Abstract

A novel method for encoding color information based on a double random phase mask and a double structured phase mask in a gyrator transform domain is proposed. The amplitude transmittance of the Fresnel zone plate is used as structured phase-mask encoding. A color image is first segregated into red, green, and blue component images. Each of these component images are then independently encrypted using first a random phase mask placed at the image plane and transmitted through the first structured phase mask. They are then encoded by the first gyrator transform. The resulting information is again encrypted by a second random phase mask placed at the gyrator transform plane and transmitted through the second structured phase mask, and then encoded by the second gyrator transform. The system parameters of the structured phase mask and gyrator transform in each channel serve as additional encryption keys and enlarge the key space. The encryption process can be realized with an electro-optical hybrid system. The proposed system avoids problems arising from misalignment and benefits of a higher space–bandwidth product. Numerical simulations are presented to confirm the security, validity, and possibility of the proposed idea.

© 2012 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  3. S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
    [CrossRef]
  4. N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253–259 (2004).
    [CrossRef]
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    [CrossRef]
  6. Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
    [CrossRef]
  7. G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
    [CrossRef]
  8. N. K. Nishchal and T. J. Naughton, “Flexible optical encryption with multiple users and multiple security levels,” Opt. Commun. 284, 735–739 (2011).
    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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    [CrossRef]
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2012 (1)

M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Opt. Lasers Eng. 50772–779 (2012).
[CrossRef]

2011 (3)

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

Z. Liu, L. Xu, C. Chen, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

2010 (2)

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Laser Eng. 48, 800–805 (2010).
[CrossRef]

Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
[CrossRef]

2009 (2)

H. Li, “Image encryption based on gyrator transform and two-step phase-shifting interferometry,” Opt. Laser Eng. 47, 45–50 (2009).
[CrossRef]

N. Singh, and A. Sinha, “Gyrator transform based optical image encryption using chaos,” Opt. Laser Eng. 47, 539–546 (2009).
[CrossRef]

2007 (5)

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Application of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[CrossRef]

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

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Gyrator transform: Properties and applications,” Opt. Express 15, 2190–2203 (2007).

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
[CrossRef]

J. A. Rodrigo, T. Alieva, and M. L. Calvo, “Experimental implementation of the gyrator transform,” J. Opt. Soc. Am. A 24, 3135–3139 (2007).

2006 (1)

2005 (2)

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

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

2004 (3)

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253–259 (2004).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[CrossRef]

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

2001 (1)

2000 (2)

1999 (1)

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

1995 (1)

1994 (1)

1979 (1)

Abuturab, M. R.

M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Opt. Lasers Eng. 50772–779 (2012).
[CrossRef]

Alieva, T.

Barrera, J. F.

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

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

Calvo, M. L.

Chen, C.

Z. Liu, L. Xu, C. Chen, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Chen, L.

Chin, C.

Dai, J.

Z. Liu, L. Xu, C. Chen, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Laser Eng. 48, 800–805 (2010).
[CrossRef]

Henao, R.

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

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

Javidi, B.

Joseph, J.

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253–259 (2004).
[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]

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).

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

Karim, M. A.

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

Li, H.

H. Li, “Image encryption based on gyrator transform and two-step phase-shifting interferometry,” Opt. Laser Eng. 47, 45–50 (2009).
[CrossRef]

Liu, S.

Z. Liu, L. Xu, C. Chen, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Laser Eng. 48, 800–805 (2010).
[CrossRef]

Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
[CrossRef]

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
[CrossRef]

S. Liu, Q. Mi, and B. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26, 1242–1244 (2001).
[CrossRef]

Liu, Z.

Z. Liu, L. Xu, C. Chen, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Laser Eng. 48, 800–805 (2010).
[CrossRef]

Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
[CrossRef]

Z. Liu and S. Liu, “Random fractional Fourier transform,” Opt. Lett. 32, 2088–2090 (2007).
[CrossRef]

Mi, Q.

Naughton, T. J.

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

Nemes, G.

Nishchal, N. K.

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

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253–259 (2004).
[CrossRef]

Refregier, P.

Rodrigo, J. A.

Shakher, C.

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

Shamir, J.

Siegman, A. E.

Simon, R.

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).

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, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253–259 (2004).
[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]

Singh, N.

N. Singh, and A. Sinha, “Gyrator transform based optical image encryption using chaos,” Opt. Laser Eng. 47, 539–546 (2009).
[CrossRef]

Sinha, A.

N. Singh, and A. Sinha, “Gyrator transform based optical image encryption using chaos,” Opt. Laser Eng. 47, 539–546 (2009).
[CrossRef]

Situ, G.

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

Sun, X.

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Laser Eng. 48, 800–805 (2010).
[CrossRef]

Torroba, R.

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

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

Unnikrishnan, G.

Wolf, K. B.

Xu, L.

Z. Liu, L. Xu, C. Chen, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

Z. Liu, L. Xu, C. Chin, and S. Liu, “Image encryption by encoding with a nonuniform optical beam in gyrator transform domains,” Appl. Opt. 49, 5632–5637 (2010).
[CrossRef]

Zhang, J.

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[CrossRef]

Zhang, S. Q.

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

Zhao, D.

Zhu, B.

