Abstract

We present a study about information disclosure in phase-truncation-based cryptosystems. The main information of the original image to be encoded can be obtained by using a decryption key in the worst case. The problem cannot be thoroughly solved by imaginary part truncating, keeping the encryption keys as private keys, or applying different phase keys for different plaintexts during each encryption process as well as the phase modulation in the frequency domain. In order to eliminate the risk of unintended information disclosure, we further propose a nonlinear spatial and spectral encoding technique using a random amplitude mask (RAM). The encryption process involving two security layers can be fully controlled by a RAM. The spatial encoding of the plaintext images and the simultaneous encryption of the plaintext images and the encryption key greatly enhance the security of system, avoiding several attacks that have cracked the phase-truncation-based cryptosystems. Besides, the hybrid encryption system retains the advantage of a trap door one-way function of phase truncation. Numerical results have demonstrated the feasibility and effectiveness of the proposed encryption algorithm.

© 2014 Optical Society of America

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  1. A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).
  2. P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
    [CrossRef]
  3. A. Alfalou and A. Mansour, “Double random phase encryption scheme to multiplex and simultaneous encode multiple images,” Appl. Opt. 48, 5933–5947 (2009).
    [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. B. Hennelly and J. T. Sheridan, “Optical image encryption by random shifting in fractional Fourier domains,” Opt. Lett. 28, 269–271 (2003).
    [CrossRef]
  6. Q. Wang, Q. Guo, and J. Zhou, “Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain,” Opt. Commun. 285, 4317–4323 (2012).
    [CrossRef]
  7. Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).
    [CrossRef]
  8. G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
    [CrossRef]
  9. G. Situ and J. Zhang, “Multiple-image encryption by wavelength multiplexing,” Opt. Lett. 30, 1306–1308 (2005).
    [CrossRef]
  10. Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
    [CrossRef]
  11. Q. Wang, Q. Guo, and L. Lei, “Double image encryption based on phase–amplitude mixed encoding and multistage phase encoding in gyrator transform domains,” Opt. Laser Technol. 48, 267–279 (2013).
    [CrossRef]
  12. T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
    [CrossRef]
  13. H. Chang and C. Chen, “Fully phase asymmetric image verification system based on joint transform correlator,” Opt. Express 14, 1458–1467 (2006).
    [CrossRef]
  14. J. F. Barrera, M. Tebaldi, C. Ríos, E. Rueda, N. Bolognini, and R. Torroba, “Experimental multiplexing of encrypted movies using a JTC architecture,” Opt. Express 20, 3388–3393 (2012).
    [CrossRef]
  15. Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
    [CrossRef]
  16. W. Chen and X. Chen, “Security-enhanced interference-based optical image encryption,” Opt. Commun. 286, 123–129 (2013).
    [CrossRef]
  17. M. R. Abuturab, “Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding,” Appl. Opt. 52, 1555–1563 (2013).
    [CrossRef]
  18. P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
    [CrossRef]
  19. W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
    [CrossRef]
  20. W. He, X. Peng, X. Meng, and X. Liu, “Optical hierarchical authentication based on interference and hash function,” Appl. Opt. 51, 7750–7757 (2012).
    [CrossRef]
  21. Q. Wang, Q. Guo, and J. Zhou, “Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain,” Appl. Opt. 52, 8854–8863 (2013).
    [CrossRef]
  22. W. Chen, X. Chen, and C. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
    [CrossRef]
  23. Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
    [CrossRef]
  24. W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
    [CrossRef]
  25. J. F. Barrera, A. Mira, and R. Torroba, “Optical encryption and QR codes: secure and noise-free information retrieval,” Opt. Express 21, 5373–5378 (2013).
    [CrossRef]
  26. A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
    [CrossRef]
  27. X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).
    [CrossRef]
  28. U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181–3186 (2006).
    [CrossRef]
  29. Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
    [CrossRef]
  30. J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35, 3553–3555 (2010).
    [CrossRef]
  31. W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).
    [CrossRef]
  32. X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
    [CrossRef]
  33. X. Ding, X. Deng, K. Song, and G. Chen, “Security improvement for asymmetric cryptosystem based on spherical wave illumination,” Appl. Opt. 52, 467–473 (2013).
    [CrossRef]
  34. I. Mehra and N. K. Nishchal, “Asymmetric cryptosystem for securing multiple images,” Opt. Laser Technol. 60, 1–7 (2014).
    [CrossRef]
  35. X. Wang and D. Zhao, “Double images encryption method with resistance against the specific attack based on an asymmetric algorithm,” Opt. Express 20, 11994–12003 (2012).
    [CrossRef]
  36. S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
    [CrossRef]
  37. S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
    [CrossRef]
  38. W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
    [CrossRef]
  39. I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
    [CrossRef]
  40. S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
    [CrossRef]
  41. W. Liu, Z. Liu, J. Wu, and S. Liu, “Asymmetric cryptosystem by using modular arithmetic operation based on double random phase encoding,” Opt. Commun. 301–302, 56–60 (2013).
    [CrossRef]
  42. W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
    [CrossRef]
  43. X. Wang and D. Zhao, “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, 3684–3686 (2013).
    [CrossRef]

