Abstract

A novel image encryption method is proposed by utilizing random phase encoding in the fractional Fourier domain to encrypt two images into one encrypted image with stationary white distribution. By applying the correct keys which consist of the fractional orders, the random phase masks and the pixel scrambling operator, the two primary images can be recovered without cross-talk. The decryption process is robust against the loss of data. The phase-based image with a larger key space is more sensitive to keys and disturbances than the amplitude-based image. The pixel scrambling operation improves the quality of the decrypted image when noise perturbation occurs. The novel approach is verified by simulations.

©2007 Optical Society of America

Full Article  |  PDF Article
OSA Recommended Articles
Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps

Liansheng Sui, Kuaikuai Duan, Junli Liang, and Xinhong Hei
Opt. Express 22(9) 10605-10621 (2014)

Optical encryption by double-random phase encoding in the fractional Fourier domain

G. Unnikrishnan, J. Joseph, and K. Singh
Opt. Lett. 25(12) 887-889 (2000)

Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding

Xiaogang Wang, Wen Chen, and Xudong Chen
Opt. Express 22(19) 22981-22995 (2014)

More Recommended Articles

References

  • View by:
  • Article Order
  • |
  • Year
  • |
  • Author
  • |
  • Publication
  1. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [Crossref] [PubMed]
  2. B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
    [Crossref]
  3. N. Towghi, B. Javidi, and Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915 (1999).
    [Crossref]
  4. G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
    [Crossref]
  5. G. Unnikrishnan and K. Singh, “Double random fractional Fourier-domain encoding for optical security,” Opt. Eng. 39, 2853–2859 (2000).
    [Crossref]
  6. N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
    [Crossref]
  7. N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis,” Opt. Eng. 43, 2266–2273 (2004).
    [Crossref]
  8. G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67, (2001).
    [Crossref]
  9. Y. Zhang, C.H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285, (2002).
    [Crossref]
  10. B. Zhu and S. Liu, “Optical Image encryption based on the generalized fractional convolution operation,” Opt. Commun. 195, 371–381, (2001).
    [Crossref]
  11. B. Zhu and S. Liu, “Optical Image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244, (2001).
    [Crossref]
  12. B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
    [Crossref] [PubMed]
  13. N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571, (2003).
    [Crossref]
  14. J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
    [Crossref]
  15. A. Sinha and K. Singh, “Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes,” Opt. Eng. 44, 057001 (2005).
    [Crossref]
  16. L. F. Chen and D. M. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Exp.14, 8552–8560 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-19-8552.
    [Crossref]
  17. X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics” Opt. Exp. 14, 1476–1486 (2006).
    [Crossref]
  18. O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
    [Crossref]
  19. M. S. Millán, E. Pérez-Cabré, and B. Javidi, “Multifactor authentication reinforces optical security,” Opt. Lett. 31, 721–723 (2006).
    [Crossref]
  20. G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
    [Crossref] [PubMed]
  21. G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391 (2006).
    [Crossref]
  22. X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
    [Crossref]
  23. Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
    [Crossref]
  24. H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The fractional Fourier transform with Applications in Optics and Signal Processing. (John Wiley & Sons, Chichester, 2001).
  25. A. W. Lohmann, “Image rotation, Wigner rotation, and the fractional Fourier transform,” J. Opt. Soc. Am. A 10, 2181- (1993)
    [Crossref]
  26. B. Javidi, N. Towghi, N. Maghzi, and S. C. Verrall, “Error-reduction techniques and error analysis for fully phase- and amplitude-based encryption,” Appl. Opt. 39, 4117–4130 (2000).
    [Crossref]
  27. J. Hua, L. Liu, and G. Li, “Extended fractional Fourier transforms,” J. Opt. Soc. Am. A 14, 3316–3322 (1997).
    [Crossref]
  28. N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
    [Crossref]

2007 (1)

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[Crossref]

2006 (3)

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics” Opt. Exp. 14, 1476–1486 (2006).
[Crossref]

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391 (2006).
[Crossref]

M. S. Millán, E. Pérez-Cabré, and B. Javidi, “Multifactor authentication reinforces optical security,” Opt. Lett. 31, 721–723 (2006).
[Crossref]

2005 (4)

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[Crossref] [PubMed]

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
[Crossref]

J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
[Crossref]

A. Sinha and K. Singh, “Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes,” Opt. Eng. 44, 057001 (2005).
[Crossref]

