Skip to main content

Double Image Encryption Based on 2D Discrete Fractional Fourier Transform and Piecewise Nonlinear Chaotic Map

  • Conference paper
  • First Online:

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 955))

Abstract

Secure transmission of sensitive data over open networks is a challenge in the present scenario of digital signal transmissions. Especially in 2D image signals, the adjacent pixel correlation is high which makes it a challenge to encrypt or hide the information from being fraudulently interpreted. Optical signal processing is preferred for image encryption owing to its high speed parallel processing. Fractional transforms are used for the digital implementation of the optical processing due to the fact that fractional orders enable to analyze a time variant signal where each fractional order correspond to an arbitrary angle of rotation. In this work, we apply a fractional Fourier transform for double image encryption, as fractional orders provide randomness and serve as secret key. The complex outcome of transform becomes a limitation due to requirement of double memory for storage and transmission besides computational complexity. To overcome this issue, a reality preserving scheme is applied to obtain real output from transform. A piecewise nonlinear chaotic map is used to introduce chaotic blending in the double image data. The larger key space of PWNCA based blending offers yet another security layer to the optical transform based encryption. The simulation results give testimony to the acquired randomness in the encrypted data. The proposed scheme is quite sensitive to keys and is robust against potential attacks.

This is a preview of subscription content, log in via an institution.

Buying options

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

References

  1. McBride, A.C., Kerr, F.H.: On Namias’s fractional Fourier transforms. IMA J. Appl. Math. 39(2), 159–175 (1987)

    Article  MathSciNet  Google Scholar 

  2. Ozaktas, H.M., Arikan, O., Kutay, M.A., Bozdagt, G.: Digital computation of the fractional Fourier transform. IEEE Trans. Signal Process. 44(9), 2141–2150 (1996)

    Article  Google Scholar 

  3. Almeida, L.B.: The fractional Fourier transform and time-frequency representations. IEEE Trans. Signal Process. 42(11), 3084–3091 (1994)

    Article  Google Scholar 

  4. Pei, S.C., Tseng, C.C., Yeh, M.H., Shyu, J.J.: Discrete fractional Hartley and Fourier transforms. IEEE Trans. Circuits Syst. II: Analog. Digit. Signal Process. 45(6), 665–675 (1998)

    Article  Google Scholar 

  5. Pei, S.C., Yeh, M.H., Tseng, C.C.: Discrete fractional Fourier transform based on orthogonal projections. IEEE Trans. Signal Process. 47(5), 1335–1348 (1999)

    Article  MathSciNet  Google Scholar 

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

    Article  Google Scholar 

  7. Refregier, P., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995)

    Article  Google Scholar 

  8. Unnikrishnan, G., Singh, K.: Double random fractional Fourier domain encoding for optical security. Opt. Eng. 39(11), 2853–2860 (2000)

    Article  Google Scholar 

  9. Singh, N., Sinha, A.: Chaos based multiple image encryption using multiple canonical transforms. Opt. Laser Technol. 42(5), 724–731 (2010)

    Article  Google Scholar 

  10. Zhou, N., Wang, Y., Gong, L., He, H., Wu, J.: Novel single-channel color image encryption algorithm based on chaos and fractional Fourier transform. Opt. Commun. 284(12), 2789–2796 (2011)

    Article  Google Scholar 

  11. Shan, M., Chang, J., Zhong, Z., Hao, B.: Double image encryption based on discrete multiple-parameter fractional Fourier transform and chaotic maps. Opt. Commun. 285(21–22), 4227–4234 (2012)

    Article  Google Scholar 

  12. Zhang, Y., Xiao, D.: Double optical image encryption using discrete Chirikov standard map and chaos-based fractional random transform. Opt. Lasers Eng. 51(4), 472–480 (2013)

    Article  Google Scholar 

  13. Bhatnagar,G., Wu, Q. J.:Biometric inspired multimedia encryption based on dual parameter fractional fourier transform. IEEE transactions on systems, man, and cybernetics: systems 44(9) 1234–1247(2014)

    Google Scholar 

  14. Ran, Q., Yuan, L., Zhao, T.: Image encryption based on nonseparable fractional Fourier transform and chaotic map. Opt. Commun. 348, 43–49 (2015)

    Article  Google Scholar 

  15. Venturini, I., Duhamel, P.: Reality preserving fractional transforms[signal processing applications]. In: Acoustics, Speech, and Signal Processing, France, pp. 205–207 (2004)

    Google Scholar 

  16. Lang, J.: Image encryption based on the reality-preserving multiple-parameter fractional Fourier transform and chaos permutation. Opt. Lasers Eng. 50(7), 929–937 (2012)

    Article  Google Scholar 

  17. Mishra, D.C., Sharma, R.K., Suman, S., Prasad, A.: Multi-layer security of color image based on chaotic system combined with RP2DFRFT and Arnold Transform. J. Inf. Secur. Appl. 37, 65–90 (2017)

    Google Scholar 

  18. Li, S.J.: Analyses and new designs of digital chaotic ciphers (Doctoral dissertation, Xi’an Jiaotong University) (2003)

    Google Scholar 

  19. Li, S., Chen, G., Mou, X.: On the dynamical degradation of digital piecewise linear chaotic maps. Int. J. Bifurc. Chaos 15(10), 3119–3151 (2005)

    Article  MathSciNet  Google Scholar 

  20. Behnia, S., Akhshani, A., Ahadpour, S., Mahmodi, H., Akhavan, A.: A fast chaotic encryption scheme based on piecewise nonlinear chaotic maps. Phys. Lett. A 366(4–5), 391–396 (2007)

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Gurpreet kaur .

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2019 Springer Nature Singapore Pte Ltd.

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

kaur, G., Agarwal, R., Patidar, V. (2019). Double Image Encryption Based on 2D Discrete Fractional Fourier Transform and Piecewise Nonlinear Chaotic Map. In: Luhach, A., Singh, D., Hsiung, PA., Hawari, K., Lingras, P., Singh, P. (eds) Advanced Informatics for Computing Research. ICAICR 2018. Communications in Computer and Information Science, vol 955. Springer, Singapore. https://doi.org/10.1007/978-981-13-3140-4_47

Download citation

  • DOI: https://doi.org/10.1007/978-981-13-3140-4_47

  • Published:

  • Publisher Name: Springer, Singapore

  • Print ISBN: 978-981-13-3139-8

  • Online ISBN: 978-981-13-3140-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics