Skip to main content
SpringerLink
Log in

An efficient image encryption scheme using Fresnelet transform and elliptic curve based scrambling

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

Abstract

This work introduces a novel and more efficient image encryption scheme, that deploys Fresnelet diffraction in the wave-propagation domain in conjunction with image scrambling effect, based on a specific elliptic curve group, that substantially reduces the computational cost for the desired outcome. Significantly elevated security of the encrypted image is guaranteed by highly complex algebraic structure of the elliptic curve over the Galois field \(\mathbb {F}_{2}^{4}\), in association with Fresnelet transform-based data-decomposition. At first stage, the proposed scheme, propagates confidential information, with selected wavelength at ceratin specific distance, using the Fresnelet transform. During this process confidential data decomposes into four complex sub-bands. We further separate these sub-bands into real and imaginary sub-band data. Then, at the second stage, elliptic curve group law is deployed to add confusion by scrambling the net sub-band data. The security and quality of the presented technique is examined through highly significant tools and we prove that when compared with other prevailing schemes, the proposed scheme offers coherent outcomes.

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

Similar content being viewed by others

References

  1. Ahmad J, Ahmed F (2012) Efficiency analysis and security evaluation of image encryption schemes. IJVIPNS 12:18–31

    Google Scholar 

  2. Ahmad J, Hwang S (2015) Chaos-based diffusion for highly autocorrelated data in encryption algorithms. Nonlinear Dyn 82(4):1839–1850

    Article  MathSciNet  MATH  Google Scholar 

  3. Ahmad J, Hwang S (2016) A secure image encryption scheme based on chaotic maps and affine transformation. Multimed Tools Appl 75:13951–13976

    Article  Google Scholar 

  4. Ahmad J, Hwang S, Ali A (2015) An experimental comparison of chaotic and non-chaotic image encryption schemes. Wirel Pers Commun 84:901–918

    Article  Google Scholar 

  5. Ahmad J, Khan MA, Ahmed F, Khan JS (2018) A novel image encryption scheme based on orthogonal matrix, skew tent map, and XOR operation. Neural Comput & Applic 30:3847–3857

    Article  Google Scholar 

  6. Alsmirat MA, Alalem F, Al-Ayyoub M, Jararweh Y, Gupta B (2019) Impact of digital fingerprint image quality on the fingerprint recognition accuracy. Multimed Tools Appl 78:3649–3688

    Article  Google Scholar 

  7. Azam NA, Hayat U, Ullah I (2018) An injective s-box design scheme over an ordered isomorphic elliptic curve and its characterization. Secur Commun Netw: 3421725

  8. Baptista M (1998) Cryptography with chaos. Phys Lett A 240 (1–2):50–54

    Article  MathSciNet  MATH  Google Scholar 

  9. Bibi N, Farwa S, Muhammad N, Jahangir A, Usman M (2018) A novel encryption scheme for high-contrast image data in the Fresnelet domain. PLoS ONE 13(4):e0194343. https://doi.org/10.1371/journal.pone.0194343

    Article  Google Scholar 

  10. Bukhari S, Yousaf A, Niazi S, Anjum MR (2018) A novel technique for the generation and application of substitution boxes (s-box) for the image encryption. The Nucleus 55(4):219–225

    Google Scholar 

  11. Chai X, Zheng X, Gan Z, Han D, Chen Y (2018) An image encryption algorithm based on chaotic system and compressive sensing. Signal Process 148:124–148

    Article  Google Scholar 

  12. Dawei Z, Guanrong C, Wenbo L (2004) A chaos-based robust wavelet-domain watermarking algorithm. Chaos, Solitons Fractals 22(1):47–54

    Article  MATH  Google Scholar 

  13. Deng S, Zhang L, Xiao D (2005) Image encryption scheme based on chaotic neural system. Advances in neural networks – ISNN 2005. ISNN 2005. Lecture Notes in Computer Science, 3497. Springer, Berlin, pp 868–872