2004 (2)

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis,” Opt. Eng. 43, 2266–2273 (2004).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[Crossref]

2003 (3)

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571, (2003).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[Crossref]

B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
[Crossref] [PubMed]

2002 (1)

Y. Zhang, C.H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285, (2002).
[Crossref]

2001 (3)

B. Zhu and S. Liu, “Optical Image encryption based on the generalized fractional convolution operation,” Opt. Commun. 195, 371–381, (2001).
[Crossref]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67, (2001).
[Crossref]

B. Zhu and S. Liu, “Optical Image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244, (2001).
[Crossref]

2000 (3)

1999 (2)

1997 (2)

J. Hua, L. Liu, and G. Li, “Extended fractional Fourier transforms,” J. Opt. Soc. Am. A 14, 3316–3322 (1997).
[Crossref]

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

1995 (1)

1993 (1)

Cai, L. Z.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
[Crossref]

Chen, L. F.

L. F. Chen and D. M. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Exp.14, 8552–8560 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-19-8552.
[Crossref]

Dong, G. Y.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
[Crossref]

Guibert, L.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

He, M. Z.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
[Crossref]

Hennelly, B.

Hua, J.

Javidi, B.

Jing, F.

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics” Opt. Exp. 14, 1476–1486 (2006).
[Crossref]

Joseph, J.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis,” Opt. Eng. 43, 2266–2273 (2004).
[Crossref]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571, (2003).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[Crossref]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
[Crossref]

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The fractional Fourier transform with Applications in Optics and Signal Processing. (John Wiley & Sons, Chichester, 2001).

Li, G.

Li, J.F.

J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
[Crossref]

Liu, L.

Liu, S.

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[Crossref]

B. Zhu and S. Liu, “Optical Image encryption based on the generalized fractional convolution operation,” Opt. Commun. 195, 371–381, (2001).
[Crossref]

B. Zhu and S. Liu, “Optical Image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244, (2001).
[Crossref]

Liu, Z.

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[Crossref]

Lohmann, A. W.

Lu, H.

J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
[Crossref]

Luo, Z.

Ma, Y.H.

J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
[Crossref]

Maghzi, N.

Matoba, O.

Meng, X. F.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
[Crossref]

Millán, M. S.

Nishchal, N. K.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis,” Opt. Eng. 43, 2266–2273 (2004).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[Crossref]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571, (2003).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[Crossref]

Ozaktas, H. M.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The fractional Fourier transform with Applications in Optics and Signal Processing. (John Wiley & Sons, Chichester, 2001).

Pérez-Cabré, E.

Refregier, P.

Sergent, A.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

Shen, X. X.

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
[Crossref]

Sheridan, J. T.

Singh, K.

A. Sinha and K. Singh, “Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes,” Opt. Eng. 44, 057001 (2005).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis,” Opt. Eng. 43, 2266–2273 (2004).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[Crossref]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571, (2003).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[Crossref]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67, (2001).
[Crossref]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
[Crossref]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier-domain encoding for optical security,” Opt. Eng. 39, 2853–2859 (2000).
[Crossref]

Sinha, A.

A. Sinha and K. Singh, “Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes,” Opt. Eng. 44, 057001 (2005).
[Crossref]

Situ, G.

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391 (2006).
[Crossref]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[Crossref] [PubMed]

Song, X.S.

J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
[Crossref]

Tanno, N.

Y. Zhang, C.H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285, (2002).
[Crossref]

Towghi, N.

Unnikrishnan, G.

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571, (2003).
[Crossref]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67, (2001).
[Crossref]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887–889 (2000).
[Crossref]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier-domain encoding for optical security,” Opt. Eng. 39, 2853–2859 (2000).
[Crossref]

Verrall, S. C.

Wang, X.

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics” Opt. Exp. 14, 1476–1486 (2006).
[Crossref]

Wei, X.

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics” Opt. Exp. 14, 1476–1486 (2006).
[Crossref]

Zalevsky, Z.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The fractional Fourier transform with Applications in Optics and Signal Processing. (John Wiley & Sons, Chichester, 2001).

Zhang, G.

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

Zhang, J.

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391 (2006).
[Crossref]

G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
[Crossref] [PubMed]

Zhang, Y.

Y. Zhang, C.H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285, (2002).
[Crossref]

Zhao, D.

