Abstract

In this paper, the security of a cryptosystem based on phase truncation and a designed amplitude modulator (AM) is evaluated. In the cryptosystem, an undercover AM used as an additional key is added to modulate the amplitude information of the spectrum in the Fourier plane. Compared to the conventional phase-truncated Fourier transform (PTFT)-based cryptosystem, the security of the cryptosystem is improved by increasing the number of unknown keys. However, it is found that the designed AM is irrelative to the plaintext, and one of the parameters in the designed AM contributes less to the security enhancement of the cryptosystem due to low key sensitivity. Based on the analysis, a special attack containing two iterative processes is proposed to crack the cryptosystem, in which the known-plaintext-attack-based iterative process I with a specific normalization operator is used to retrieve the designed AM and the amplitude-phase-retrieval-technique-based iterative process II is used to retrieve the corresponding plaintext from the arbitrarily given ciphertext with the help of the retrieved AM. In addition, an inherent drawback widely existing in PTFT-based cryptosystems is reported for the first time: most information of the original image could be retrieved using two correct phase keys (or only the first phase key) generated in the encryption process, even without the corresponding ciphertext in PTFT-based cryptosystems. To address this issue, a security-enhanced cryptosystem is proposed in this paper. Numerical simulation is carried out to demonstrate the effectiveness and feasibility of the proposed attack and cryptosystem.

© 2019 Optical Society of America

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2018 (4)

Y. Xiong, C. Quan, and C. J. Tay, “Multiple image encryption scheme based on pixel exchange operation and vector decomposition,” Opt. Lasers Eng. 101, 113–121 (2018).
[Crossref]

Y. Xiong, A. He, and C. Quan, “Cryptoanalysis of an optical cryptosystem based on phase-truncated Fourier transform and nonlinear operations,” Opt. Commun. 428, 120–130 (2018).
[Crossref]

Y. Xiong, A. He, and C. Quan, “Security analysis of a double-image encryption technique based on an asymmetric algorithm,” J. Opt. Soc. Am. A 35, 320–326 (2018).
[Crossref]

Y. Xiong, A. He, and C. Quan, “Hybrid attack on an optical cryptosystem based on phase-truncated Fourier transforms and a random amplitude mask,” Appl. Opt. 57, 6010–6016 (2018).
[Crossref]

2016 (3)

A. Sinha, “Nonlinear optical cryptosystem resistant to standard and hybrid attacks,” Opt. Lasers Eng. 81, 79–86 (2016).
[Crossref]

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Z. Liu, C. Shen, J. Tan, and S. Liu, “A recovery method of double random phase encoding system with a parallel phase retrieval,” IEEE Photon. 8, 1–7 (2016).
[Crossref]

2015 (2)

Y. Wang, C. Quan, and C. J. Tay, “Optical color image encryption without information disclosure using phase-truncated Fresnel transform and a random amplitude mask,” Opt. Commun. 344, 147–155 (2015).
[Crossref]

X. Wang, W. Chen, and X. Chen, “Optical information authentication using compressed double-random-phase-encoded images and quick-response codes,” Opt. Express 23, 6239–6253 (2015).
[Crossref]

2014 (7)

X. Wang, Y. Chen, C. Dai, and D. Zhao, “Discussion and a new attack of the optical asymmetric cryptosystem based on phase-truncated Fourier transform,” Appl. Opt. 53, 208–213 (2014).
[Crossref]

A. Markman and B. Javidi, “Full-phase photon-counting double-random-phase encryption,” J. Opt. Soc. Am. A 31, 394–403 (2014).
[Crossref]

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

B. Deepan, C. Quan, Y. Wang, and C. J. Tay, “Multiple-image encryption by space multiplexing based on compressive sensing and the double-random phase-encoding technique,” Appl. Opt. 53, 4539–4547 (2014).
[Crossref]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude- and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
[Crossref]

W. Chen and X. Chen, “Double random phase encoding using phase reservation and compression,” J. Opt. 16, 025402 (2014).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and Y. Zhang, “Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding,” J. Opt. 16, 125403 (2014).
[Crossref]

2013 (8)

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (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, 472–480 (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, “Known-plaintext attack-based optical cryptosystem using phase-truncated Fresnel transform,” Appl. Opt. 52, 871–878 (2013).
[Crossref]

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, 4343–4352 (2013).
[Crossref]

A. M. Elshamy, A. N. Rashed, A. E. Mohamed, O. S. Faragalla, Y. Mu, S. A. Alshebeili, and F. A. EI-Samie, “Optical image encryption based on chaotic baker map and double random phase encoding,” J. Lightwave Technol. 31, 2533–2539 (2013).
[Crossref]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (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]