2014 (1)

I. Mehra and N. K. Nishchal, “Asymmetric cryptosystem for securing multiple images,” Opt. Laser Technol. 60, 1–7 (2014).
[CrossRef]

2013 (11)

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
[CrossRef]

W. Liu, Z. Liu, J. Wu, and S. Liu, “Asymmetric cryptosystem by using modular arithmetic operation based on double random phase encoding,” Opt. Commun. 301–302, 56–60 (2013).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[CrossRef]

X. Wang and D. Zhao, “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, 3684–3686 (2013).
[CrossRef]

Q. Wang, Q. Guo, and L. Lei, “Double image encryption based on phase–amplitude mixed encoding and multistage phase encoding in gyrator transform domains,” Opt. Laser Technol. 48, 267–279 (2013).
[CrossRef]

W. Chen and X. Chen, “Security-enhanced interference-based optical image encryption,” Opt. Commun. 286, 123–129 (2013).
[CrossRef]

M. R. Abuturab, “Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding,” Appl. Opt. 52, 1555–1563 (2013).
[CrossRef]

Q. Wang, Q. Guo, and J. Zhou, “Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain,” Appl. Opt. 52, 8854–8863 (2013).
[CrossRef]

J. F. Barrera, A. Mira, and R. Torroba, “Optical encryption and QR codes: secure and noise-free information retrieval,” Opt. Express 21, 5373–5378 (2013).
[CrossRef]

X. Ding, X. Deng, K. Song, and G. Chen, “Security improvement for asymmetric cryptosystem based on spherical wave illumination,” Appl. Opt. 52, 467–473 (2013).
[CrossRef]

2012 (8)

2011 (3)

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

2010 (4)

2009 (3)

2008 (1)

2007 (2)

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Resistance of the double random phase encryption against various attacks,” Opt. Express 15, 10253–10265 (2007).
[CrossRef]

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

2006 (3)

2005 (2)

2004 (1)

2003 (1)

2000 (2)

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]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

1995 (1)

Abuturab, M. R.

Alfalou, A.

Arcos, S.

Barrera, J. F.

Bolognini, N.

Brosseau, C.

Carnicer, A.

Castro, A.

Chang, H.

Chen, C.

Chen, G.

Chen, H.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Chen, W.

W. Chen and X. Chen, “Security-enhanced interference-based optical image encryption,” Opt. Commun. 286, 123–129 (2013).
[CrossRef]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

W. Chen, X. Chen, and C. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Chen, X.

W. Chen and X. Chen, “Security-enhanced interference-based optical image encryption,” Opt. Commun. 286, 123–129 (2013).
[CrossRef]

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

W. Chen, X. Chen, and C. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

Dai, J.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Deng, X.

Ding, X.

Frauel, Y.

Gopinathan, U.

Guo, Q.

Q. Wang, Q. Guo, and L. Lei, “Double image encryption based on phase–amplitude mixed encoding and multistage phase encoding in gyrator transform domains,” Opt. Laser Technol. 48, 267–279 (2013).
[CrossRef]

Q. Wang, Q. Guo, and J. Zhou, “Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain,” Appl. Opt. 52, 8854–8863 (2013).
[CrossRef]

Q. Wang, Q. Guo, and J. Zhou, “Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain,” Opt. Commun. 285, 4317–4323 (2012).
[CrossRef]

He, W.