    Google Scholar 

  14. Erivelton G, Lucas G, Janier G, Denis N, Tutueva A (2019) Image encryption based on the pseudo-orbits from 1d chaotic map. Chaos 29:061101. https://doi.org/10.1063/1.5099261

    Article  MathSciNet  Google Scholar 

  15. Farwa S, Muhammad N, Shah T, Ahmad S (2017) A novel image encryption based on algebraic s-box and Arnold transform. 3D Research, Springer, 8(26). https://doi.org/10.1007/s13319-017-0135-x

  16. Farwa S, Sohail A, Muhammad N (2020) A novel application of elliptic curves in the dynamical components of block ciphers. Wirel Pers Commun. In Press

  17. Golea N, Melkemi K (2019) ROI-based fragile watermarking for medical image tamper detection. Int J High Perform Comput Appl 13(2):199–210

    Google Scholar 

  18. Ghoneim A, Muhammad G, Amin SU, Gupta B (2018) Medical image forgery detection for smart healthcare. IEEE Commun Mag 56(4):33–37

    Article  Google Scholar 

  19. Hayat U, Azam N (2019) A novel image encryption scheme based on an elliptic curve. Signal Process 155:391–402

    Article  Google Scholar 

  20. Idrees B, Zafar S, Rashid T (2020) Image encryption algorithm using S-box and dynamic hénon bit level permutation. Multimed Tools Appl 79:6135–6162

    Article  Google Scholar 

  21. Khan M, Asghar Z (2018) 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 

  22. Kumar A (2019) Design of secure image fusion technique using cloud for Privacy-Preserving and copyright protection. IJCAC 9:22–36

    Google Scholar 

  23. Li C, Lin D, Lu J (2017) Cryptanalyzing an image-scrambling encryption algorithm of pixel bits. IEEE MultiMedia 24(3):64–71

    Article  Google Scholar 

  24. Li T, Du B, Liang X (2020) Image encryption algorithm based on logistic and two-dimensional lorenz. IEEE Access 8:13792–13805

    Article  Google Scholar 

  25. Liebling M, Blu T, Unser M (2004) Complex-wave retrieval from a single off-axis hologram. J Opt Soc Am A 21:367–377

    Article  Google Scholar 

  26. Liu H, Wang X (2010) Color image encryption based on one-time keys and robust chaotic maps. Comput Math Appl 59(10):3320–3327

    Article  MathSciNet  MATH  Google Scholar 

  27. Liu H, Wang X (2011) Color image encryption using spatial bit-level permutation and high-dimension chaotic system. Opt Commun 284(16–17):3895–3903

    Article  Google Scholar 

  28. Liu L, Hao S, Lin J, Wang Z, Hu X, Miao S (2018) Image block encryption algorithm based on chaotic maps. IET Signal Process 12 (1):22–30

    Article  Google Scholar 

  29. Liu Y, Zhang J, Han D, Wu P, Sun Y, Moon YS (2020) A multidimensional chaotic image encryption algorithm based on the region of interest. Multimed Tools Appl. https://doi.org/10.1007/s11042-020-08645-8

  30. Luo Y, Yu J, Lai W, Liu L (2019) A novel chaotic image encryption algorithm based on improved baker map and logistic map. Multimed Tools Appl 78:22023–22043

    Article  Google Scholar 

  31. Mehmood S, Farwa S, Rafiq M, Riaz SMJ, Shah T, Jamal SS (2018) To study the effect of the generating polynomial on the quality of nonlinear components in block ciphers. Secur Commun Netw

  32. Mondal B, Behera PK, Gangopadhyay S (2020) A secure image encryption scheme based on a novel 2d sine–cosine cross-chaotic (SC3) map, real-time image processing. Springer

  33. Muhammad N, Bibi N (2015) Digital image watermarking using partial pivoting lower and upper triangular decomposition into the wavelet domain. IET Image Process 9(9):795–803

