Abstract

A new optical security system for image encryption based on a nonlinear joint transform correlator (JTC) in the Fresnel domain (FrD) is proposed. The proposal of the encryption process is a lensless optical system that produces a real encrypted image and is a simplified version of some previous JTC-based encryption systems. We use a random complex mask as the key in the nonlinear system for the purpose of increasing the security of the encrypted image. In order to retrieve the primary image in the decryption process, a nonlinear operation has to be introduced in the encrypted function. The optical decryption process is implemented through the Fresnel transform and the fractional Fourier transform. The security system proposed in this paper preserves the shift-invariance property of the JTC-based encryption system in the Fourier domain, with respect to the lateral displacement of the key random mask in the decryption process. This system shows an improved resistance to chosen-plaintext and known-plaintext attacks, as they have been proposed in the cryptanalysis of the JTC encrypting system. Numerical simulations show the validity of this new optical security system.

© 2014 Optical Society of America

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2013 (3)

J. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Improved decryption quality and security of a joint transform correlator-based encryption system,” J. Opt. 15, 025401 (2013).
[CrossRef]

X. Shi, D. Zhao, and Y. Huang, “Double images hiding by using joint transform correlator architecture adopting two-step phase-shifting digital holography,” Opt. Commun. 297, 32–37 (2013).
[CrossRef]

J. M. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Joint transform correlator-based encryption system using the Fresnel transform and nonlinear filtering,” Proc. SPIE 8785, 87853J (2013).
[CrossRef]

2012 (2)

J. Li, T. Zheng, Q.-z. Liu, and R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285, 1704–1709 (2012).
[CrossRef]

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]

2011 (1)

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

2010 (4)

G. Situ, G. Pedrini, and W. Osten, “Strategy for cryptanalysis of optical encryption in the Fresnel domain,” Appl. Opt. 49, 457–462 (2010).
[CrossRef]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283, 3917–3921 (2010).
[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]

P. Kumar, J. Joseph, and K. Singh, “Holographic encryption system in the Fresnel domain with convergent random illumination,” Opt. Eng. 49, 095803 (2010).
[CrossRef]

2009 (3)

2008 (1)

C.-L. Chen, L.-C. Lin, and C.-J. Cheng, “Design and implementation of an optical joint transform encryption system using complex-encoded key mask,” Opt. Eng. 47, 068201 (2008).
[CrossRef]

2007 (2)

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (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 (6)

2005 (2)

2004 (2)

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

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

2003 (1)

2002 (1)

E. Pérez, M. S. Millán, and K. Chałasińska-Macukow, “Optical pattern recognition with adjustable sensitivity to shape and texture,” Opt. Commun. 202, 239–255 (2002).
[CrossRef]

2000 (3)

1999 (1)

1997 (1)

E. Pérez, K. Chałasińska-Macukow, K. Styczyński, R. Kotyński, and M. S. Millán, “Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results,” J. Mod. Opt. 44, 1535–1552 (1997).
[CrossRef]

1996 (1)

1995 (1)

1994 (1)

1988 (1)

1972 (1)

R. W. Gerchberg and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Alieva, T.

Amaya, D.

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

Arcos, S.

Barrera, J. F.

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]

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]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283, 3917–3921 (2010).
[CrossRef]

E. Rueda, J. F. Barrera, R. Henao, and R. Torroba, “Optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Commun. 282, 3243–3249 (2009).
[CrossRef]

Bolognini, N.

Cai, L. Z.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Calvo, M. L.

Carnicer, A.

Castro, A.

Chalasinska-Macukow, K.

E. Pérez, M. S. Millán, and K. Chałasińska-Macukow, “Optical pattern recognition with adjustable sensitivity to shape and texture,” Opt. Commun. 202, 239–255 (2002).
[CrossRef]

E. Pérez, K. Chałasińska-Macukow, K. Styczyński, R. Kotyński, and M. S. Millán, “Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results,” J. Mod. Opt. 44, 1535–1552 (1997).
[CrossRef]

Chang, H. T.

Chen, C.-C.

Chen, C.-L.

C.-L. Chen, L.-C. Lin, and C.-J. Cheng, “Design and implementation of an optical joint transform encryption system using complex-encoded key mask,” Opt. Eng. 47, 068201 (2008).
[CrossRef]

Chen, L.

