Abstract

A single channel asymmetric color image encryption scheme is proposed that uses an amplitude- and phase- truncation approach with interference of polarized wavefronts. Instead of commonly used random phase masks, wavelength-dependent structured phase masks (SPM) are used in the fractional Fourier transform domain for image encoding. The primary color components bonded with different SPMs are combined into one grayscale image using convolution. We then apply the amplitude and phase truncation to the fractional spectrum, which helps generate unique decryption keys. The encrypted image bonded with a different SPM is then encoded into a polarization selective diffractive optical element. The proposed scheme alleviates the alignment problem of interference and does not need iterative encoding and offers multiple levels of security. The effect of a special attack to the proposed asymmetric cryptosystem has been studied. To measure the effectiveness of the proposed method, we calculated the mean square error between the original and the decrypted images. The computer simulation results support the proposed idea.

© 2012 Optical Society of America

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References

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2012 (5)

H.-E. Hwang, “Optical color image encryption based on the wavelength multiplexing using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 285, 567–573 (2012).
[CrossRef]

X. Deng and D. Zhao, “Single channel color image encryption based on asymmetric cryptosystem,” Opt. Laser Technol. 44, 136–140 (2012).
[CrossRef]

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

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

P. Memmolo, A. Finizio, M. Paturzo, P. Ferraro, and B. Javidi, “Multi-wavelength digital holography: reconstruction, synthesis and display of holograms using adaptive transformation,” Opt. Lett. 37, 1445–1447 (2012).
[CrossRef]

2011 (12)

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

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50, 080501 (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]

X. Shi and D. Zhao, “Color image hiding based on the phase retrieval technique and Arnold transform,” Appl. Opt. 50, 2134–2139 (2011).
[CrossRef]

X. Deng and D. Zhao, “Single channel color image encryption using a modified Gerchberg-Saxton algorithm and mutual encoding in the Fresnel domain,” Appl. Opt. 50, 6019–6025 (2011).
[CrossRef]

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).
[CrossRef]

H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Opt. Commun. 284, 3895–3903 (2011).
[CrossRef]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).
[CrossRef]

B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical stream-cipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
[CrossRef]

E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
[CrossRef]

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

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

2010 (7)

P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35, 2391–2393 (2010).
[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (2010).
[CrossRef]

X. Li and D. Zhao, “Optical color image encryption with redefined fractional Hartley transform,” Optik 121, 673–677 (2010).
[CrossRef]

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

C. H. Niu, X. L. Wang, N. G. Lv, Z. H. Zhou, and X. Y. Li, “An encryption method with multiple encrypted keys based on interference principle,” Opt. Express 18, 7827–7834(2010).
[CrossRef]

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

2009 (7)

N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009).
[CrossRef]

L. Chen and D. Zhao, “Color image encoding in dual fractional Fourier-wavelet domain with random phases,” Opt. Commun. 282, 3433–3438 (2009).
[CrossRef]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photon. 1, 589–636 (2009).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Phase image encryption of colored images using double random phase encoding techniques in HSV color space,” Opt. Rev. 16, 511–516 (2009).
[CrossRef]

Q.-p. Yuan, X.-p. Yang, L.-j. Gao, and H.-c. Zhai, “Color image single-channel encryption based on tricolor grating theory,” Optoelectron. Lett. 5, 0147–0149 (2009).
[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]

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. Signal Process. Lett. 16, 853–856 (2009).
[CrossRef]

2008 (2)

2007 (2)

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).
[CrossRef]

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]

2006 (5)

2005 (3)

J. F. Barerra, R. Henao, and R. Torroba, “Optical encryption method using toroidal zone plate,” Opt. Commun. 248, 35–40(2005).
[CrossRef]

J. F. Barerra, R. Henao, and R. Torroba, “Fault tolerances using toroidal zone plate encryption,” Opt. Commun. 256, 489–494 (2005).
[CrossRef]

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

1999 (1)

S. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Tech. Lett. 21, 318–323 (1999).
[CrossRef]

1996 (1)

1995 (1)

1993 (1)

Alfalou, A.

Arcos, S.

Barerra, J. F.

J. F. Barerra, R. Henao, and R. Torroba, “Optical encryption method using toroidal zone plate,” Opt. Commun. 248, 35–40(2005).
[CrossRef]

J. F. Barerra, R. Henao, and R. Torroba, “Fault tolerances using toroidal zone plate encryption,” Opt. Commun. 256, 489–494 (2005).
[CrossRef]

Brosseau, C.

Cao, Y.