    Article  Google Scholar 

  34. Muhammad N, Bibi N, Mahmood Z, Kim DG (2015) Blind data hiding technique using the Fresnelet transform. SpringerPlus 4(1):1–15

    Article  Google Scholar 

  35. Muhammad N, Bibi N, Mahmood Z, Akram T, Naqvi SR (2017) Reversible integer wavelet transform for blind image hiding method, vol 12

  36. Muhammad N, Bibi N, Qasim I, Jahangir A, Mahmood Z (2017) Digital watermarking using hall property image decomposition method. Pattern Anal Applic 21(4):1–16

    MathSciNet  Google Scholar 

  37. Muhammad N, Kim DG, Bibi N, Malik YM (2013) A Fresnelet-based encryption of medical images using Arnold transform. Int J Adv Comput Sci Appl 4(3):131–140

    Google Scholar 

  38. Ozkaynak F (2018) Brief review on application of nonlinear dynamics in image encryption. Nonlinear Dyn 92:305–313

    Article  Google Scholar 

  39. Ping P, Xu F, Mao Y, Wang Z (2018) Designing permuation-substitution image encryption networks with Henon map. Neurocomputing 283:53–63

    Article  Google Scholar 

  40. Sallen M, Ibrahim S, Isnin IF (2003) Enhanced chaotic image encryption algorithm based on Baker’s map. In: IEEE proceedings of ISCAS 2003, vol 2, pp 508—511

  41. Shannon CE (1949) Communication theory of secrecy systems. Bell Sys Tech J 28:656–715

    Article  MathSciNet  MATH  Google Scholar 

  42. Wang X, Wang Q (2014) A novel image encryption algorithm based on dynamic S-boxes constructed by chaos. Nonlinear Dyn 75(3):567–576

    Article  Google Scholar 

  43. Wang X, Teng L, Qin X (2012) A novel colour image encryption algorithm based on chaos. Signal Process 92(4):1101–1108

    Article  MathSciNet  Google Scholar 

  44. Wang X, Zhang Y, Bao X (2015) A novel chaotic image encryption scheme using DNA sequence operations. Opt Lasers Eng 73:53–61

    Article  Google Scholar 

  45. Xie EY, Li C, Yu S, Lu J (2017) On the cryptanalysis of Fridrich’s chaotic image encryption scheme. Signal Process 132:150–154

    Article  Google Scholar 

  46. Yu C, Li J, Li X, Ren X, Gupta B (2018) Four-image encryption scheme based on quaternion Fresnel transform, chaos and computer generated hologram. Multimed Tools Appl 77:4585–4608

    Article  Google Scholar 

  47. Yue U, Noonan JP, Agaian S (2011) NPCR and UACI randomness tests for image encryption. Cyber J.: Mult J Sci & Tech. (JSAT) 1(2):31–38

    Google Scholar 

  48. Zhang Y, Wang X (2015) A new image encryption algorithm based on non-adjacent coupled map lattices. Appl Soft Comput 26:10–20

    Article  Google Scholar 

  49. Zhou Y, Bao L, Chen CLP (2014) A new 1 − D chaotic system for image encryption. Signal Process 97:172–184

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, COMSATS University Islamabad, Wah Campus, Wah Cantt, Pakistan

    Shabieh Farwa

  2. Department of Computer Science, Fatima Jinnah Women University, Rawalpindi, Pakistan

    Nargis Bibi

  3. Department of IT & CS, Pak-Austria Fachhochschule Institute of Applied Sciences and Technology, Haripur, Pakistan

    Nazeer Muhammad

Authors
  1. Shabieh Farwa
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Nargis Bibi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nazeer Muhammad
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Nazeer Muhammad.

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

Farwa, S., Bibi, N. & Muhammad, N. An efficient image encryption scheme using Fresnelet transform and elliptic curve based scrambling. Multimed Tools Appl 79, 28225–28238 (2020). https://doi.org/10.1007/s11042-020-09324-4

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11042-020-09324-4

Keywords

Search

Navigation