Cheng, C.-J.

C.-L. Chen, L.-C. Lin, and C.-J. Cheng, “Design and implementation of an optical joint transform encryption system using complex-encoded key mask,” Opt. Eng. 47, 068201 (2008).
[CrossRef]

Cheng, X. C.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Dong, G. Y.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Dorsch, R. G.

Eddins, S. L.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab, 2nd ed. (Gatesmark, 2009).

Frauel, Y.

Fuentes, F. J.

Gerchberg, R. W.

R. W. Gerchberg and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Gonzalez, R. C.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab, 2nd ed. (Gatesmark, 2009).

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

Henao, R.

E. Rueda, J. F. Barrera, R. Henao, and R. Torroba, “Optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Commun. 282, 3243–3249 (2009).
[CrossRef]

Hennelly, B. M.

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

Horrillo, S.

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

Huang, Y.

X. Shi, D. Zhao, and Y. Huang, “Double images hiding by using joint transform correlator architecture adopting two-step phase-shifting digital holography,” Opt. Commun. 297, 32–37 (2013).
[CrossRef]

Iemmi, C.

Javidi, B.

Joseph, J.

P. Kumar, J. Joseph, and K. Singh, “Holographic encryption system in the Fresnel domain with convergent random illumination,” Opt. Eng. 49, 095803 (2010).
[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]

Juvells, I.

Kotynski, R.

E. Pérez, K. Chałasińska-Macukow, K. Styczyński, R. Kotyński, and M. S. Millán, “Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results,” J. Mod. Opt. 44, 1535–1552 (1997).
[CrossRef]

Kumar, P.

P. Kumar, J. Joseph, and K. Singh, “Holographic encryption system in the Fresnel domain with convergent random illumination,” Opt. Eng. 49, 095803 (2010).
[CrossRef]

Kutay, M. A.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).

La Mela, C.

Li, J.

J. Li, T. Zheng, Q.-z. Liu, and R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285, 1704–1709 (2012).
[CrossRef]

Li, R.

J. Li, T. Zheng, Q.-z. Liu, and R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285, 1704–1709 (2012).
[CrossRef]

Lin, L.-C.

C.-L. Chen, L.-C. Lin, and C.-J. Cheng, “Design and implementation of an optical joint transform encryption system using complex-encoded key mask,” Opt. Eng. 47, 068201 (2008).
[CrossRef]

Liu, Q.-z.

J. Li, T. Zheng, Q.-z. Liu, and R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285, 1704–1709 (2012).
[CrossRef]

Liu, W.

Matoba, O.

Mendlovic, D.

Meng, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Mikan, S.

Millán, M. S.

J. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Improved decryption quality and security of a joint transform correlator-based encryption system,” J. Opt. 15, 025401 (2013).
[CrossRef]

J. M. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Joint transform correlator-based encryption system using the Fresnel transform and nonlinear filtering,” Proc. SPIE 8785, 87853J (2013).
[CrossRef]

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

E. Pérez, M. S. Millán, and K. Chałasińska-Macukow, “Optical pattern recognition with adjustable sensitivity to shape and texture,” Opt. Commun. 202, 239–255 (2002).
[CrossRef]

E. Pérez, K. Chałasińska-Macukow, K. Styczyński, R. Kotyński, and M. S. Millán, “Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results,” J. Mod. Opt. 44, 1535–1552 (1997).
[CrossRef]

M. S. Millán and E. Pérez-Cabré, “Optical data encryption,” Optical and Digital Image Processing: Fundamentals and Applications, G. Cristóbal, P. Schelkens, and H. Thienpont, eds. (Wiley, 2011), pp. 739–767.

Montes-Usategui, M.

Morimoto, Y.

Naughton, T. J.

Navarro, R.

Nieto-Vesperinas, M.

Nomura, T.

Osten, W.

Ozaktas, H. M.

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).

Pedrini, G.

Pellat-Finet, P.

Peng, X.

Pérez, E.

E. Pérez, M. S. Millán, and K. Chałasińska-Macukow, “Optical pattern recognition with adjustable sensitivity to shape and texture,” Opt. Commun. 202, 239–255 (2002).
[CrossRef]

E. Pérez, K. Chałasińska-Macukow, K. Styczyński, R. Kotyński, and M. S. Millán, “Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results,” J. Mod. Opt. 44, 1535–1552 (1997).
[CrossRef]

Pérez-Cabré, E.