2012 (5)

Z. Zhong, J. Chang, M. Shan, and B. Hao, “Double image encryption using double pixel scrambling and random phase encoding,” Opt. Commun. 285, 582–588 (2012).
[Crossref]

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[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]

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]

M. R. Abuturab, “Color information cryptosystem based on optical superposition principle and phase-truncated gyrator transform,” Appl. Opt. 51, 7994–8002 (2012).
[Crossref]

2011 (3)

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284, 4441–4445 (2011).
[Crossref]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284, 148–152 (2011).
[Crossref]

X. Wang and D. Zhao, “Security enhancement of a phase-truncation based image encryption algorithm,” Appl. Opt. 50, 6645–6651 (2011).
[Crossref]

2010 (4)

2009 (3)

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

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A 11, 075402 (2009).
[Crossref]

2006 (2)

2002 (1)

1995 (1)

1979 (1)

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man, Cybern. 9, 62–66 (1979).
[Crossref]

Abril, H. C.

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[Crossref]

Abuturab, M. R.

Ahmad, M. A.

Alfalou, A.

Alshebeili, S. A.

Barrera, J. F.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Brosseau, C.

Carnicer, A.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Chang, H. T.

Chang, J.

Z. Zhong, J. Chang, M. Shan, and B. Hao, “Double image encryption using double pixel scrambling and random phase encoding,” Opt. Commun. 285, 582–588 (2012).
[Crossref]

Chen, G.

Chen, J. X.

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and Y. Zhang, “Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding,” J. Opt. 16, 125403 (2014).
[Crossref]

Chen, W.

Chen, X.

Chen, Y.

Cho, M.

Dai, C.

Deepan, B.

Deng, X.

Ding, X.

EI-Samie, F. A.

Elshamy, A. M.

Faragalla, O. S.

Fu, C.

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and Y. Zhang, “Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding,” J. Opt. 16, 125403 (2014).
[Crossref]

Guo, Q.

Hao, B.

Z. Zhong, J. Chang, M. Shan, and B. Hao, “Double image encryption using double pixel scrambling and random phase encoding,” Opt. Commun. 285, 582–588 (2012).
[Crossref]

He, A.

He, W.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

Javidi, B.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

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

A. Markman and B. Javidi, “Full-phase photon-counting double-random-phase encryption,” J. Opt. Soc. Am. A 31, 394–403 (2014).
[Crossref]

M. Cho and B. Javidi, “Three-dimensional photon counting double-random-phase encryption,” Opt. Lett. 38, 3198–3201 (2013).
[Crossref]

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[Crossref]

Y. Rivenson, A. Stern, and B. Javidi, “Single exposure super-resolution compressive imaging by double phase encoding,” Opt. Express 18, 15094–15103 (2010).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[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]

Kuo, C. J.

Li, S.

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[Crossref]

Liu, S.

Z. Liu, C. Shen, J. Tan, and S. Liu, “A recovery method of double random phase encoding system with a parallel phase retrieval,” IEEE Photon. 8, 1–7 (2016).
[Crossref]

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[Crossref]

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).
[Crossref]

Liu, W.

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[Crossref]

Liu, Z.

Z. Liu, C. Shen, J. Tan, and S. Liu, “A recovery method of double random phase encoding system with a parallel phase retrieval,” IEEE Photon. 8, 1–7 (2016).
[Crossref]

Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[Crossref]

Z. Liu, Q. Guo, L. Xu, M. A. Ahmad, and S. Liu, “Double image encryption by using iterative random binary encoding in gyrator domains,” Opt. Express 18, 12033–12043 (2010).
[Crossref]

Lu, W. C.

Markman, A.

Matoba, O.

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Mehra, I.

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude- and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
[Crossref]

Millan, M. S.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Mohamed, A. E.

Mu, Y.

Nishchal, N. K.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude- and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
[Crossref]

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, 4343–4352 (2013).
[Crossref]

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

Nomura, T.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

Obi, T.

Ohyama, N.

Otsu, N.

N. Otsu, “A threshold selection method from gray-level histograms,” IEEE Trans. Syst. Man, Cybern. 9, 62–66 (1979).
[Crossref]

Peng, X.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

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

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A 11, 075402 (2009).
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W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A 11, 075402 (2009).
[Crossref]

Quan, C.