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics” Opt. Exp. 14, 1476–1486 (2006).
[Crossref]

Zhao, D. M.

L. F. Chen and D. M. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Exp.14, 8552–8560 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-19-8552.
[Crossref]

Zhao, J.

J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
[Crossref]

Zheng, C.H.

Y. Zhang, C.H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285, (2002).
[Crossref]

Zhu, B.

B. Zhu and S. Liu, “Optical Image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244, (2001).
[Crossref]

B. Zhu and S. Liu, “Optical Image encryption based on the generalized fractional convolution operation,” Opt. Commun. 195, 371–381, (2001).
[Crossref]

Appl. Opt. (1)

J. Opt. A: Pure Appl. Opt. (2)

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A: Pure Appl. Opt. 8, 391 (2006).
[Crossref]

X. F. Meng, L. Z. Cai, M. Z. He, G. Y. Dong, and X. X. Shen, “Cross-talk-free double-image encryption and watermarking with amplitude-phase separate modulations,” J. Opt. A: Pure Appl. Opt. 7, 624 (2005).
[Crossref]

J. Opt. Soc. Am. A (3)

Opt. Commun. (5)

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
[Crossref]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51–67, (2001).
[Crossref]

Y. Zhang, C.H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277–285, (2002).
[Crossref]

B. Zhu and S. Liu, “Optical Image encryption based on the generalized fractional convolution operation,” Opt. Commun. 195, 371–381, (2001).
[Crossref]

J. Zhao, H. Lu, X.S. Song, J.F. Li, and Y.H. Ma, “Optical image encryption based on multistage fractional Fourier transforms and pixel scrambling technique,” Opt. Commun. 249, 493–499, (2005).
[Crossref]

Opt. Eng. (6)

A. Sinha and K. Singh, “Image encryption by using fractional Fourier transform and jigsaw transform in image bit planes,” Opt. Eng. 44, 057001 (2005).
[Crossref]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier-domain encoding for optical security,” Opt. Eng. 39, 2853–2859 (2000).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase encryption using fractional Fourier transform,” Opt. Eng. 42, 1583–1588 (2003).
[Crossref]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-based encryption using fractional order Fourier domain random phase encoding: Error analysis,” Opt. Eng. 43, 2266–2273 (2004).
[Crossref]

B. Javidi, A. Sergent, G. Zhang, and L. Guibert, “Fault tolerance properties of a double phase encoding encryption technique,” Opt. Eng. 36, 992–998 (1997).
[Crossref]

N. K. Nishchal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. 42, 3566–3571, (2003).
[Crossref]

Opt. Exp. (1)

X. Wang, D. Zhao, F. Jing, and X. Wei, “Information synthesis (complex amplitude addition and subtraction) and encryption with digital holography and virtual optics” Opt. Exp. 14, 1476–1486 (2006).
[Crossref]

Opt. Lasers Eng. (1)

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[Crossref]

Opt. Lett. (7)

Other (2)

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The fractional Fourier transform with Applications in Optics and Signal Processing. (John Wiley & Sons, Chichester, 2001).

L. F. Chen and D. M. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Exp.14, 8552–8560 (2006), http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-19-8552.
[Crossref]

Cited By

OSA participates in Crossref's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (15)

Fig. 1.
Fig. 1. Schematic of encryption

Download Full Size | PPT Slide | PDF

Fig. 2.
Fig. 2. Schematic of decryption

Download Full Size | PPT Slide | PDF

Fig. 3.
Fig. 3. Optical implementation of the encryption

Download Full Size | PPT Slide | PDF

Fig. 4.
Fig. 4. (a). Primary grayscale image of Lena; (b) Primary binary text; (c) The encrypted result.

Download Full Size | PPT Slide | PDF

Fig. 5.
Fig. 5. When decrypting with wrong mask M 1: (a) The recovered amplitude-based image; (b) The recovered phase-based image.

Download Full Size | PPT Slide | PDF

Fig. 6.
Fig. 6. When decrypting with wrong mask M 2: (a) The recovered amplitude-based image; (b) The recovered phase-based image.

Download Full Size | PPT Slide | PDF

Fig. 7.
Fig. 7. When decrypting with correct keys: (a) The recovered amplitude-based image; (b) The recovered phase-based image.