J. M. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Joint transform correlator-based encryption system using the Fresnel transform and nonlinear filtering,” Proc. SPIE 8785, 87853J (2013).
[CrossRef]

J. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Improved decryption quality and security of a joint transform correlator-based encryption system,” J. Opt. 15, 025401 (2013).
[CrossRef]

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

M. S. Millán and E. Pérez-Cabré, “Optical data encryption,” Optical and Digital Image Processing: Fundamentals and Applications, G. Cristóbal, P. Schelkens, and H. Thienpont, eds. (Wiley, 2011), pp. 739–767.

Réfrégier, P.

Ríos, C.

Rodrigo, J. A.

Rueda, E.

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]

E. Rueda, J. F. Barrera, R. Henao, and R. Torroba, “Optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Commun. 282, 3243–3249 (2009).
[CrossRef]

Saxton, O.

R. W. Gerchberg and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Shen, X. X.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Sheridan, J. T.

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

Shi, X.

X. Shi, D. Zhao, and Y. Huang, “Double images hiding by using joint transform correlator architecture adopting two-step phase-shifting digital holography,” Opt. Commun. 297, 32–37 (2013).
[CrossRef]

Singh, K.

P. Kumar, J. Joseph, and K. Singh, “Holographic encryption system in the Fresnel domain with convergent random illumination,” Opt. Eng. 49, 095803 (2010).
[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]

Situ, G.

Styczynski, K.

E. Pérez, K. Chałasińska-Macukow, K. Styczyński, R. Kotyński, and M. S. Millán, “Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results,” J. Mod. Opt. 44, 1535–1552 (1997).
[CrossRef]

Tajahuerce, E.

Tebaldi, M.

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]

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283, 3917–3921 (2010).
[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]

Torroba, R.

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]

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283, 3917–3921 (2010).
[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]

E. Rueda, J. F. Barrera, R. Henao, and R. Torroba, “Optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Commun. 282, 3243–3249 (2009).
[CrossRef]

Unnikrishnan, G.

Vargas, C.

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283, 3917–3921 (2010).
[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]

Verrall, S. C.

Vilardy, J.

J. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Improved decryption quality and security of a joint transform correlator-based encryption system,” J. Opt. 15, 025401 (2013).
[CrossRef]

Vilardy, J. M.

J. M. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Joint transform correlator-based encryption system using the Fresnel transform and nonlinear filtering,” Proc. SPIE 8785, 87853J (2013).
[CrossRef]

Wang, Y. R.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Wei, H.

Woods, R. E.

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab, 2nd ed. (Gatesmark, 2009).

Xie, H.

Xu, X. F.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Yang, G.

Yang, X. L.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Yu, B.

Zalevsky, Z.

Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg–Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996).
[CrossRef]

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).

Zhang, H.

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

Zhang, J.

Zhang, P.

Zhao, D.

X. Shi, D. Zhao, and Y. Huang, “Double images hiding by using joint transform correlator architecture adopting two-step phase-shifting digital holography,” Opt. Commun. 297, 32–37 (2013).
[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]

Zheng, T.

J. Li, T. Zheng, Q.-z. Liu, and R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285, 1704–1709 (2012).
[CrossRef]

Appl. Opt. (3)

J. Mod. Opt. (1)

E. Pérez, K. Chałasińska-Macukow, K. Styczyński, R. Kotyński, and M. S. Millán, “Dual nonlinear correlator based on computer controlled joint transform processor: digital analysis and optical results,” J. Mod. Opt. 44, 1535–1552 (1997).
[CrossRef]

J. Opt. (1)

J. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Improved decryption quality and security of a joint transform correlator-based encryption system,” J. Opt. 15, 025401 (2013).
[CrossRef]

J. Opt. A (2)

G. Situ and J. Zhang, “Position multiplexing for multiple-image encryption,” J. Opt. A 8, 391–397 (2006).
[CrossRef]

X. F. Meng, L. Z. Cai, Y. R. Wang, X. L. Yang, X. F. Xu, G. Y. Dong, X. X. Shen, H. Zhang, and X. C. Cheng, “Hierarchical image encryption based on cascaded iterative phase retrieval algorithm in the Fresnel domain,” J. Opt. A 9, 1070–1075 (2007).
[CrossRef]