Y. He, Y. Cao, and X. Lu, “Color image encryption based on orthogonal composite grating and double random phase encoding technique,” Optik (2012) (in press).

Carnicer, A.

Castro, A.

Chang, P.

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]

Chen, L.

L. Chen and D. Zhao, “Color image encoding in dual fractional Fourier-wavelet domain with random phases,” Opt. Commun. 282, 3433–3438 (2009).
[CrossRef]

L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14, 8552–8560 (2006).
[CrossRef]

Chen, W.

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

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (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, “Optical color image encryption based on asymmetric cryptosystem in the Fresnel domain,” Opt. Commun. 284, 3913–3917 (2011).
[CrossRef]

W. Chen and X. Chen, “Space-based optical image encryption,” Opt. Express 18, 27095–27104 (2010).
[CrossRef]

Cho, M.

Clemente, P.

Deng, X.

X. Deng and D. Zhao, “Single channel color image encryption based on asymmetric cryptosystem,” Opt. Laser Technol. 44, 136–140 (2012).
[CrossRef]

X. Deng and D. Zhao, “Single channel color image encryption using a modified Gerchberg-Saxton algorithm and mutual encoding in the Fresnel domain,” Appl. Opt. 50, 6019–6025 (2011).
[CrossRef]

Dowling, T.

Durán, V.

Fainman, Y.

Ferraro, P.

Finizio, A.

Ford, J. E.

Frauel, Y.

Fu, Y.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

Gao, B.

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50, 080501 (2011).
[CrossRef]

Gao, L.-j.

Q.-p. Yuan, X.-p. Yang, L.-j. Gao, and H.-c. Zhai, “Color image single-channel encryption based on tricolor grating theory,” Optoelectron. Lett. 5, 0147–0149 (2009).
[CrossRef]

Gong, L.

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).
[CrossRef]

He, H.

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).
[CrossRef]

He, Y.

Y. He, Y. Cao, and X. Lu, “Color image encryption based on orthogonal composite grating and double random phase encoding technique,” Optik (2012) (in press).

Henao, R.

J. F. Barerra, R. Henao, and R. Torroba, “Fault tolerances using toroidal zone plate encryption,” Opt. Commun. 256, 489–494 (2005).
[CrossRef]

J. F. Barerra, R. Henao, and R. Torroba, “Optical encryption method using toroidal zone plate,” Opt. Commun. 248, 35–40(2005).
[CrossRef]

Hennelly, B. M.

Hwang, H.-E.

H.-E. Hwang, “Optical color image encryption based on the wavelength multiplexing using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 285, 567–573 (2012).
[CrossRef]

Javidi, B.

Jin, W.

W. Jin, L. Ma, and C. Yan, “Real color fractional Fourier transform holograms,” Opt. Commun. 259, 513–516 (2006).
[CrossRef]

Joseph, J.

Joshi, M.

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Phase image encryption of colored images using double random phase encoding techniques in HSV color space,” Opt. Rev. 16, 511–516 (2009).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).
[CrossRef]

Juvells, I.

Karim, M. A.

S. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Tech. Lett. 21, 318–323 (1999).
[CrossRef]

Kumar, P.

Lancis, J.

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]

Li, X.

X. Li and D. Zhao, “Optical color image encryption with redefined fractional Hartley transform,” Optik 121, 673–677 (2010).
[CrossRef]

Li, X. Y.

Li, Y.

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. Signal Process. Lett. 16, 853–856 (2009).
[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, H.

H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Opt. Commun. 284, 3895–3903 (2011).
[CrossRef]

Liu, J.

Liu, S.

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]

B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical stream-cipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
[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]

Liu, Z.

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]

B. Yang, Z. Liu, B. Wang, Y. Zhang, and S. Liu, “Optical stream-cipher-like system for image encryption based on Michelson interferometer,” Opt. Express 19, 2634–2642 (2011).
[CrossRef]

Lu, X.

Y. He, Y. Cao, and X. Lu, “Color image encryption based on orthogonal composite grating and double random phase encoding technique,” Optik (2012) (in press).

Lv, N. G.

Ma, J.

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. Signal Process. Lett. 16, 853–856 (2009).
[CrossRef]

Ma, L.

W. Jin, L. Ma, and C. Yan, “Real color fractional Fourier transform holograms,” Opt. Commun. 259, 513–516 (2006).
[CrossRef]

Memmolo, P.

Meng, X.

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50, 080501 (2011).
[CrossRef]

Montes-Usategui, M.

Naughton, T. J.

Nishchal, N. K.