W. He, X. Peng, X. Meng, and X. Liu, “Optical hierarchical authentication based on interference and hash function,” Appl. Opt. 51, 7750–7757 (2012).
[CrossRef]

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).
[CrossRef]

Hennelly, B.

Javidi, B.

Joseph, J.

Juvells, I.

Kumar, P.

Lei, L.

Q. Wang, Q. Guo, and L. Lei, “Double image encryption based on phase–amplitude mixed encoding and multistage phase encoding in gyrator transform domains,” Opt. Laser Technol. 48, 267–279 (2013).
[CrossRef]

Li, P.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Lin, C.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Liu, S.

W. Liu, Z. Liu, J. Wu, and S. Liu, “Asymmetric cryptosystem by using modular arithmetic operation based on double random phase encoding,” Opt. Commun. 301–302, 56–60 (2013).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

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

Liu, T.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Liu, W.

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[CrossRef]

W. Liu, Z. Liu, J. Wu, and S. Liu, “Asymmetric cryptosystem by using modular arithmetic operation based on double random phase encoding,” Opt. Commun. 301–302, 56–60 (2013).
[CrossRef]

Liu, X.

Liu, Z.

W. Liu, Z. Liu, J. Wu, and S. Liu, “Asymmetric cryptosystem by using modular arithmetic operation based on double random phase encoding,” Opt. Commun. 301–302, 56–60 (2013).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

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

Mansour, A.

Mehra, I.

I. Mehra and N. K. Nishchal, “Asymmetric cryptosystem for securing multiple images,” Opt. Laser Technol. 60, 1–7 (2014).
[CrossRef]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[CrossRef]

Meng, X.

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).
[CrossRef]

W. He, X. Peng, X. Meng, and X. Liu, “Optical hierarchical authentication based on interference and hash function,” Appl. Opt. 51, 7750–7757 (2012).
[CrossRef]

Mira, A.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Nishchal, N. K.

I. Mehra and N. K. Nishchal, “Asymmetric cryptosystem for securing multiple images,” Opt. Laser Technol. 60, 1–7 (2014).
[CrossRef]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

Nomura, T.

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

Peng, X.

Qin, W.

Quan, C.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Rajput, S. K.

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
[CrossRef]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

Refregier, P.

Ríos, C.

Rueda, E.

Sheppard, C.

Sheridan, J. T.

Singh, K.

Situ, G.

Song, K.

Sun, X.

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Tay, C. J.

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Tebaldi, M.

Torroba, R.

Unnikrishnan, G.

Vargas, C.

Wang, B.

Wang, Q.

Q. Wang, Q. Guo, and J. Zhou, “Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain,” Appl. Opt. 52, 8854–8863 (2013).
[CrossRef]

Q. Wang, Q. Guo, and L. Lei, “Double image encryption based on phase–amplitude mixed encoding and multistage phase encoding in gyrator transform domains,” Opt. Laser Technol. 48, 267–279 (2013).
[CrossRef]

Q. Wang, Q. Guo, and J. Zhou, “Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain,” Opt. Commun. 285, 4317–4323 (2012).
[CrossRef]

Wang, X.

Wei, H.

Wu, J.

W. Liu, Z. Liu, J. Wu, and S. Liu, “Asymmetric cryptosystem by using modular arithmetic operation based on double random phase encoding,” Opt. Commun. 301–302, 56–60 (2013).
[CrossRef]

Xu, L.

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

Zhang, J.

Zhang, P.

Zhang, Y.

Zhao, D.

Zhou, J.

Q. Wang, Q. Guo, and J. Zhou, “Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain,” Appl. Opt. 52, 8854–8863 (2013).
[CrossRef]

Q. Wang, Q. Guo, and J. Zhou, “Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain,” Opt. Commun. 285, 4317–4323 (2012).
[CrossRef]

Adv. Opt. Photon. (1)

Appl. Opt. (8)

A. Alfalou and A. Mansour, “Double random phase encryption scheme to multiplex and simultaneous encode multiple images,” Appl. Opt. 48, 5933–5947 (2009).
[CrossRef]

M. R. Abuturab, “Security enhancement of color image cryptosystem by optical interference principle and spiral phase encoding,” Appl. Opt. 52, 1555–1563 (2013).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using a jigsaw transform for silhouette removal in interference-based methods and decryption with a single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
[CrossRef]