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

J. Phys. Conf. Ser. (1)

M. Tebaldi, S. Horrillo, E. Pérez-Cabré, M. S. Millán, D. Amaya, R. Torroba, and N. Bolognini, “Experimental color encryption in a joint transform correlator architecture,” J. Phys. Conf. Ser. 274, 012054 (2011).
[CrossRef]

Opt. Commun. (5)

X. Shi, D. Zhao, and Y. Huang, “Double images hiding by using joint transform correlator architecture adopting two-step phase-shifting digital holography,” Opt. Commun. 297, 32–37 (2013).
[CrossRef]

E. Rueda, J. F. Barrera, R. Henao, and R. Torroba, “Optical encryption with a reference wave in a joint transform correlator architecture,” Opt. Commun. 282, 3243–3249 (2009).
[CrossRef]

J. Li, T. Zheng, Q.-z. Liu, and R. Li, “Double-image encryption on joint transform correlator using two-step-only quadrature phase-shifting digital holography,” Opt. Commun. 285, 1704–1709 (2012).
[CrossRef]

J. F. Barrera, C. Vargas, M. Tebaldi, and R. Torroba, “Chosen-plaintext attack on a joint transform correlator encrypting system,” Opt. Commun. 283, 3917–3921 (2010).
[CrossRef]

E. Pérez, M. S. Millán, and K. Chałasińska-Macukow, “Optical pattern recognition with adjustable sensitivity to shape and texture,” Opt. Commun. 202, 239–255 (2002).
[CrossRef]

Opt. Eng. (4)

C.-L. Chen, L.-C. Lin, and C.-J. Cheng, “Design and implementation of an optical joint transform encryption system using complex-encoded key mask,” Opt. Eng. 47, 068201 (2008).
[CrossRef]

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

P. Kumar, J. Joseph, and K. Singh, “Holographic encryption system in the Fresnel domain with convergent random illumination,” Opt. Eng. 49, 095803 (2010).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Random phase and jigsaw encryption in the Fresnel domain,” Opt. Eng. 43, 2239–2249 (2004).
[CrossRef]

Opt. Express (6)

Opt. Lett. (12)

Z. Zalevsky, D. Mendlovic, and R. G. Dorsch, “Gerchberg–Saxton algorithm applied in the fractional Fourier or the Fresnel domain,” Opt. Lett. 21, 842–844 (1996).
[CrossRef]

P. Pellat-Finet, “Fresnel diffraction and the fractional-order Fourier transform,” Opt. Lett. 19, 1388–1390 (1994).
[CrossRef]

X. Peng, P. Zhang, H. Wei, and B. Yu, “Known-plaintext attack on optical encryption based on double random phase keys,” Opt. Lett. 31, 1044–1046 (2006).
[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]

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]

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]

C. La Mela and C. Iemmi, “Optical encryption using phase-shifting interferometry in a joint transform correlator,” Opt. Lett. 31, 2562–2564 (2006).
[CrossRef]

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

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

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

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24, 762–764 (1999).
[CrossRef]

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

Optik (1)

R. W. Gerchberg and O. Saxton, “A practical algorithm for the determination of the phase from image and diffraction plane pictures,” Optik 35, 237–246 (1972).

Proc. SPIE (1)

J. M. Vilardy, M. S. Millán, and E. Pérez-Cabré, “Joint transform correlator-based encryption system using the Fresnel transform and nonlinear filtering,” Proc. SPIE 8785, 87853J (2013).
[CrossRef]

Other (4)

H. M. Ozaktas, Z. Zalevsky, and M. A. Kutay, The Fractional Fourier Transform: with Applications in Optics and Signal Processing (Wiley, 2001).

R. C. Gonzalez, R. E. Woods, and S. L. Eddins, Digital Image Processing Using Matlab, 2nd ed. (Gatesmark, 2009).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996).

M. S. Millán and E. Pérez-Cabré, “Optical data encryption,” Optical and Digital Image Processing: Fundamentals and Applications, G. Cristóbal, P. Schelkens, and H. Thienpont, eds. (Wiley, 2011), pp. 739–767.

