Abstract

A novel multiple-image encryption scheme using the nonlinear iterative phase retrieval algorithm in the gyrator transform domain under the illumination of an optical vortex beam is proposed. In order to increase the randomness, the chaotic structured phase mask based on the logistic map, Fresnel zone plate and radial Hilbert mask is proposed. With the help of two chaotic phase masks, each plain image is encoded into two phase-only masks that are considered as the private keys by using the iterative phase retrieval process in the gyrator domain. Then, the second keys of all plain images are modulated into the ciphertext, which has the stationary white noise distribution. Due to the use of the chaotic structured phase masks, the problem of axis alignment in the optical setup can easily be solved. Two private keys are directly relative to the plain images, which makes that the scheme has high resistance against various potential attacks. Moreover, the use of the vortex beam that can integrates more system parameters as the additional keys into one phase mask can improve the security level of the cryptosystem, which makes the key space enlarged widely. Simulation results are given to verify the feasibility and robustness of the proposed encryption scheme.

© 2016 Optical Society of America

Full Article  |  PDF Article
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References

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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref] [PubMed]
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    [Crossref]
  38. H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
    [Crossref]
  39. Original images: http://sipi.usc.edu/database/database.php .
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    [Crossref]

2015 (11)

X. W. Li and I. K. Lee, “Robust copyright protection using multiple ownership watermarks,” Opt. Express 23(3), 3035–3046 (2015).
[Crossref] [PubMed]

N. Rawat, B. Kim, I. Muniraj, G. Situ, and B. G. Lee, “Compressive sensing based robust multispectral double-image encryption,” Appl. Opt. 54(7), 1782–1793 (2015).
[Crossref]

D. Maluenda, A. Carnicer, R. Martínez-Herrero, I. Juvells, and B. Javidi, “Optical encryption using photon-counting polarimetric imaging,” Opt. Express 23(2), 655–666 (2015).
[Crossref] [PubMed]

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and H. Yu, “Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains,” Opt. Lasers Eng. 66, 1–9 (2015).
[Crossref]

L. Sui, K. Duan, and J. Liang, “Double-image encryption based on discrete multiple-parameter fractional angular transform and two-coupled logistic maps,” Opt. Commun. 343, 140–149 (2015).
[Crossref]

N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Opt. Commun. 343, 10–21 (2015).
[Crossref]

A. Alfalou and C. Brosseau, “Chapter two – Recent advances in optical image processing,” Progress in Opt. 60, 119–262 (2015).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, H. Yu, and L. B. Zhang, “An efficient image encryption scheme using gray code based permutation approach,” Opt. Lasers Eng. 67, 191–204 (2015).
[Crossref]

X. Wang, L. Liu, and Y. Zhang, “A novel chaotic block image encryption algorithm based on dynamic random growth technique,” Opt. Lasers Eng. 66, 10–18 (2015).
[Crossref]

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

2014 (7)

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

S. Vashisth, H. Singh, A. K. Yadav, and K. Singh, “Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval,” Optik (Stuttg.) 125(18), 5309–5315 (2014).
[Crossref]

X. Wang, W. Chen, and X. Chen, “Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding,” Opt. Express 22(19), 22981–22995 (2014).
[Crossref] [PubMed]

J. Li, J. Li, L. Shen, Y. Pan, and R. Li, “Optical image encryption and hiding based on a modified Mach-Zehnder interferometer,” Opt. Express 22(4), 4849–4860 (2014).
[Crossref] [PubMed]

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

L. Sui, K. Duan, J. Liang, and X. Hei, “Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps,” Opt. Express 22(9), 10605–10621 (2014).
[Crossref] [PubMed]

M. Zafari, R. Kheradmand, and S. Ahmadi-Kandjani, “Optical encryption with selective computational ghost imaging,” J. Opt. 16(10), 105405 (2014).
[Crossref]

2013 (7)

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[Crossref] [PubMed]

S. Liansheng, X. Meiting, and T. Ailing, “Multiple-image encryption based on phase mask multiplexing in fractional Fourier transform domain,” Opt. Lett. 38(11), 1996–1998 (2013).
[Crossref] [PubMed]

S. K. Rajput and N. K. Nishchal, “Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform,” Appl. Opt. 52(4), 871–878 (2013).
[Crossref] [PubMed]

S. K. Rajput and N. K. Nishchal, “Image encryption using polarized light encoding and amplitude and phase truncation in the Fresnel domain,” Appl. Opt. 52(18), 4343–4352 (2013).
[Crossref] [PubMed]

R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 524–532 (2013).