Y. Xiong, C. Quan, and C. J. Tay, “Multiple image encryption scheme based on pixel exchange operation and vector decomposition,” Opt. Lasers Eng. 101, 113–121 (2018).
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Y. Xiong, A. He, and C. Quan, “Cryptoanalysis of an optical cryptosystem based on phase-truncated Fourier transform and nonlinear operations,” Opt. Commun. 428, 120–130 (2018).
[Crossref]

Y. Xiong, A. He, and C. Quan, “Hybrid attack on an optical cryptosystem based on phase-truncated Fourier transforms and a random amplitude mask,” Appl. Opt. 57, 6010–6016 (2018).
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Z. Liu, C. Shen, J. Tan, and S. Liu, “A recovery method of double random phase encoding system with a parallel phase retrieval,” IEEE Photon. 8, 1–7 (2016).
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A. Sinha, “Nonlinear optical cryptosystem resistant to standard and hybrid attacks,” Opt. Lasers Eng. 81, 79–86 (2016).
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Y. Xiong, C. Quan, and C. J. Tay, “Multiple image encryption scheme based on pixel exchange operation and vector decomposition,” Opt. Lasers Eng. 101, 113–121 (2018).
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Torroba, R.

B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
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Y. Xiong, C. Quan, and C. J. Tay, “Multiple image encryption scheme based on pixel exchange operation and vector decomposition,” Opt. Lasers Eng. 101, 113–121 (2018).
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Zhong, Z.

Z. Zhong, J. Chang, M. Shan, and B. Hao, “Double image encryption using double pixel scrambling and random phase encoding,” Opt. Commun. 285, 582–588 (2012).
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Zhu, Z. L.

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and Y. Zhang, “Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding,” J. Opt. 16, 125403 (2014).
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IEEE Photon. (1)

Z. Liu, C. Shen, J. Tan, and S. Liu, “A recovery method of double random phase encoding system with a parallel phase retrieval,” IEEE Photon. 8, 1–7 (2016).
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B. Javidi, A. Carnicer, M. Yamaguchi, T. Nomura, E. Perez-Cabre, M. S. Millan, N. K. Nishchal, R. Torroba, J. F. Barrera, W. He, and X. Peng, “Roadmap on optical security,” J. Opt. 18, 083001 (2016).
[Crossref]

J. X. Chen, Z. L. Zhu, C. Fu, L. B. Zhang, and Y. Zhang, “Cryptanalysis and improvement of an optical image encryption scheme using a chaotic Baker map and double random phase encoding,” J. Opt. 16, 125403 (2014).
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W. Chen and X. Chen, “Double random phase encoding using phase reservation and compression,” J. Opt. 16, 025402 (2014).
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E. Perez-Cabre, H. C. Abril, M. S. Millan, and B. Javidi, “Photon-counting double-random-phase encoding for secure image verification and retrieval,” J. Opt. 14, 094001 (2012).
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J. Opt. A (1)

W. Qin and X. Peng, “Vulnerability to known-plaintext attack of optical encryption schemes based on two fractional Fourier transform order keys and double random phase keys,” J. Opt. A 11, 075402 (2009).
[Crossref]

J. Opt. Soc. Am. A (2)

Opt. Commun. (6)

Z. Zhong, J. Chang, M. Shan, and B. Hao, “Double image encryption using double pixel scrambling and random phase encoding,” Opt. Commun. 285, 582–588 (2012).
[Crossref]

X. Wang and D. Zhao, “Multiple-image encryption based on nonlinear amplitude-truncation and phase-truncation in Fourier domain,” Opt. Commun. 284, 148–152 (2011).
[Crossref]

Y. Wang, C. Quan, and C. J. Tay, “Optical color image encryption without information disclosure using phase-truncated Fresnel transform and a random amplitude mask,” Opt. Commun. 344, 147–155 (2015).
[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]

X. Wang and D. Zhao, “Double-image self-encoding and hiding based on phase-truncated Fourier transforms and phase retrieval,” Opt. Commun. 284, 4441–4445 (2011).
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Y. Xiong, A. He, and C. Quan, “Cryptoanalysis of an optical cryptosystem based on phase-truncated Fourier transform and nonlinear operations,” Opt. Commun. 428, 120–130 (2018).
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Opt. Express (5)

Opt. Lasers Eng. (5)

A. Sinha, “Nonlinear optical cryptosystem resistant to standard and hybrid attacks,” Opt. Lasers Eng. 81, 79–86 (2016).
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I. Mehra, S. K. Rajput, and N. K. Nishchal, “Cryptanalysis of an image encryption scheme based on joint transform correlator with amplitude- and phase-truncation approach,” Opt. Lasers Eng. 52, 167–173 (2014).
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Z. Liu, S. Li, W. Liu, Y. Wang, and S. Liu, “Image encryption algorithm by using fractional Fourier transform and pixel scrambling operation based on double random phase encoding,” Opt. Lasers Eng. 51, 8–14 (2013).
[Crossref]