W. He, X. Peng, X. Meng, and X. Liu, “Optical hierarchical authentication based on interference and hash function,” Appl. Opt. 51, 7750–7757 (2012).
[CrossRef]

Q. Wang, Q. Guo, and J. Zhou, “Multiple-image encryption using polarized light encoding and the optical interference principle in the Fresnel-transform domain,” Appl. Opt. 52, 8854–8863 (2013).
[CrossRef]

X. Ding, X. Deng, K. Song, and G. Chen, “Security improvement for asymmetric cryptosystem based on spherical wave illumination,” Appl. Opt. 52, 467–473 (2013).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Image encryption based on interference that uses fractional Fourier domain asymmetric keys,” Appl. Opt. 51, 1446–1452 (2012).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Asymmetric color cryptosystem using polarization selective diffractive optical element and structured phase mask,” Appl. Opt. 51, 5377–5386 (2012).
[CrossRef]

J. Opt. (1)

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).
[CrossRef]

Opt. Commun. (9)

W. Chen, C. Quan, and C. J. Tay, “Optical color image encryption based on Arnold transform and interference method,” Opt. Commun. 282, 3680–3685 (2009).
[CrossRef]

Q. Wang, Q. Guo, and J. Zhou, “Double image encryption based on linear blend operation and random phase encoding in fractional Fourier domain,” Opt. Commun. 285, 4317–4323 (2012).
[CrossRef]

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

W. Chen and X. Chen, “Optical color image encryption based on an asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

W. Chen and X. Chen, “Security-enhanced interference-based optical image encryption,” Opt. Commun. 286, 123–129 (2013).
[CrossRef]

Z. Liu, L. Xu, T. Liu, H. Chen, P. Li, C. Lin, and S. Liu, “Color image encryption by using Arnold transform and color-blend operation in discrete cosine transform domains,” Opt. Commun. 284, 123–128 (2011).
[CrossRef]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack on encryption domain independent optical asymmetric cryptosystem,” Opt. Commun. 309, 231–235 (2013).
[CrossRef]

W. Liu, Z. Liu, J. Wu, and S. Liu, “Asymmetric cryptosystem by using modular arithmetic operation based on double random phase encoding,” Opt. Commun. 301–302, 56–60 (2013).
[CrossRef]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
[CrossRef]

Opt. Eng. (2)

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Collision in Fresnel domain asymmetric cryptosystem using phase truncation and authentication verification,” Opt. Eng. 52, 028202 (2013).
[CrossRef]

T. Nomura and B. Javidi, “Optical encryption using a joint transform correlator architecture,” Opt. Eng. 39, 2031–2035 (2000).
[CrossRef]

Opt. Express (6)

Opt. Laser Technol. (3)

W. He, X. Peng, and X. Meng, “A hybrid strategy for cryptanalysis of optical encryption based on double-random phase–amplitude encoding,” Opt. Laser Technol. 44, 1203–1206 (2012).
[CrossRef]

I. Mehra and N. K. Nishchal, “Asymmetric cryptosystem for securing multiple images,” Opt. Laser Technol. 60, 1–7 (2014).
[CrossRef]

Q. Wang, Q. Guo, and L. Lei, “Double image encryption based on phase–amplitude mixed encoding and multistage phase encoding in gyrator transform domains,” Opt. Laser Technol. 48, 267–279 (2013).
[CrossRef]

Opt. Lett. (13)

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33, 2443–2445 (2008).
[CrossRef]

G. Situ and J. Zhang, “Double random-phase encoding in the Fresnel domain,” Opt. Lett. 29, 1584–1586 (2004).
[CrossRef]

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

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

P. Refregier and B. Javidi, “Optical image encryption based on input plane and Fourier plane random encoding,” Opt. Lett. 20, 767–769 (1995).
[CrossRef]

J. F. Barrera, C. Vargas, M. Tebaldi, R. Torroba, and N. Bolognini, “Known-plaintext attack on a joint transform correlator encrypting system,” Opt. Lett. 35, 3553–3555 (2010).
[CrossRef]

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
[CrossRef]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261–3263 (2006).
[CrossRef]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120 (2010).
[CrossRef]

W. Chen, X. Chen, and C. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).
[CrossRef]

W. Liu, Z. Liu, and S. Liu, “Asymmetric cryptosystem using random binary phase modulation based on mixture retrieval type of Yang–Gu algorithm,” Opt. Lett. 38, 1651–1653 (2013).
[CrossRef]

X. Wang and D. Zhao, “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, 3684–3686 (2013).
[CrossRef]

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Figures (11)

Fig. 1.
Fig. 1.