S. Yuan, T. Zhang, X. Zhou, X. Liu, and M. Liu, “Optical authentication technique based on interference image hiding system and phase-only correlation,” Opt. Commun. 304, 129–135 (2013).
[Crossref]

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

2012 (4)

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285(21–22), 4294–4301 (2012).
[Crossref]

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51(6), 686–691 (2012).
[Crossref] [PubMed]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical color-image encryption and synthesis using coherent diffractive imaging in the Fresnel domain,” Opt. Express 20(4), 3853–3865 (2012).
[Crossref] [PubMed]

2011 (2)

2010 (1)

2009 (2)

A. Alfalou and A. Mansour, “Double random phase encryption scheme to multiplex and simultaneous encode multiple images,” Appl. Opt. 48(31), 5933–5947 (2009).
[Crossref] [PubMed]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

2008 (1)

2006 (2)

2005 (1)

1995 (1)

Abuturab, R.

R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 524–532 (2013).

Ahmadi-Kandjani, S.

M. Zafari, R. Kheradmand, and S. Ahmadi-Kandjani, “Optical encryption with selective computational ghost imaging,” J. Opt. 16(10), 105405 (2014).
[Crossref]

Ailing, T.

Alfalou, A.

A. Alfalou and C. Brosseau, “Chapter two – Recent advances in optical image processing,” Progress in Opt. 60, 119–262 (2015).
[Crossref]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

A. Alfalou and A. Mansour, “Double random phase encryption scheme to multiplex and simultaneous encode multiple images,” Appl. Opt. 48(31), 5933–5947 (2009).
[Crossref] [PubMed]

Arcos, S.

Brosseau, C.

A. Alfalou and C. Brosseau, “Chapter two – Recent advances in optical image processing,” Progress in Opt. 60, 119–262 (2015).
[Crossref]

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

Carnicer, A.

Chen, J. X.

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and H. Yu, “Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains,” Opt. Lasers Eng. 66, 1–9 (2015).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, H. Yu, and L. B. Zhang, “An efficient image encryption scheme using gray code based permutation approach,” Opt. Lasers Eng. 67, 191–204 (2015).
[Crossref]

Chen, L.

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

Chen, W.

Chen, X.

Duan, K.

L. Sui, K. Duan, and J. Liang, “Double-image encryption based on discrete multiple-parameter fractional angular transform and two-coupled logistic maps,” Opt. Commun. 343, 140–149 (2015).
[Crossref]

L. Sui, K. Duan, J. Liang, and X. Hei, “Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps,” Opt. Express 22(9), 10605–10621 (2014).
[Crossref] [PubMed]

Fu, C.

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and H. Yu, “Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains,” Opt. Lasers Eng. 66, 1–9 (2015).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, H. Yu, and L. B. Zhang, “An efficient image encryption scheme using gray code based permutation approach,” Opt. Lasers Eng. 67, 191–204 (2015).
[Crossref]

Gao, Q.

Ge, F.

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

Hei, X.

Javidi, B.

Joseph, J.

Juvells, I.

Kheradmand, R.

M. Zafari, R. Kheradmand, and S. Ahmadi-Kandjani, “Optical encryption with selective computational ghost imaging,” J. Opt. 16(10), 105405 (2014).
[Crossref]

Kim, B.

Kumar, P.

Lee, B. G.

Lee, I. K.

Li, H.

N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Opt. Commun. 343, 10–21 (2015).
[Crossref]

Y. Shi, T. Li, Y. Wang, Q. Gao, S. Zhang, and H. Li, “Optical image encryption via ptychography,” Opt. Lett. 38(9), 1425–1427 (2013).
[Crossref] [PubMed]

Li, J.

Li, R.

Li, T.

Li, X. W.

Liang, J.

L. Sui, K. Duan, and J. Liang, “Double-image encryption based on discrete multiple-parameter fractional angular transform and two-coupled logistic maps,” Opt. Commun. 343, 140–149 (2015).
[Crossref]

L. Sui, K. Duan, J. Liang, and X. Hei, “Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps,” Opt. Express 22(9), 10605–10621 (2014).
[Crossref] [PubMed]

Liansheng, S.

Liu, H.

