K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).

[CrossRef]

J. Zang, Z. Xie, and Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38, 1289–1291 (2013).

[CrossRef]

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).

[CrossRef]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).

[CrossRef]

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

[CrossRef]

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).

[CrossRef]

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).

[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).

[CrossRef]

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

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17, 22462–22473 (2009).

[CrossRef]

Y. Sheng, Z. Xin, M. S. Alam, L. Xi, and L. Xiao-feng, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17, 3270–3284 (2009).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).

[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[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]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

Y. Hayasaki, Y. Matsuba, A. Nagaoka, H. Yamamoto, and N. Nishida, “Hiding an image with a light scattering medium and use of a contrast-discrimination method for readout,” Appl. Opt. 43, 1552–1558 (2004).

[CrossRef]

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).

[CrossRef]

N. Takai and Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41, 865–873 (2002).

[CrossRef]

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).

[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).

[CrossRef]

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul 8, 3–30 (1998).

[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

M. G. Lippmann, “Epreuves reversible donnant lasensation du relief,” J. Phys. 7, 821–825 (1908).

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).

[CrossRef]

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

K. Gandolfi, C. Mourtel, and F. Olivier, “Electromagnetic analysis: Concrete results,” in Cryptographic Hardware and Embedded Systems (CHES2001) (Springer, 2001), pp. 251–261.

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).

[CrossRef]

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).

[CrossRef]

Y. Hayasaki, Y. Matsuba, A. Nagaoka, H. Yamamoto, and N. Nishida, “Hiding an image with a light scattering medium and use of a contrast-discrimination method for readout,” Appl. Opt. 43, 1552–1558 (2004).

[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

B. M. Hennelly and J. T. Sheridan, “Image encryption and fractional Fourier transform,” Optik 114, 251–265 (2003).

[CrossRef]

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).

[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

S. Kishk and B. Javidi, “3D object watermarking by a 3D hidden object,” Opt. Express 11, 874–888 (2003).

[CrossRef]

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).

[CrossRef]

J. Rosen and B. Javidi, “Hidden images in halftone pictures,” Appl. Opt. 40, 3346–3353 (2001).

[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical storage with wavelength key and random codes,” Appl. Opt. 38, 6785–6790 (1999).

[CrossRef]

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

[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).

[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]

B. Javidi, Optical and Digital Techniques for Information Security (Advanced Sciences and Technologies for Security Applications) (Springer, 2005).

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

[CrossRef]

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).

[CrossRef]

M. G. Lippmann, “Epreuves reversible donnant lasensation du relief,” J. Phys. 7, 821–825 (1908).

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).

[CrossRef]

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul 8, 3–30 (1998).

[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

K. Gandolfi, C. Mourtel, and F. Olivier, “Electromagnetic analysis: Concrete results,” in Cryptographic Hardware and Embedded Systems (CHES2001) (Springer, 2001), pp. 251–261.

K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).

[CrossRef]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).

[CrossRef]

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).

[CrossRef]

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul 8, 3–30 (1998).

[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

K. Gandolfi, C. Mourtel, and F. Olivier, “Electromagnetic analysis: Concrete results,” in Cryptographic Hardware and Embedded Systems (CHES2001) (Springer, 2001), pp. 251–261.

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).

[CrossRef]

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).

[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).

[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and fractional Fourier transform,” Optik 114, 251–265 (2003).

[CrossRef]

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

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).

[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).

[CrossRef]

K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).

[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[CrossRef]

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

R. Pappu, B. Recht, J. Taylor, and N. Gershenfeld, “Physical one-way functions,” Science 297, 2026–2030 (2002).

[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).

[CrossRef]

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).

[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[CrossRef]

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).

[CrossRef]

K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).

[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[CrossRef]

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

H. Suzuki, H. Tashima, M. Yamaguchi, T. Obi, M. Yachida, and N. Ohyama, “File encryption software using fingerprint keys based on double random encoding,” in Frontiers in Optics, OSA Technical Digest Series (Optical Society of America, 2005), paper JWA50, http://www.opticsinfobase.org/abstract.cfm?URI=FiO-2005-JWA50 .

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).

[CrossRef]

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).

[CrossRef]

M. Matsumoto and T. Nishimura, “Mersenne twister: A 623-dimensionally equidistributed uniform pseudorandom number generator,” ACM Trans. Model. Comput. Simul 8, 3–30 (1998).

[CrossRef]

I. Glaser, “Lenslet array processors,” Appl. Opt. 21, 1271–1280 (1982).

[CrossRef]

K. Hamanaka, H. Nemoto, M. Oikawa, E. Okuda, and T. Kishimoto, “Multiple imaging and multiple Fourier transformation using planar microlens arrays,” Appl. Opt. 29, 4064–4070 (1990).

