Secure and noise-free nonlinear optical cryptosystem based on phase-truncated Fresnel diffraction and QR code

  • Jiandong Wang
  • Li Song
  • Xianhong Liang
  • Yidong Liu
  • Pusheng Liu
Part of the following topical collections:
  1. Laser Technologies and Laser Applications


A novel secure and noise-free nonlinear optical cryptosystem based on phase-truncated Fresnel diffraction (PTFD) and QR code is proposed. In this paper, we introduce QR code to resist the noise which contaminates the retrievals of normal optical cryptosystems. The plaintext is transformed into a QR code and then the code is encrypted into a real-valued noise-like ciphertext by employing the PTFD-based cryptosystem. The two private encryption keys (EKs) are generated by the PTFD of a random amplitude mask with the two public keys. In the process of generating the EKs, just the amplitude in the Fresnel and output planes need to be recorded. There are no iterative calculations in the whole encryption and decryption process. Moreover, owing to the nonlinear operation of PTFD and the two generated private EKs, the proposed scheme is supposed to against existing attacks. Numerical simulations are carried out to demonstrate the validity and security of the proposed cryptosystem.


Optical image encryption Fresnel diffraction Nonlinear optical cryptosystem QR code 



This work is supported by the Fundarmental Research Funds for the Central Universities (Grant No. ZYGX2015J042).