H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Opt. Commun. 284(16–17), 3895–3903 (2011).
[Crossref]

Liu, J.

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

Liu, L.

X. Wang, L. Liu, and Y. Zhang, “A novel chaotic block image encryption algorithm based on dynamic random growth technique,” Opt. Lasers Eng. 66, 10–18 (2015).
[Crossref]

Liu, M.

S. Yuan, T. Zhang, X. Zhou, X. Liu, and M. Liu, “Optical authentication technique based on interference image hiding system and phase-only correlation,” Opt. Commun. 304, 129–135 (2013).
[Crossref]

Liu, X.

S. Yuan, T. Zhang, X. Zhou, X. Liu, and M. Liu, “Optical authentication technique based on interference image hiding system and phase-only correlation,” Opt. Commun. 304, 129–135 (2013).
[Crossref]

Maluenda, D.

Mansour, A.

Mao, H.

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

Martínez-Herrero, R.

Mehra, I.

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

Meiting, X.

Montes-Usategui, M.

Muniraj, I.

Nishchal, N. K.

Pan, S.

N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Opt. Commun. 343, 10–21 (2015).
[Crossref]

Pan, Y.

Peng, X.

Qin, W.

Rajput, S. K.

Rawat, N.

Refregier, P.

Shen, L.

Sheppard, C. J. R.

Shi, Y.

Singh, H.

H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

S. Vashisth, H. Singh, A. K. Yadav, and K. Singh, “Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval,” Optik (Stuttg.) 125(18), 5309–5315 (2014).
[Crossref]

Singh, K.

H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

S. Vashisth, H. Singh, A. K. Yadav, and K. Singh, “Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval,” Optik (Stuttg.) 125(18), 5309–5315 (2014).
[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(13), 1805–1811 (2011).
[Crossref] [PubMed]

Situ, G.

Sui, L.

L. Sui, K. Duan, and J. Liang, “Double-image encryption based on discrete multiple-parameter fractional angular transform and two-coupled logistic maps,” Opt. Commun. 343, 140–149 (2015).
[Crossref]

L. Sui, K. Duan, J. Liang, and X. Hei, “Asymmetric double-image encryption based on cascaded discrete fractional random transform and logistic maps,” Opt. Express 22(9), 10605–10621 (2014).
[Crossref] [PubMed]

Vashisth, S.

H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

S. Vashisth, H. Singh, A. K. Yadav, and K. Singh, “Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval,” Optik (Stuttg.) 125(18), 5309–5315 (2014).
[Crossref]

Wang, B.

Wang, D.

N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Opt. Commun. 343, 10–21 (2015).
[Crossref]

Wang, Q.

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285(21–22), 4294–4301 (2012).
[Crossref]

Wang, X.

X. Wang, L. Liu, and Y. Zhang, “A novel chaotic block image encryption algorithm based on dynamic random growth technique,” Opt. Lasers Eng. 66, 10–18 (2015).
[Crossref]

X. Wang, W. Chen, and X. Chen, “Fractional Fourier domain optical image hiding using phase retrieval algorithm based on iterative nonlinear double random phase encoding,” Opt. Express 22(19), 22981–22995 (2014).
[Crossref] [PubMed]

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51(6), 686–691 (2012).
[Crossref] [PubMed]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Opt. Commun. 284(16–17), 3895–3903 (2011).
[Crossref]

Wang, Y.

Wei, H.

Wen, J.

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

Xiao, D.

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

Yadav, A. K.

H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

S. Vashisth, H. Singh, A. K. Yadav, and K. Singh, “Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval,” Optik (Stuttg.) 125(18), 5309–5315 (2014).
[Crossref]

Yu, B.

Yu, H.

J. X. Chen, Z. L. Zhu, C. Fu, H. Yu, and L. B. Zhang, “An efficient image encryption scheme using gray code based permutation approach,” Opt. Lasers Eng. 67, 191–204 (2015).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and H. Yu, “Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains,” Opt. Lasers Eng. 66, 1–9 (2015).
[Crossref]

Yuan, S.

S. Yuan, T. Zhang, X. Zhou, X. Liu, and M. Liu, “Optical authentication technique based on interference image hiding system and phase-only correlation,” Opt. Commun. 304, 129–135 (2013).
[Crossref]

Zafari, M.