Download Full Size | PPT Slide | PDF

Fig. 8.
Fig. 8. The recovered phase-based image with wrong inverse pixel scrambling operator

Download Full Size | PPT Slide | PDF

Fig. 9.
Fig. 9. MSE between the original image and the decrypted image when errors are introduced in fractional order parameters

Download Full Size | PPT Slide | PDF

Fig. 10.
Fig. 10. (a) When 25% pixels of Fig. 4c are occluded; (b) The recovered amplitude-based image; (c) The recovered phase-based image

Download Full Size | PPT Slide | PDF

Fig. 11.
Fig. 11. (a) When 50% pixels of Fig. 4c are occluded; (b) The recovered amplitude-based image; (c) The recovered phase-based image

Download Full Size | PPT Slide | PDF

Fig. 12.
Fig. 12. Decrypting from the phase information of the encrypted image: (a) The recovered amplitude-based image; (b) The recovered phase-based image.

Download Full Size | PPT Slide | PDF

Fig. 13.
Fig. 13. Performance of noise perturbation

Download Full Size | PPT Slide | PDF

Fig. 14.
Fig. 14. The recovered two images obtained from the noisy encrypted image when the forward and inverse pixel scrambling is not applied. (a) The recovered amplitude-based image; (b) The recovered phase-based image

Download Full Size | PPT Slide | PDF

Fig. 15.
Fig. 15. The recovered two images obtained from the noisy encrypted image when the forward and inverse pixel scrambling is applied. (a) The recovered amplitude-based image; (b) The recovered phase-based image

Download Full Size | PPT Slide | PDF

Equations (14)

Equations on this page are rendered with MathJax. Learn more.

F a [ f ( x 0 ) ] = ∫ − ∞ + ∞ f ( x 0 ) K a ( x 0 , x a ) d x 0 ,
K a ( x 0 , x a ) = { A ϕ exp [ i π ( x 0 2 cot ⁡ ϕ − 2 x 0 x a csc ϕ + x a 2 cot ⁡ ϕ ) ] if a ≠ 2 n δ ( x 0 − x a ) if a = 4 n δ ( x 0 + x a ) if a = 4 n ± 2 ,
A ϕ = ∣ sin ⁡ ϕ ∣ − 1 ⁄ 2 exp [ − i π sgn ( ϕ ) 4 + i ϕ 2 ] , ϕ = a π 2 .
C ( x 0 ) = f ( x 0 ) exp [ i π J [ g ( x 0 ) ] ] .
ψ ( x b ) = F b − a { F a [ C ( x 0 ) • M 1 ( x 0 ) ] • M 2 ( x a ) }
= F b − a { F a { f ( x 0 ) exp [ i π J [ g ( x 0 ) ] ] • M 1 ( x 0 ) } • M 2 ( x a ) } .
C ( x 0 ) = F − a { F a − b [ ψ ( x b ) ] • M 2 * ( x a ) } • M 1 * ( x 0 ) = f ( x 0 ) exp { i π J [ g ( x 0 ) ] } .
ψ ′ ( x b ) = ψ ( x b ) + n ( x b ) ,
C ′ ( x 0 ) = f ′ ( x 0 ) exp [ i π g ˜ ( x 0 ) ] = f ( x 0 ) exp [ i π J [ g ( x 0 ) ] ] + n ′ ( x 0 ) ,
n ′ ( x 0 ) = F − a { F − ( b − a ) [ n ( x b ) ] • M 2 * ( x a ) } M 1 * ( x 0 ) ,
f ′ ( x 0 ) = ∣ C ′ ( x 0 ) ∣ , g ′ ( x 0 ) = J − 1 [ g ˜ ( x 0 ) ] = J − 1 [ ∣ arg { C ′ ( x 0 ) } ⁄ π ∣ ] ,
∣ f ′ ( x 0 ) ∣ 2 = ∣ f ( x 0 ) exp { i π J [ g ( x 0 ) ] } + n ′ ( x 0 ) ∣ 2
= ∣ f ( x 0 ) ∣ 2 + ∣ n ′ ( x 0 ) ∣ 2 + f ( x 0 ) exp { − i π J [ g ( x 0 ) ] } n ′ ( x 0 ) + f ( x 0 ) exp { i π J [ g ( x 0 ) ] } n ′ * ( x 0 ) .
MSE = 1 MN ∑ i = 1 M ∑ j = 1 N ( I ( i , j ) − H ( i , j ) ) 2 ,

Metrics