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

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

Niu, C. H.

Paturzo, M.

Peng, X.

Pérez-Cabré, E.

Qin, W.

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50, 080501 (2011).
[CrossRef]

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

Quan, C.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (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]

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M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Phase image encryption of colored images using double random phase encoding techniques in HSV color space,” Opt. Rev. 16, 511–516 (2009).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).
[CrossRef]

Shi, X.

Singh, K.

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).
[CrossRef]

P. Kumar, J. Joseph, and K. Singh, “Optical image encryption using jigsaw transform for silhouette removal in interference based methods and decryption with single spatial light modulator,” Appl. Opt. 50, 1805–1811 (2011).
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M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Phase image encryption of colored images using double random phase encoding techniques in HSV color space,” Opt. Rev. 16, 511–516 (2009).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).
[CrossRef]

Stallings, W.

W. Stallings, Cryptography and Network Security: Principles and Practice, 5th ed. (Prentice Hall, 2011).

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D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. Signal Process. Lett. 16, 853–856 (2009).
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Tay, C. J.

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
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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).
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Tyan, R. C.

Urquhart, K.

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X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated fractional Fourier transforms,” Opt. Commun. 285, 1078–1081 (2012).
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H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Opt. Commun. 284, 3895–3903 (2011).
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Wang, X. L.

Wang, Y.

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).
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N. Zhu, Y. Wang, J. Liu, J. Xie, and H. Zhang, “Optical image encryption based on interference of polarized light,” Opt. Express 17, 13418–13424 (2009).
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D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. Signal Process. Lett. 16, 853–856 (2009).
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Wie, H.

Wu, J.

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).
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W. Jin, L. Ma, and C. Yan, “Real color fractional Fourier transform holograms,” Opt. Commun. 259, 513–516 (2006).
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Q.-p. Yuan, X.-p. Yang, L.-j. Gao, and H.-c. Zhai, “Color image single-channel encryption based on tricolor grating theory,” Optoelectron. Lett. 5, 0147–0149 (2009).
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Q.-p. Yuan, X.-p. Yang, L.-j. Gao, and H.-c. Zhai, “Color image single-channel encryption based on tricolor grating theory,” Optoelectron. Lett. 5, 0147–0149 (2009).
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L. Chen and D. Zhao, “Color image encoding in dual fractional Fourier-wavelet domain with random phases,” Opt. Commun. 282, 3433–3438 (2009).
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L. Chen and D. Zhao, “Optical color image encryption by wavelength multiplexing and lensless Fresnel transform holograms,” Opt. Express 14, 8552–8560 (2006).
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N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).
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Adv. Opt. Photon. (1)

Appl. Opt. (5)

IEEE Trans. Signal Process. Lett. (1)

D. Wei, Q. Ran, Y. Li, J. Ma, and L. Tan, “A convolution and product theorem for the linear canonical transform,” IEEE Trans. Signal Process. Lett. 16, 853–856 (2009).
[CrossRef]

J. Opt. Soc. Am. A (1)

Microwave Opt. Tech. Lett. (1)

S. Zhang and M. A. Karim, “Color image encryption using double random phase encoding,” Microwave Opt. Tech. Lett. 21, 318–323 (1999).
[CrossRef]

Opt. Commun. (14)

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]

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]

W. Jin, L. Ma, and C. Yan, “Real color fractional Fourier transform holograms,” Opt. Commun. 259, 513–516 (2006).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Color image encryption and decryption using fractional Fourier transform,” Opt. Commun. 279, 35–42 (2007).
[CrossRef]

N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
[CrossRef]

J. F. Barerra, R. Henao, and R. Torroba, “Optical encryption method using toroidal zone plate,” Opt. Commun. 248, 35–40(2005).
[CrossRef]

J. F. Barerra, R. Henao, and R. Torroba, “Fault tolerances using toroidal zone plate encryption,” Opt. Commun. 256, 489–494 (2005).
[CrossRef]

L. Chen and D. Zhao, “Color image encoding in dual fractional Fourier-wavelet domain with random phases,” Opt. Commun. 282, 3433–3438 (2009).
[CrossRef]

M. Joshi, C. Shakher, and K. Singh, “Fractional Fourier transform based image multiplexing and encryption technique for four-color images using input images as keys,” Opt. Commun. 283, 2496–2505 (2010).
[CrossRef]

H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Opt. Commun. 284, 3895–3903 (2011).
[CrossRef]

N. Zhou, Y. Wang, L. Gong, H. He, and J. Wu, “Novel single channel color image encryption based on chaos and fractional Fourier transform,” Opt. Commun. 284, 2789–2796 (2011).
[CrossRef]