M. Zafari, R. Kheradmand, and S. Ahmadi-Kandjani, “Optical encryption with selective computational ghost imaging,” J. Opt. 16(10), 105405 (2014).
[Crossref]

Zhang, L. B.

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and H. Yu, “Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains,” Opt. Lasers Eng. 66, 1–9 (2015).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, H. Yu, and L. B. Zhang, “An efficient image encryption scheme using gray code based permutation approach,” Opt. Lasers Eng. 67, 191–204 (2015).
[Crossref]

Zhang, P.

Zhang, S.

Zhang, T.

S. Yuan, T. Zhang, X. Zhou, X. Liu, and M. Liu, “Optical authentication technique based on interference image hiding system and phase-only correlation,” Opt. Commun. 304, 129–135 (2013).
[Crossref]

Zhang, Y.

X. Wang, L. Liu, and Y. Zhang, “A novel chaotic block image encryption algorithm based on dynamic random growth technique,” Opt. Lasers Eng. 66, 10–18 (2015).
[Crossref]

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

Y. Zhang and B. Wang, “Optical image encryption based on interference,” Opt. Lett. 33(21), 2443–2445 (2008).
[Crossref] [PubMed]

Zhao, D.

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

X. Wang and D. Zhao, “Optical image hiding with silhouette removal based on the optical interference principle,” Appl. Opt. 51(6), 686–691 (2012).
[Crossref] [PubMed]

Zhou, N.

N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Opt. Commun. 343, 10–21 (2015).
[Crossref]

Zhou, X.

S. Yuan, T. Zhang, X. Zhou, X. Liu, and M. Liu, “Optical authentication technique based on interference image hiding system and phase-only correlation,” Opt. Commun. 304, 129–135 (2013).
[Crossref]

Zhou, Z.

N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Opt. Commun. 343, 10–21 (2015).
[Crossref]

Zhu, Z. L.

J. X. Chen, Z. L. Zhu, C. Fu, H. Yu, and L. B. Zhang, “An efficient image encryption scheme using gray code based permutation approach,” Opt. Lasers Eng. 67, 191–204 (2015).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and H. Yu, “Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains,” Opt. Lasers Eng. 66, 1–9 (2015).
[Crossref]

Adv. Opt. Photonics (2)

A. Alfalou and C. Brosseau, “Optical image compression and encryption methods,” Adv. Opt. Photonics 1(3), 589–636 (2009).
[Crossref]

W. Chen, B. Javidi, and X. Chen, “Advances in optical security systems,” Adv. Opt. Photonics 6(2), 120–155 (2014).
[Crossref]

Appl. Opt. (6)

J. Opt. (1)

M. Zafari, R. Kheradmand, and S. Ahmadi-Kandjani, “Optical encryption with selective computational ghost imaging,” J. Opt. 16(10), 105405 (2014).
[Crossref]

Opt. Commun. (7)

L. Sui, K. Duan, and J. Liang, “Double-image encryption based on discrete multiple-parameter fractional angular transform and two-coupled logistic maps,” Opt. Commun. 343, 140–149 (2015).
[Crossref]

N. Zhou, H. Li, D. Wang, S. Pan, and Z. Zhou, “Image compression and encryption scheme based on 2D compressive sensing and fractional Mellin transform,” Opt. Commun. 343, 10–21 (2015).
[Crossref]

Q. Wang, “Optical image encryption with silhouette removal based on interference and phase blend processing,” Opt. Commun. 285(21–22), 4294–4301 (2012).
[Crossref]

S. Yuan, T. Zhang, X. Zhou, X. Liu, and M. Liu, “Optical authentication technique based on interference image hiding system and phase-only correlation,” Opt. Commun. 304, 129–135 (2013).
[Crossref]

H. Liu and X. Wang, “Color image encryption using spatial bit-level permutation and high-dimension chaotic system,” Opt. Commun. 284(16–17), 3895–3903 (2011).
[Crossref]

X. Wang and D. Zhao, “A special attack on the asymmetric cryptosystem based on phase-truncated Fourier transforms,” Opt. Commun. 285(6), 1078–1081 (2012).
[Crossref]

L. Chen, J. Liu, J. Wen, H. Mao, F. Ge, and D. Zhao, “Pseudo color image encryption based on three-beams interference principle and common vector composition,” Opt. Commun. 338, 110–116 (2015).
[Crossref]

Opt. Express (6)

Opt. Laser Technol. (2)

R. Abuturab, “Color information security system using Arnold transform and double structured phase encoding in gyrator transform domain,” Opt. Laser Technol. 45, 524–532 (2013).

