000118

    Article  Google Scholar 

  40. Rajput SK, Nishchal NK (2013) Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform. Appl Opt, AO 52:871–878. https://doi.org/10.1364/AO.52.000871

    Article  Google Scholar 

  41. Rajput SK, Nishchal NK (2013) Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem. Opt Commun 309:231–235. https://doi.org/10.1016/j.optcom.2013.06.036

    Article  Google Scholar 

  42. Rakheja P, Vig R, Singh P (2019) Optical asymmetric watermarking using 4D hyperchaotic system and modified equal modulus decomposition in hybrid multi resolution wavelet domain. Optik 176:425–437. https://doi.org/10.1016/j.ijleo.2018.09.088

    Article  Google Scholar 

  43. Refregier P, Javidi B (1995) Optical image encryption based on input plane and Fourier plane random encoding. Opt Lett, OL 20:767–769. https://doi.org/10.1364/OL.20.000767

    Article  Google Scholar 

  44. Sharma N, Saini I, Yadav A, Singh P (2017) Phase-image encryption based on 3D-Lorenz chaotic system and double random phase encoding. 3D Res 8:. doi:https://doi.org/10.1007/s13319-017-0149-4

  45. Singh H (2018) Hybrid structured phase mask in frequency plane for optical double image encryption in gyrator transform domain. J Mod Opt 65:2065–2078. https://doi.org/10.1080/09500340.2018.1496286

    Article  MathSciNet  Google Scholar 

  46. Singh P, Yadav AK, Singh K, Saini I (2017) Optical image encryption in the fractional Hartley domain, using Arnold transform and singular value decomposition. AIP Conference Proceedings 1802:020017. https://doi.org/10.1063/1.4973267

    Article  Google Scholar 

  47. Singh P, Saini I, Yadav AK (2017) Analysis of Lorenz-chaos and exclusive-OR based image encryption scheme. Int J Soc Comput Cyber-Phys Syst 2:59. https://doi.org/10.1504/IJSCCPS.2017.10009739

    Article  Google Scholar 

  48. Situ G, Zhang J (2004) Double random-phase encoding in the Fresnel domain. Opt Lett, OL 29:1584–1586. https://doi.org/10.1364/OL.29.001584

    Article  Google Scholar 

  49. Sui L, Gao B (2013) Single-channel color image encryption based on iterative fractional Fourier transform and chaos. Opt Laser Technol 48:117–127. https://doi.org/10.1016/j.optlastec.2012.10.016

    Article  Google Scholar 

  50. Tajahuerce E, Matoba O, Verrall SC, Javidi B (2000) Optoelectronic information encryption with phase-shifting interferometry. Appl Opt, AO 39:2313–2320. https://doi.org/10.1364/AO.39.002313

    Article  Google Scholar 

  51. Unnikrishnan G, Joseph J, Singh K (2000) Optical encryption by double-random phase encoding in the fractional Fourier domain. Opt Lett, OL 25:887–889. https://doi.org/10.1364/OL.25.000887

    Article  Google Scholar 

  52. Wang Z, Sheikh HR (2004) Image quality assessment: from error visibility to structural similarity. IEEE Trans Image Process 13:14

    Google Scholar 

  53. Wang X, Zhao D (2011) Security enhancement of a phase-truncation based image encryption algorithm. Appl Opt 50:6645–6651

    Article  Google Scholar 

  54. Wang X, Zhao D (2012) A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt Commun 285:1078–1081. https://doi.org/10.1016/j.optcom.2011.12.017

    Article  Google Scholar 

  55. Wang X, Zhao D (2013) Simultaneous nonlinear encryption of grayscale and color images based on phase-truncated fractional Fourier transform and optical superposition principle. Appl Opt 52:6170–6178

    Article  Google Scholar 

  56. Wang X, Zhao D (2013) Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask. Opt Lett, OL 38:3684–3686. https://doi.org/10.1364/OL.38.003684

    Article  Google Scholar 

  57. Wang X, Chen Y, Dai C, Zhao D (2014) Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform. Appl Opt, AO 53:208–213. https://doi.org/10.1364/AO.53.000208

    Article  Google Scholar 

  58. Wang Y, Quan C, Tay CJ (2015) Improved method of attack on an asymmetric cryptosystem based on phase-truncated Fourier transform. Appl Opt, AO 54:6874–6881. https://doi.org/10.1364/AO.54.006874

    Article  Google Scholar 

  59. Wang Y, Quan C, Tay CJ (2016) New method of attack and security enhancement on an asymmetric cryptosystem based on equal modulus decomposition. Appl Opt 55:679–686

    Article  Google Scholar 

  60. Xu H, Xu W, Wang S, Wu S (2018) Phase-only asymmetric optical cryptosystem based on random modulus decomposition. J Mod Opt 65:1245–1252. https://doi.org/10.1080/09500340.2018.1431314

    Article  Google Scholar 

  61. Zhao S, Wang L, Liang W et al (2015) High performance optical encryption based on computational ghost imaging with QR code and compressive sensing technique. Opt Commun 353:90–95. https://doi.org/10.1016/j.optcom.2015.04.063

    Article  Google Scholar 

  62. Zhou N, Wang Y, Gong L (2011) Novel optical image encryption scheme based on fractional Mellin transform. Opt Commun 284:3234–3242. https://doi.org/10.1016/j.optcom.2011.02.065

    Article  Google Scholar 

  63. Zhou N, Li H, Wang D et al (2015) Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform. Opt Commun 343:10–21. https://doi.org/10.1016/j.optcom.2014.12.084

    Article  Google Scholar 

  64. Zhou NR, Hua TX, Gong LH et al (2015) Quantum image encryption based on generalized Arnold transform and double random-phase encoding. Quantum Inf Process 14:1193–1213. https://doi.org/10.1007/s11128-015-0926-z

    Article  MathSciNet  MATH  Google Scholar 

  65. Zhou N, Pan S, Cheng S, Zhou Z (2016) Image compression–encryption scheme based on hyper-chaotic system and 2D compressive sensing. Opt Laser Technol 82:121–133. https://doi.org/10.1016/j.optlastec.2016.02.018

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of EECE, The NorthCap University, Gurugram, 122017, India

    Pankaj Rakheja & Rekha Vig

  2. Department of Mathematics, Central University of Haryana, Mahendergarh, 609602, India

    Phool Singh

Authors
  1. Pankaj Rakheja
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Rekha Vig
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Phool Singh
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Pankaj Rakheja.

Additional information

Publisher’s note

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

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Rakheja, P., Vig, R. & Singh, P. An asymmetric hybrid cryptosystem using hyperchaotic system and random decomposition in hybrid multi resolution wavelet domain. Multimed Tools Appl 78, 20809–20834 (2019). https://doi.org/10.1007/s11042-019-7406-x

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-019-7406-x

Keywords

Search

Navigation