Y. Xiong, C. Quan, and C. J. Tay, “Multiple image encryption scheme based on pixel exchange operation and vector decomposition,” Opt. Lasers Eng. 101, 113–121 (2018).
[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, 472–480 (2013).
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Opt. Lett. (6)

Proc. IEEE (1)

O. Matoba, T. Nomura, E. Perez-Cabre, M. S. Millan, and B. Javidi, “Optical techniques for information security,” Proc. IEEE 97, 1128–1148 (2009).
[Crossref]

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Figures (14)

Fig. 1.
Fig. 1. Schematic diagram of (a) encryption process and (b) decryption process with amplitude modulation in Ref. [43].
Fig. 2.
Fig. 2. Results of key sensitivity test on A 1 ( u , v ) : (a) plaintext “Peppers,” (b) ciphertext obtained by the cryptosystem in Ref. [43], (c) decrypted image obtained by using the correct private keys, (d)  relation between parameter m of A 1 ( u , v ) and the CC values, (e) decrypted image with m = 0.02 ( s = 60 ) , (f) relation between parameter p of A 1 ( u , v ) and the CC values, (g) decrypted image with p = 0.0402 ( s = 60 ) .
Fig. 3.
Fig. 3. Schematic diagram of the KPA-based iterative process I.
Fig. 4.
Fig. 4. Results of the KPA-based iterative process I: (a) relation between the CC values of the retrieved AM and iteration number k ; (b)–(d) histograms of A 1 ( u , v ) , A 1 ( u , v ) , A 1 ( u , v ) .
Fig. 5.
Fig. 5. Schematic diagram of the amplitude-phase-retrieval-technique-based iterative process II.
Fig. 6.
Fig. 6. Results of iterative process II: (a) original image “Cameraman,” (b) arbitrary given ciphertext, (c) decrypted image obtained using the correct private keys, (d) retrieved image obtained by the proposed attack ( CC = 0.8698 ), (e) relations between the CC values of retrieved private keys and iteration number K , (f) relation between the CC values of the retrieved image f ( x , y ) and iteration number K .
Fig. 7.
Fig. 7. Simulation results on the cryptosystem in Ref. [43]: (a) random amplitude function used as the ciphertext, (b) and (c) private phase keys generated in the encryption process, (d) decrypted image using the keys in (b), (c) and the normalized estimated AM A 1 ( u , v ) , (e) retrieved image f ( x , y ) from (a) with 100 iterations using the iterative process II with correct P 2 ( x , y ) and the normalized estimated AM A 1 ( u , v ) , (f) relation between the CC values of f ( x , y ) [or P 1 ( u , v ) ] and iteration number k , (g) retrieved image f ( x , y ) from (a) with 100 iterations using the iterative process II with correct P 1 ( u , v ) and the normalized estimated AM A 1 ( u , v ) , (h) relation between the CC values of f ( x , y ) [or P 2 ( x , y ) ] and the normalized estimated AM A 1 ( u , v ) .
Fig. 8.
Fig. 8. Schematic diagram of the security-enhanced cryptosystem.
Fig. 9.
Fig. 9. Optical implementation of decryption process in the security-enhanced cryptosystem.
Fig. 10.
Fig. 10. (a) Original image “Baboon” to be encoded, (b) ciphertext obtained by the security-enhanced cryptosystem, (e) and (d) two amplitude keys [ K 1 ( u , v ) and K 2 ( x , y ) ], (e) and (f) two binary modulators [ r 1 ( u , v ) and r 2 ( x , y ) ], (g) decrypted image obtained using the correct private keys.
Fig. 11.
Fig. 11. (a) Retrieved image from a random ciphertext with all correct private keys [ D 1 ( u , v ) and D 2 ( x , y ) ], CC = 0.2274 , (b) retrieved image from Fig. 10(b) with the wrong private key D 1 ( u , v ) , CC = 0.0080 , (c) retrieved image from Fig. 10(b) with the wrong private key D 2 ( x , y ) , CC = 0.0003 .
Fig. 12.
Fig. 12. KPA on the security-enhanced cryptosystem: (a) original image to be retrieved; (b) ciphertext of (a) obtained using the security-enhanced system; (c) retrieved image from (b) using the keys obtained by the KPA, CC = 0.0478 .
Fig. 13.
Fig. 13. Schematic diagram of the potential special attack on the security-enhanced cryptosystem.
Fig. 14.
Fig. 14. Special attack on the security-enhanced cryptosystem: (a) relations between the CC values of the retrieved image and iteration number k ; (b) retrieved image obtained by the special attack with 200 iterations.