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

Opt. Lasers Eng. (5)

J. X. Chen, Z. L. Zhu, C. Fu, H. Yu, and L. B. Zhang, “An efficient image encryption scheme using gray code based permutation approach,” Opt. Lasers Eng. 67, 191–204 (2015).
[Crossref]

X. Wang, L. Liu, and Y. Zhang, “A novel chaotic block image encryption algorithm based on dynamic random growth technique,” Opt. Lasers Eng. 66, 10–18 (2015).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and H. Yu, “Analysis and improvement of a double-image encryption scheme using pixel scrambling technique in gyrator domains,” Opt. Lasers Eng. 66, 1–9 (2015).
[Crossref]

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

H. Singh, A. K. Yadav, S. Vashisth, and K. Singh, “Double phase-image encryption using gyrator transforms and structured phase mask in the frequency plane,” Opt. Lasers Eng. 67, 145–156 (2015).
[Crossref]

Opt. Lett. (8)

Optik (Stuttg.) (1)

S. Vashisth, H. Singh, A. K. Yadav, and K. Singh, “Image encryption using fractional Mellin transform, structured phase filters, and phase retrieval,” Optik (Stuttg.) 125(18), 5309–5315 (2014).
[Crossref]

Progress in Opt. (1)

A. Alfalou and C. Brosseau, “Chapter two – Recent advances in optical image processing,” Progress in Opt. 60, 119–262 (2015).
[Crossref]

Other (1)

Original images: http://sipi.usc.edu/database/database.php .

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Figures (13)

Fig. 1
Fig. 1 (a) Generated SPM based on FZP, (b) generated SPM based on RHM, (c) generated SPM based on FZP and RHM and (d) the proposed chaotic SPM.
Fig. 2
Fig. 2 The optoelectronic setup of the decryption process.
Fig. 3
Fig. 3 The optoelectronic setup of the iterative phase retrieval process.
Fig. 4
Fig. 4 (a) Flowchart of encryption process and (b) Flowchart of the decryption process.
Fig. 5
Fig. 5 (a) Image “Lena”, (b) ciphertext and (c) decrypted “Lena”.
Fig. 6
Fig. 6 Decrypted “Lena” with (a) incorrectf, (b) incorrectλ, (c) incorrectP, (d) incorrect α 1 , (e) incorrect α 2 and (f) incorrect α 3 .
Fig. 7
Fig. 7 MSE versus the deviation of the (a) focal lengthf, (b) wavelengthλ, (c) transformation orderP, (d) rotation order α 1 , (e) rotation order α 2 and (f) rotation order α 3 .
Fig. 8
Fig. 8 (a) Decrypted “Lena” with the random P ^ i 1 ( x 1 , y 1 ) , (b) decrypted “Lena” with the random P ^ i 2 ( x 2 , y 2 ) , (c) decrypted image when the left 50% data of P ^ i 1 ( x 1 , y 1 ) is unknown, (d) decrypted image when the left 25%data of P ^ i 2 ( x 2 , y 2 ) is unknown.
Fig. 9
Fig. 9 Decrypted “Lena” with the coefficient: (a) k=0.4 (b) k=0.6 (c) k=0.8 (d) k=1.0 .
Fig. 10
Fig. 10 Ciphertext with (a) 25% occlusion, (b) 50% occlusion, (c) decrypted result from (a) and (d) decrypted result from (b).
Fig. 11
Fig. 11 (a) decrypted image with first group of fake keys, (b) decrypted image width second group of fake keys and (c) decrypted image with third group of fake keys.
Fig. 12
Fig. 12 (a) Horizontal correlation of “Lena”, (b) vertical correlation of “Lena”, (c) diagonal correlation of “Lena”, (d) horizontal correlation of ciphertext, (e) vertical correlation of ciphertext and (f) diagonal correlation of ciphertext.
Fig. 13
Fig. 13 Histogram of (a) ciphertext encrypted with images “Lena”, “Baboon” and “Zelda”, (b) first phase key of “Lena”, (c) second phase key of “Lena”, (d) ciphertext encrypted with images “Goldhill”, “Cameraman” and “Barb”, (e) first phase key of “Goldhill” and (f) second phase key of “Goldhill”.

Tables (1)

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Table 1 Correlation coefficients of the plain images and the ciphertext.