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Figures (4)

Fig. 1.
Fig. 1.

Scheme of the optical setup composed by an encryption system based on a nonlinear JTC architecture in the FrD and a decryption system based on an optical FrT combined with an optical fractional Fourier transform.

Fig. 2.
Fig. 2.

(a) Original image to be encrypted f(x). (b) Random distribution code s(x) of the RPM r(x). (c) Histogram of s(x) (uniform random distribution). (d) Encrypted image ez(u) for the keys λ=532nm and z=70mm.

Fig. 3.
Fig. 3.

(a) Absolute value of the output plane after the decryption procedure with the correct keys λ, z, and the RCM h(x). (b) Magnified region of interest of (a) corresponding to the decrypted image. (c) Ideal decrypted image obtained by calculating just the right term of Eq. (8). Decrypted images from Fig. 2(d): (d) when the nonlinearity |hz(u)|2 of Eq. (6) is not introduced in the encrypted function and all the correct keys are used for decryption and (e) using just an incorrect distance of propagation z=73mm, but the rest of keys [λ and the RCM h(x)] are correct.

Fig. 4.
Fig. 4.

Nonuniform random distributions: (a) Weibull for m(x) and (b) Chi-square for n(x). Histograms of (c) m(x) and (d) n(x). (e) Encrypted image ez(u) and (f) Decrypted image using all the correct keys.

Equations (21)

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

r(x)=exp{i2πs(x)},h(x)=m(x)exp{i2πn(x)},
g(x)=exp{i2πv0(xv0)λz}r(x)f(x),
c(x)=exp{i2πv0(x+v0)λz}h(x).
tz(u)=FrTλ,z{r(x)f(x)},hz(u)=FrTλ,z{h(x)}=|hz(u)|exp{i2πϕz(u)}.
JFPDz(u)=|FrTλ,z{g(xx0)+c(x+x0)}|2.
ez(u)=JFPDz(u)|hz(u)|2=|tz(u)|2|hz(u)|2+1+tz*(u)hz(u)|hz(u)|2exp{iπλz(4x0)u}+tz(u)hz*(u)|hz(u)|2exp{iπλz(4x0)u}.
dz(u)=ez(u)FrTλ,z{c(x+x0)}=exp{iπλz(2x0ux02)}hz(u)|hz(u)|2|tz(u)|2+exp{iπλz(2x0ux02)}hz(u)+exp{iπλz(6x0ux02)}tz*(u)hz2(u)|hz(u)|2+exp{iπλz(2x0u+x02)}tz(u)hz*(u)hz(u)|hz(u)|2.
f˜(xx0)=|FrTλ,z{exp[iπλz(2x0u+x02)]tz(u)}|.
f˜(x2x0+x1)=|FrTλ,z{exp[iπλz(2(2x0x1)u+x12)]tz(u)}|.
RMSE=(x=1M[f(x)f˜(x)]2x=1M[f(x)]2)12,
ez(u)=1.
ez(u)=1λz|hz(u)|2+1+2λz|hz(u)|cos(2π[ϕz(u)u2λz(u4x0)s(0)zλ+18]),
fz(u)=FrTλ,z{f(x)}=+f(x)hλ,z(u,x)dx,
hλ,z(u,x)=Mλ,zexp{iπλz(ux)2},andMλ,z=1iλzexp{i2πzλ},
FrTλ,z1{FrTλ,z2[f(x)]}=FrTλ,z1+z2{f(x)},
FrTλ,z{exp(i2πv0xλz)f(xx0)}=exp{iπλz(2uv0v02)}fz(ux0v0),
FrTλ,z{exp(i2πx0xλz)f(xx0)}=exp{iπλz(2ux0+x02)}fz(u).
fα(σ)=Fα{f(ρ)}=+f(ρ)Kα(σ,ρ)dρ
Kα(σ,ρ)=Cαexp{iπ[(σ2+ρ2)cotα2σρcscα]},Cα=exp{i(π4sgn(α)α2)}|sinα|,π<απ,
fz(λzσL)=λzKMλ,zCα1exp{iπσ2tanα}×Fα{f(λzρK)},
ρ=(1/λz)12Kx,σ=(1/λz)12Lu,K2=tanα,L2=sinαcosα,0απ/2.

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