(a) Target image, (b) amplitude mask Ea, and phase masks (c) Pa and (d) Pa.

Fig. 2.
Fig. 2.

Images reconstructed from (a) Pa, (b) Ea and Pa, (c) Pa and Pa, and (d) the key obtained by imaginary part truncation in the Fourier domain.

Fig. 3.
Fig. 3.

Image reconstructed from (a) Pa, (b) (Ea,Pa), and (c) (Pa,Pa).

Fig. 4.
Fig. 4.

Flowchart for double-image encryption process.

Fig. 5.
Fig. 5.

Flowchart for decryption process.

Fig. 6.
Fig. 6.

Electro-optical setup for encryption and decryption.

Fig. 7.
Fig. 7.

(a) Cameraman; spatially encoded images: (b) A and (c) P. Two decryption keys: (d) K1, (e) K2; (f) ciphertext.

Fig. 8.
Fig. 8.

Image reconstructed from (a) K1, (b) (E,K1), (c) (K1,K2); (d) key obtained by imaginary part truncation in the Fourier domain.

Fig. 9.
Fig. 9.

(a)–(d) are decrypted images obtained by using a wrong phase key. (e) and (f) are the two correctly recovered images.

Fig. 10.
Fig. 10.

Results of occlusion attack on the encrypted image for (a) 25%, (b) 50%, and (c) 75% occlusion; (b), (d), and (f) show the corresponding decrypted Cameraman images.

Fig. 11.
Fig. 11.

Two fake images: (a) Woodstatue and (b) Screen. (c)–(f) are decrypted images obtained by using fake keys.

Equations (24)

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ga(u,υ)=PT{FT[f(x,y)R1(x,y)]},
Ea(x,y)=PT{FT1[ga(u,υ)R2(u,υ)]},
Pa(u,υ)=AT{FT[f(x,y)R1(x,y)]},
Pa(x,y)=AT{FT1[ga(u,υ)R2(u,υ)]},
ga(u,υ)=PT{FT[Ea(x,y)Pa(x,y)]},
Da(x,y)=PT{FT1[ga(u,υ)Pa(u,υ)]}.
Pa(u,υ)=Pa(u,υ)·R¯2(u,υ),
Da(x,y)=[Ea(x,y)·Pa(x,y)]*FT1[Pa(u,υ)]=FT1{FT[Ea(x,y)·Pa(x,y)]·Pa(u,υ)}=FT1{ga(u,υ)·R2(u,υ)·Pa(u,υ)·R¯2(u,υ)}=FT1{ga(u,υ)·Pa(u,υ)}=FT1{FT[f(x,y)R1(x,y)]}=f(x,y)R1(x,y),
A(x,y)=PT{C(x,y)}=sinθ1(x,y),
P(x,y)=AT{C(x,y)}=exp[iθ2(x,y)],
θ1(x,y)=M(x,y)+12πarcsinf1(x,y)2,
θ2(x,y)=2πM(x,y)+arcsinf2(x,y)2.
g(u,υ)=PT{FT[C(x,y)]}=PT{FT[A(x,y)P(x,y)]},
K1(u,υ)=AT{FT[C(x,y)]}=AT{FT[A(x,y)P(x,y)]},
R(u,υ)=exp[i2πM(u,υ)].
E(x,y)=PT{FT1[g(u,υ)R(u,υ)]},
K2(x,y)=AT{FT1[g(u,υ)R(u,υ)]}.
PT{FT[E(x,y)K2(x,y)]}=g(u,υ),
AT{FT[E(x,y)K2(x,y)]}=R(u,υ).
PT{FT1[g(u,υ)K1(u,υ)]}=A(x,y),
AT{FT1[g(u,υ)K1(u,υ)]}=P(x,y).
f1(x,y)=2sin[2πθ1(x,y)2πM(x,y)],
f2(x,y)=2sin[θ2(x,y)2πM(x,y)].
RMSE=Σn=1NΣm=1MR(m,n)O(m,n)2M×N,

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