H.-E. Hwang, “Optical color image encryption based on the wavelength multiplexing using cascaded phase-only masks in Fresnel transform domain,” Opt. Commun. 285, 567–573 (2012).
[CrossRef]

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

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

Opt. Eng. (2)

W. Qin, X. Peng, X. Meng, and B. Gao, “Universal and special keys based on phase-truncated Fourier transform,” Opt. Eng. 50, 080501 (2011).
[CrossRef]

M. Joshi and K. Singh, “Simultaneous encryption of a color and a gray-scale image using byte-level encoding based on single-channel double random-phase encoding architecture in fractional Fourier domain,” Opt. Eng. 50, 047007 (2011).
[CrossRef]

Opt. Express (6)

Opt. Laser Technol. (2)

X. Deng and D. Zhao, “Single channel color image encryption based on asymmetric cryptosystem,” Opt. Laser Technol. 44, 136–140 (2012).
[CrossRef]

C. J. Tay, C. Quan, W. Chen, and Y. Fu, “Color image encryption based on interference and virtual optics,” Opt. Laser Technol. 42, 409–415 (2010).
[CrossRef]

Opt. Lett. (11)

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

X. Peng, H. Wie, and P. Zhang, “Asymmetric cryptography based on wavefront sensing,” Opt. Lett. 31, 3579–3581 (2006).
[CrossRef]

W. Qin and X. Peng, “Asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Lett. 35, 118–120(2010).
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E. Pérez-Cabré, M. Cho, and B. Javidi, “Information authentication using photon-counting double-random-phase encrypted images,” Opt. Lett. 36, 22–24 (2011).
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P. Clemente, V. Durán, V. Torres-Company, E. Tajahuerce, and J. Lancis, “Optical encryption based on computational ghost imaging,” Opt. Lett. 35, 2391–2393 (2010).
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F. Xu, R. C. Tyan, Y. Fainman, and J. E. Ford, “Single-substrate birefringent computer generated holograms,” Opt. Lett. 21, 516–518 (1996).
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J. E. Ford, F. Xu, K. Urquhart, and Y. Fainman, “Polarization-selective computer-generated holograms,” Opt. Lett. 18, 456–458 (1993).
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A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, “Vulnerability to chosen-cyphertext attacks of the optical encryption schemes based on double random phase keys,” Opt. Lett. 30, 1644–1646 (2005).
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X. Peng, P. Chang, H. Wei, and B. Yu, “Known plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
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P. Memmolo, A. Finizio, M. Paturzo, P. Ferraro, and B. Javidi, “Multi-wavelength digital holography: reconstruction, synthesis and display of holograms using adaptive transformation,” Opt. Lett. 37, 1445–1447 (2012).
[CrossRef]

Opt. Rev. (1)

M. Joshi, C. Shakher, and K. Singh, “Phase image encryption of colored images using double random phase encoding techniques in HSV color space,” Opt. Rev. 16, 511–516 (2009).
[CrossRef]

Optik (1)

X. Li and D. Zhao, “Optical color image encryption with redefined fractional Hartley transform,” Optik 121, 673–677 (2010).
[CrossRef]

Optoelectron. Lett. (1)

Q.-p. Yuan, X.-p. Yang, L.-j. Gao, and H.-c. Zhai, “Color image single-channel encryption based on tricolor grating theory,” Optoelectron. Lett. 5, 0147–0149 (2009).
[CrossRef]

Other (2)

Y. He, Y. Cao, and X. Lu, “Color image encryption based on orthogonal composite grating and double random phase encoding technique,” Optik (2012) (in press).

W. Stallings, Cryptography and Network Security: Principles and Practice, 5th ed. (Prentice Hall, 2011).

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Figures (9)

Fig. 1.
Fig. 1.

Block diagram for proposed color cryptosystem: (a) encryption scheme and (b) decryption scheme. PSDOE, polarization selective diffractive optical element; AT, amplitude truncation; PT, phase truncation; FRT, fractional Fourier transform.

Fig. 2.
Fig. 2.

Proposed optical setup for decryption. d and d1, distance parameters; SLM, spatial light modulator; CCD, charge-coupled device camera; PC, personal computer.

Fig. 3.
Fig. 3.

(a) Color image of baboon used for encryption. Color components of the baboon image; (b) red component; (c) green component; and (d) blue component.

Fig. 4.
Fig. 4.

Analytically generated zone plates used for encryption: (a) SPM1; (b) SPM2; and (c) SPM3.