  1. Barrera, J.F., Mira, A., Torroba, R.: Optical encryption and QR codes: secure and noise-free information retrieval. Opt. Exp. 21(5), 5373–5378 (2013). doi: 10.1364/OE.21.005373 ADSCrossRefGoogle Scholar
  2. Barrera, J.F., Vélez, A., Torroba, R.: Experimental scrambling and noise reduction applied to the optical encryption of QR codes. Opt. Express 22(17), 20268–20277 (2014). doi: 10.1364/OE.22.020268 ADSCrossRefGoogle Scholar
  3. Carnicer, A., Montes-Usategui, M., Arcos, S., Juvells, I.: Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys. Opt. Lett. 30(13), 1644–1646 (2005). doi: 10.1364/OL.30.001644 ADSCrossRefGoogle Scholar
  4. Chen, W., Quan, C., Tay, C.: Optical color image encryption based on Arnold transform and interference method. Opt. Commun. 282(18), 3680–3685 (2009). doi: 10.1016/j.optcom.2009.06.014 ADSCrossRefGoogle Scholar
  5. Chen, L., Zhao, D.: Optical image encryption based on fractional wavelet transform. Opt. Commun. 254(4–6), 361–367 (2005). doi: 10.1016/j.optcom.2005.05.052 ADSCrossRefGoogle Scholar
  6. Cheng, X.C., Cai, L.Z., Wang, Y.R., Meng, X.F., Zhang, H., Xu, X.F., Shen, X.X., Dong, G.Y.: Security enhancement of double-random phase encryption by amplitude modulation. Opt. Lett. 33(14), 1575–1577 (2008). doi: 10.1364/OL.33.001575 ADSCrossRefGoogle Scholar
  7. Deng, X.: Optical image encryption based on real-valued coding and subtracting with the help of QR code. Opt. Commun. 349, 48–53 (2015). doi: 10.1016/j.optcom.2015.03.047 ADSCrossRefGoogle Scholar
  8. Dey, S., Mondal, K., Nath, J., Nath, A.: Advanced steganography algorithm using randomized intermediate QR host embedded with any encrypted secret message: ASA_QR algorithm. Int. J. Mod. Educ. Comput. Sci. 4(6), 59–67 (2012). doi: 10.5815/ijmecs.2012.06.08 CrossRefGoogle Scholar
  9. Goodman, J.W.: Introduction to Fourier Optics, 3rd edn. Roberts & Company Publishers, Englewood, Colorado (2005)Google Scholar
  10. He, W., Peng, X., Meng, X.: A hybrid strategy for cryptanalysis of optical encryption based on double-random phase-amplitude encoding. Opt. Laser Technol. 44, 1203–1206 (2012). doi: 10.1016/j.optlastec.2012.01.021 ADSCrossRefGoogle Scholar
  11. ISO/IEC 18004: 2015: Information technology–automatic identification and data capture techniques–QR Code bar code symbology specification (2015)Google Scholar
  12. Javidi, B., Nomura, T.: Securing information by use of digital holography. Opt. Lett. 25(1), 28–30 (2000). doi: 10.1364/OL.25.000028 ADSCrossRefGoogle Scholar
  13. Kumar, P., Kumar, A., Joseph, J., Singh, K.: Vulnerability of the security enhanced double random phase-amplitude encryption scheme to point spread function attack. Opt. Lasers Eng. 50(9), 1196–1201 (2012). doi: 10.1016/j.optlaseng.2012.04.004 CrossRefGoogle Scholar
  14. Lin, C., Shen, X., Li, B.: Four-dimensional key design in amplitude, phase, polarization and distance for optical encryption based on polarization digital holography and QR code. Opt. Express 22(17), 20727–20739 (2014). doi: 10.1364/OE.22.020727 ADSCrossRefGoogle Scholar
  15. Liu, W., Liu, Z., Liu, S.: Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm. Opt. Lett. 38(10), 1651–1653 (2013). doi: 10.1364/OL.38.001651 ADSCrossRefGoogle Scholar
  16. Nomura, T., Javidi, B.: Optical encryption using a joint transform correlator architecture. Opt. Eng. 39(8), 2031–2035 (2000). doi: 10.1117/1.1304844 ADSCrossRefGoogle Scholar
  17. Peng, X., Cui, Z., Tan, T.: Information encryption with virtual-optics imaging system. Opt. Commun. 212(4), 235–245 (2002). doi: 10.1016/S0030-4018(02)02003-5 ADSCrossRefGoogle Scholar
  18. Peng, X., Wei, H., Zhang, P.: Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain. Opt. Lett. 31(22), 3261–3263 (2006). doi: 10.1364/OL.31.003261 ADSCrossRefGoogle Scholar
  19. Peng, X., Zhang, P., Wei, H., Yu, B.: Known-plaintext attack on optical encryption based on double random phase keys. Opt. Lett. 31(8), 1044–1046 (2006). doi: 10.1364/OL.31.001044 ADSCrossRefGoogle Scholar
  20. Qin, W., Peng, X.: Asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt. Lett. 35(2), 118–120 (2010). doi: 10.1364/OL.35.000118 ADSCrossRefGoogle Scholar
  21. Refregier, P., Javidi, B.: Optical image encryption based on input plane and Fourier plane random encoding. Opt. Lett. 20(7), 767–769 (1995). doi: 10.1364/OL.20.000767 ADSCrossRefGoogle Scholar
  22. Ren, Z., Su, P., Ma, J., Jin, G.: Secure and noise-free holographic encryption with a quick-response code. Chin. Opt. Lett. 12(1), 010601 (2014). doi: 10.3788/COL201412.010601 ADSGoogle Scholar
  23. Situ, G., Zhang, J.: Double random-phase encoding in the Fresnel domain. Opt. Lett. 29(14), 1584–1586 (2004). doi: 10.1364/OL.29.001584 ADSCrossRefGoogle Scholar
  24. Tajahuerce, E., Matoba, O., Verrall, S.C., Javidi, B.: Optoelectronic information encryption with phase-shifting interferometry. Appl. Opt. 39(14), 2313–2320 (2000). doi: 10.1364/AO.39.002313 ADSCrossRefGoogle Scholar
  25. Tay, C., Quan, C., Chen, W., Fu, Y.: Color image encryption based on interference and virtual optics. Opt. Laser Technol. 42, 409–415 (2010). doi: 10.1016/j.optlastec.2009.08.016 ADSCrossRefGoogle Scholar
  26. Unnikrishnan, G., Joseph, J., Singh, K.: Optical encryption by double-random phase encoding in the fractional Fourier domain. Opt. Lett. 25(12), 887–889 (2000). doi: 10.1364/OL.25.000887 ADSCrossRefGoogle Scholar
  27. Wang, X., Chen, Y., Dai, C., Zhao, D.: Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform. Appl. Opt. 53(2), 208–213 (2014). doi: 10.1364/AO.53.000208 ADSCrossRefGoogle Scholar
  28. Wang, Y., Quan, C., Tay, C.: Optical color image encryption without information disclosure using phase-truncated Fresnel transform and a random amplitude mask. Opt. Commun. 344(1), 147–155 (2015). doi: 10.1016/j.optcom.2015.01.045 ADSGoogle Scholar
  29. Wang, Zp, Zhang, S., Liu, Hz, Qin, Y.: Single-intensity-recording optical encryption technique based on phase retrieval algorithm and QR code. Opt. Commun. 332, 36–41 (2014). doi: 10.1016/j.optcom.2014.06.070 ADSCrossRefGoogle Scholar
  30. Wang, X., Zhao, D.: A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms. Opt. Commun. 285(6), 1078–1081 (2012). doi: 10.1016/j.optcom.2011.12.017 ADSCrossRefGoogle Scholar
  31. Wang, X., Zhao, D.: Amplitude-phase retrieval attack free cryptosystem based on direct attack to phase-truncated Fourier-transform-based encryption using a random amplitude mask. Opt. Lett. 38(18), 3684–3686 (2013). doi: 10.1364/OL.38.003684 ADSCrossRefGoogle Scholar
  32. Zhang, C., He, W., Wu, J., Peng, X.: Optical cryptosystem based on phase-truncated Fresnel diffraction and transport of intensity equation. Opt. Exp. 23(7), 8845–8854 (2015). doi: 10.1364/OE.23.008845 ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2016

Authors and Affiliations

  • Jiandong Wang
    • 1
  • Li Song
    • 1
  • Xianhong Liang
    • 1
  • Yidong Liu
    • 1
  • Pusheng Liu
    • 1
  1. 1.School of Physical ElectronicsUniversity of Electronic Science and Technology of ChinaChengduChina

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