Appl. Opt. (2)

J. Opt. Soc. Am. A (3)

Microw. Opt. Technol. Lett. (1)

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

Opt. Commun. (7)

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, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235, 253–259 (2004).
[CrossRef]

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 115–122 (2004).
[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. A. Rodrigo, T. Alieva, and M. L. Calvo, “Application of gyrator transform for image processing,” Opt. Commun. 278, 279–284 (2007).
[CrossRef]

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

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

Opt. Eng. (1)

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).

Opt. Express (2)

Opt. Laser Eng. (3)

Z. Liu, J. Dai, X. Sun, and S. Liu, “Color image encryption by using the rotation of color vector in Hartley transform domains,” Opt. Laser Eng. 48, 800–805 (2010).
[CrossRef]

H. Li, “Image encryption based on gyrator transform and two-step phase-shifting interferometry,” Opt. Laser Eng. 47, 45–50 (2009).
[CrossRef]

N. Singh, and A. Sinha, “Gyrator transform based optical image encryption using chaos,” Opt. Laser Eng. 47, 539–546 (2009).
[CrossRef]

Opt. Lasers Eng. (3)

Z. Liu, L. Xu, C. Chen, J. Dai, and S. Liu, “Image encryption scheme by using iterative random phase encoding in gyrator transform domains,” Opt. Lasers Eng. 49, 542–546 (2011).
[CrossRef]

M. R. Abuturab, “Securing color information using Arnold transform in gyrator transform domain,” Opt. Lasers Eng. 50772–779 (2012).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Fully phase-encrypted memory using cascaded extended fractional Fourier transform,” Opt. Lasers Eng. 42, 141–151 (2004).
[CrossRef]

Opt. Lett. (4)

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Figures (7)

Fig. 1.
Fig. 1.

(a) Flowchart corresponding to proposed color image encryption algorithm. (b) Flowchart corresponding to proposed color image decryption algorithm.

Fig. 2.
Fig. 2.

(a) Rotation of the generalized lenses L1 and L2. (b) Electro-optical hybrid color image architecture of proposed system.

Fig. 3.
Fig. 3.

Results of proposed color image encryption and decryption: (a) Original image with 512×512 pixels and 24 bits used in numerical simulation. (b) First Fresnel zone plate as first structured phase encoding of focal length (f1=4cm), radius (r1=0.1mm), red wavelength (λr1=650.0nm), green wavelength (λg1=545.0nm), and blue wavelength (λb1=445.0nm). (c) Second Fresnel zone plate as second structured phase encoding of focal length (f2=5cm), radius (r2=0.2mm), red wavelength (λr2=632.8nm), green wavelength (λg2=532.0nm), and blue wavelength (λb2=488.0nm). (d) Encrypted image, (e) decrypted image with all the correct keys. (f) Decrypted image with one of the transformation angle for each component image is changed by 0.008° but all the other parameters are correct. (g) Decrypted image with one of the random phase mask for each component image is incorrect but all the other parameters are correct.

Fig. 4.
Fig. 4.

(a) MSE as a function of the transformation angle between original red, green, and blue component images and their corresponding decrypted images. (b) MSE as a function of the focal length of the FZP between original red, green, and blue component images and their corresponding recovered images. (c) MSE as a function of the radius of the FZP between original red, green, and blue component images and their corresponding retrieved images. (d) MSE as a function of the wavelength of the FZP between original red, green, and blue component images and their corresponding retrieved images.

Fig. 5.
Fig. 5.

Robustness test of the proposed method against occlusion attack on the encrypted image: (a) with 50% occlusion, (b) corresponding recovered image from (a), (c) with 70% occlusion, (d) corresponding retrieved image from (c).

Fig. 6.
Fig. 6.

The robustness test of the proposed method against: (a) Gaussian noise attack on the encrypted image with variance 0.2, (b) corresponding reconstructed image from (a), (c) speckle noise attack on the encrypted image with variance 0.4, (d) corresponding retrieved image from (c).

Fig. 7.
Fig. 7.

(a) The MSE as a function of occlusion part on the encrypted red, green and blue component images, and their corresponding decrypted images. (b) MSE as a function of Gaussian noise attack on the encrypted red, green, and blue component images, and their corresponding decrypted images. (c) MSE as a function of speckle noise attack on the encrypted red, green, and blue component images, and their corresponding decrypted images.

Equations (9)

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

fo(xo,yo)=1|sinα|+fi(xi,yi)exp(i2π(xoyo+xiyi)cosα(xiyo+xoyi)sinα)dxidyi,
t(x,y)=exp(iπλf(x2+y2)),
f(xi,yi)=fr(xi,yi)+fg(xi,yi)+fb(xi,yi).
E(xo,yo)=Er(xo,yo)+Eg(xo,yo)+Eb(xo,yo).
Er(xo,yo)=Gαr2{{Gαr1{(fr(xi,yi)exp(i2πφr1(xi,yi)))tr1(xi,yi)}exp(i2πφr2(x,y))}tr2(x,y)}.
D(xi,yi)=f(xi,yi)=Dr(xi,yi)+Dg(xi,yi)+Db(xi,yi).
Dr(xi,yi)=Gαr1{{(Gαr2{Er(xo,yo)})tr2*(x,y)}exp(i2πφr2*(x,y))}tr1*(xi,yi)exp(i2πφr1*(x,y))
sin2ϕ1=cot(α/2),sin2ϕ2=(sinα)/2.
MSE=1M×Ni=1Mj=1N[|Ii(i,j)Io(i,j)|]2,

Metrics