Equations (27)

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{ g 1 ( u , v ) = PT { FT [ f ( x , y ) · R 1 ( x , y ) ] } , E ( x , y ) = PT { IFT [ g 1 ( u , v ) · A 1 ( u , v ) · R 2 ( u , v ) ] } ,
A 1 ( u , v ) = { 1 ( p ) m ( 1 p ) ,
{ P 1 ( u , v ) = PR { FT [ f ( x , y ) · R 1 ( x , y ) ] } , P 2 ( x , y ) = PR { IFT [ g 1 ( u , v ) · A 1 ( u , v ) · R 2 ( u , v ) ] } ,
{ g 1 ( u , v ) = m · g 1 ( u , v ) = PT { FT [ E ( x , y ) · P 2 ( x , y ) ] } · A 2 ( u , v ) , f ( x , y ) = m · f ( x , y ) = PT { IFT [ g 1 ( u , v ) · P 1 ( u , v ) ] } ,
A 1 ( u , v ) · A 2 ( u , v ) = m .
CC = E { [ f E [ f ] ] [ f E [ f ] ] } E { [ f E [ f ] ] 2 } E { [ f E [ f ] ] 2 } ,
{ m = m + s · m p = p + s · p ( 1 < s < 1 ) ,
g 1 ( u , v ) = PT { FT [ I ( x , y ) · R 1 ( x , y ) ] } ,
P 2 k ( x , y ) = PR { IFT [ g 1 ( u , v ) · A 1 k ( u , v ) · R 2 ( u , v ) ] } ,
g 1 k ( u , v ) = PT { FT [ C ( x , y ) · P 2 k ( x , y ) ] } ,
A 1 k ( u , v ) = g 1 k ( u , v ) g 1 ( u , v ) ,
thres = graythresh { A 1 ( u , v ) } ,
{ g p 0 = { ( u , v ) | A 1 ( u , v ) < = thres } , g p 1 = { ( u , v ) | A 1 ( u , v ) > thres } .
A 1 ( u , v ) = { μ 0 μ 1 , ( u , v ) g p 0 1 , ( u , v ) g p 1 ,
{ g 1 K ( u , v ) = PT { FT [ f K ( x , y ) · R 1 ( x , y ) ] } P 1 K ( u , v ) = PR { FT [ f K ( x , y ) · R 1 ( x , y ) ] } ,
P 2 K ( x , y ) = PR { IFT [ g 1 K ( u , v ) · A 1 ( u , v ) · R 2 ( u , v ) ] } .
g 1 K ( u , v ) = PT { FT [ E ( x , y ) · P 2 K ( x , y ) ] } A 1 ( u , v ) .
f K ( x , y ) = MF { PT { FT [ g 1 K ( u , v ) · P 1 K ( u , v ) ] } } ,
{ F 1 ( u , v ) = FT [ f ( x , y ) · R 1 ( x , y ) ] K 1 ( u , v ) = PT [ F 1 ( u , v ) ] ,
r 1 ( u , v ) = { 1 , Im [ F 1 ( u , v ) ] < 0 0 , Im [ F 1 ( u , v ) ] 0 , PM 1 ( u , v ) = exp [ i π r 1 ( u , v ) ] ,
F 1 ( u , v ) = F 1 ( u , v ) · exp [ i π r 1 ( u , v ) ] .
{ w 1 ( u , v ) = PR [ F 1 ( u , v ) ] F 2 ( x , y ) = IFT [ w 1 ( u , v ) · R 2 ( u , v ) ] .
K 2 ( x , y ) = PT [ F 2 ( x , y ) ] .
r 2 ( x , y ) = { 1 , Im [ F 2 ( x , y ) ] < 0 0 , Im [ F 2 ( x , y ) ] 0 , PM 2 ( x , y ) = exp [ i π r 2 ( x , y ) ] ,
{ F 2 ( x , y ) = F 2 ( x , y ) · exp [ i π r 2 ( x , y ) ] , C ( x , y ) = PR [ F 2 ( x , y ) ] .
{ D 1 ( u , v ) = K 1 ( u , v ) · PM 1 * ( u , v ) · R 2 * ( u , v ) D 2 ( x , y ) = K 2 ( x , y ) · PM 2 * ( x , y ) ,
f ( x , y ) = | IFT { [ FT ( C ( x , y ) · D 2 ( x , y ) ) ] · D 1 ( u , v ) } | .

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