Fig. 5.
Fig. 5.

(a) Combined image obtained after convolution of r, g, and b color components; (b) encrypted image; and (c) analytically generated PSDOE.

Fig. 6.
Fig. 6.

Decrypted image components obtained after using all correct keys. (a) red component; (b) green component; (c) blue component; (d) full-color image of baboon.

Fig. 7.
Fig. 7.

Decrypted image components obtained after using (a) correct SPMs but no decryption keys; (b) decryption keys generated with wrong SPMs; (c) wrong FRT order; and (d) PSDOE generated with changed parameters.

Fig. 8.
Fig. 8.

(a) Plot between MSE and focal length of the used SPM; (b) plot between MSE and radius of used SPM; and (c) plot between MSE and wavelength.

Fig. 9.
Fig. 9.

(a) Decrypted image obtained after applying special attack; (b) plot of MSE values between El(ξ,η) and encrypted image E(ξ,η) and the number of iterations, and (c) plot of MSE values between estimated value em(u,v) and convolved image e(u,v), and the number of iterations.

Equations (42)

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S(x,y)=t0cos(πx2+y2λf),
frm(x,y)=fr(x,y)Sr(x,y)fgm(x,y)=fg(x,y)Sg(x,y)fbm(x,y)=fb(x,y)Sb(x,y)}.
c(x,y)=frm(x,y)fgm(x,y)fbm(x,y),
F(u,v)=Kc(x,y)×exp[jπx2+y2+u2+v2tanα2jπxyuvsinα]dxdy,
F(u,v)=Frm(u,v)×Fgm(u,v)×Fbm(u,v),
k(u,v)=AT[F(u,v)],
e(u,v)=PT[F(u,v)],
e(u,v)=|Frm(u,v)|·|Fgm(u,v)|·|Fbm(u,v)|.
kr=AT[Frm(u,v)]|Fgm(u,v)|×|Fbm(u,v)|,
kg=AT[Fgm(u,v)]|Frm(u,v))|×|Fbm(u,v)|,
kb=AT[Fbm(u,v)]|Frm(u,v)|×|Fgm(u,v)|.
e(ξ,η)=Iβ[e(u,v)×S(u,v)].
k1(ξ,η)=AT[e(ξ,η)],
E(ξ,η)=PT[e(ξ,η)].
E(ξ,η)=[E(ξ,η)×S(ξ,η)].
E(ξ,η)=Iγ[exp[iRo(x,y)]+exp[iRe(x,y)]].
exp[iRo(x,y)]+exp[iRe(x,y)]=Iγ[E(ξ,η)].
D=Iγ[E(ξ,η)].
exp[iRe(x,y)]=Dexp[iRo(x,y)].
|Dexp[iRo(x,y)]|2={Dexp[iRo(x,y)]}{Dexp[iRo(x,y)]}*=1.
Ro(x,y)=arg(D)+cos1{|D|2},
Re(x,y)=arg{Dexp(iRo)},
ϕo(x,y)=2πλ(no1)t,
ϕe(x,y)=2πλ(ne1)t,
ϕo(x,y)=Ro(x,y)+2pπ,
ϕe(x,y)=Re(x,y)+2qπ,
Ro(x,y)+2pπ=2πλ(no1)t,
Re(x,y)+2qπ=2πλ(ne1)t.
Ro(x,y)+2pπ+δp=2πλ(no1)t,
Re(x,y)+2qπ+δq=2πλ(ne1)t.
t=λ2π(no1)×[Ro(x,y)+2pπ+δp]=λ2π(ne1)×[Re(x,y)+2pπ+δq].
E(ξ,η)={E(ξ,η)×S(ξ,η)}.
e(u,v)=PT{Iβ[E(ξ,η)×k1(ξ,η)]}.
fi(x,y)=Iα[e(u,v)×ki(u,v)].
MSE=x=0N1y=0N1[f(x,y)d(x,y)]2N×N,
MSErgb=MSEr+MSEg+MSEb3,
en(u,v)=PT{Iσ[E(ξ,η)×Sn(ξ,η)]},
En+1(ξ,η)=PT{Iσ[en(u,v)×S(u,v)]},
Sn+1(ξ,η)=AT{Iσ[en(u,v)×S(u,v)]},
fin(x,y)=PT{Iσ[e0(u,v)×Sn(u,v)]},
ein+1(u,v)=PT{Iσ[fin(x,y)×Si(x,y)]},
kin+1(u,v)=AT{Iσ[fin(x,y)×Si(x,y)]},

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