Equations (35)

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f o ( x o , y o )= G α [ f i ( x i , y i ) ]( x o , y o )= 1 | sinα | f( x i , y i ) K α ( x i , y i , x o , y o )d x i d y i ,
K α ( x i , y i , x o , y o )=exp( i2π ( x o y o + x i y i )cosα( x i y o + x o y i ) sinα ).
G α [f(x,y)]= G α+2π [f(x,y)].
G α { G β [f(x,y)]}= G α+β [f(x,y)].
x n+1 =p× x n ×(1 x n ),
R(x,y)=exp(j2π y i,j ),
F(r)=exp( j π λf r 2 ),
H(ρ,θ)=exp( jPθ ),
M(x,y)=F(r)×H(ρ,θ).
C(x,y)=exp{ j{ arg{ R(x,y) }×arg{ F(r) }×arg{ H(ρ,θ) } } },
G 0 ( x 0 , y 0 )= A 0 ( x 0 , y 0 )P( x 0 , y 0 ),
f i ( x,y )=| G α 3 { G α 2 { G α 1 { G 0 ( x 0 , y 0 ) } D i 1 ( x 1 , y 1 ) } D i 2 ( x 2 , y 2 ) } |,
G 1 ( x 1 , y 1 )= G α 1 { G 0 ( x 0 , y 0 ) }.
G 2 k ( x 2 , y 2 )= G α 2 { G 1 ( x 1 , y 1 ) C i 1,k ( x 1 , y 1 ) },
C 2 ( x 2 , y 2 )=exp{ jarg{ G 2 k ( x 2 , y 2 ) } },
G 3 k ( x,y )= G α 2 { | G 2 k ( x 2 , y 2 ) | C i 2,k ( x 2 , y 2 ) },
C 3 ( x,y )=exp{ jarg{ G 3 k ( x,y ) } }.
G ^ 2 k ( x 2 , y 2 )= G α 3 { f i (x,y) C 3 (x,y) }.
G ^ 1 k ( x 1 , y 1 )= G α 2 { | G ^ 2 k ( x 2 , y 2 ) | C 2 ( x 2 , y 2 ) }.
C i 1,k+1 ( x 1 , y 1 )=exp{ jarg{ G ^ 1 k ( x 1 , y 1 ) G 1 ( x 1 , y 1 ) } },
C i 2,k+1 ( x 2 , y 2 )=exp{ jarg{ G ^ 2 k ( x 2 , y 2 ) } }.
P i 1 ( x 1 , y 1 )= C i 1,k+1 ( x 1 , y 1 ),
G 2 ( x 2 , y 2 )= G α 2 { G 1 ( x 1 , y 1 ) P i 1 ( x 1 , y 1 ) },
C 2 ( x 2 , y 2 )=exp{ jarg{ G 2 ( x 2 , y 2 ) } },
P i 2 ( x 2 , y 2 )= C i 2,k+1 ( x 2 , y 2 )conj{ C 2 ( x 2 , y 2 ) },
f ^ i ( x,y )=| G α 3 { G 2 ( x 2 , y 2 ) P i 2 ( x 2 , y 2 ) } |.
CC= E{[f( x,y )E[f( x,y )]][ f ^ ( x,y )E[ f ^ ( x,y )]]} E{ [f( x,y )E[f( x,y )]] 2 E{ [ f ^ ( x,y )E[ f ^ ( x,y )]] 2
MSE= 0 M1 0 N1 [f( x,y ) f ^ ( x,y )] 2 M×N ,
Cipher( x 2 , y 2 )= k=1 N P k 2 ( x 2 , y 2 ) .
P ^ i 2 ( x 2 , y 2 )=exp{ j( k=1,ki N arg{ P k 2 ( x 2 , y 2 ) } ) }.
P ^ i 1 ( x 1 , y 1 )= P i 1 ( x 1 , y 1 ).
D i 1 ( x 1 , y 1 )= P ^ i 1 ( x 1 , y 1 ),
D i 2 ( x 2 , y 2 )=Cipher( x 2 , y 2 )conj{ P ^ i 2 ( x 2 , y 2 ) }.
C =C(1+kG),
Cor= i=1 N ( x i x ¯ )( y i y ¯ ) ( i=1 N ( x i x ¯ ) 2 )( i=1 N ( y i y ¯ ) 2 ) ,

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