[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical storage with wavelength key and random codes,” Appl. Opt. 38, 6785–6790 (1999).

[CrossRef]

J. Rosen and B. Javidi, “Hidden images in halftone pictures,” Appl. Opt. 40, 3346–3353 (2001).

[CrossRef]

N. Takai and Y. Mifune, “Digital watermarking by a holographic technique,” Appl. Opt. 41, 865–873 (2002).

[CrossRef]

S. Kishk and B. Javidi, “Information hiding technique with double phase encoding,” Appl. Opt. 41, 5462–5470 (2002).

[CrossRef]

Y. Hayasaki, Y. Matsuba, A. Nagaoka, H. Yamamoto, and N. Nishida, “Hiding an image with a light scattering medium and use of a contrast-discrimination method for readout,” Appl. Opt. 43, 1552–1558 (2004).

[CrossRef]

J. W. Goodman, A. R. Dias, and L. M. Woody, “Fully parallel, high-speed incoherent optical method for performing discrete Fourier transforms,” Appl. Opt. 16, 2611–2612 (1977).

[CrossRef]

K. Nakano, M. Takeda, H. Hiroyuki, and M. Yamaguchi, “Evaluations of phase-only double random phase encoding based on key-space analysis,” Appl. Opt. 52, 1276–1283 (2013).

[CrossRef]

Z. Liu, H. Chen, T. Liu, P. Li, J. Dai, X. Sun, and S. Liu, “Double-image encryption based on the affine transform and the gyrator transform,” J. Opt. 12, 035407 (2010).

[CrossRef]

M. G. Lippmann, “Epreuves reversible donnant lasensation du relief,” J. Phys. 7, 821–825 (1908).

Y. Hayasaki, I. Tohyama, T. Yatagai, M. Mori, and S. Ishihara, “Optical learning neural network using Selfoc microlens array,” Jpn. J. Appl. Phys. 31, 1689–1693 (1992).

H. Suzuki, T. Yamaya, T. Obi, M. Yamaguchi, and N. Ohyama, “Fingerprint verification for smart card holders identification based on optical image encryption,” Jpn. J. Opt. 33, 37–44 (2004).

Z. Liu and S. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275, 324–329 (2007).

[CrossRef]

H. Li and Y. Wang, “Double-image encryption based on iterative gyrator transform,” Opt. Commun. 281, 5745–5749 (2008).

[CrossRef]

Z. Liu, J. Dai, X. Sun, and S. Liu, “Triple image encryption scheme in fractional Fourier transform domains,” Opt. Commun. 282, 518–522 (2009).

[CrossRef]

K. Nakano, M. Takeda, H. Suzuki, and M. Yamaguchi, “Generalized model of double random phase encoding based on linear algebra,” Opt. Commun. 286, 91–94 (2013).

[CrossRef]

B. Javidi, A. Sergent, and E. Ahouzi, “Performance of double phase encoding encryption technique using binarized encrypted images,” Opt. Eng. 37, 565–569 (1998).

[CrossRef]

N. K. Nishchal, “Hierarchical encrypted image watermarking using fractional Fourier domain random phase encoding,” Opt. Eng. 50, 097003 (2011).

[CrossRef]

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

[CrossRef]

Y. Sheng, Z. Xin, M. S. Alam, L. Xi, and L. Xiao-feng, “Information hiding based on double random-phase encoding and public-key cryptography,” Opt. Express 17, 3270–3284 (2009).

[CrossRef]

M. He, Q. Tan, L. Cao, Q. He, and G. Jin, “Security enhanced optical encryption system by random phase key and permutation key,” Opt. Express 17, 22462–22473 (2009).

[CrossRef]

H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, “Experimental evaluation of fingerprint verification system based on double random phase encoding,” Opt. Express 14, 1755–1766 (2006).

[CrossRef]

S. Kishk and B. Javidi, “3D object watermarking by a 3D hidden object,” Opt. Express 11, 874–888 (2003).

[CrossRef]

R. Tao, Y. Xin, and Y. Wang, “Double image encryption based on random phase encoding in the fractional Fourier domain,” Opt. Express 15, 16067–16079 (2007).

[CrossRef]

J. Zang, Z. Xie, and Y. Zhang, “Optical image encryption with spatially incoherent illumination,” Opt. Lett. 38, 1289–1291 (2013).

[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]

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

[CrossRef]

I. Glaser, “Noncoherent parallel optical processor for discrete two-dimensional linear transformations,” Opt. Lett. 5, 449–451 (1980).

[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]

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]

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

[CrossRef]

W. Chen, X. Chen, and C. J. R. Sheppard, “Optical image encryption based on diffractive imaging,” Opt. Lett. 35, 3817–3819 (2010).

[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and fractional Fourier transform,” Optik 114, 251–265 (2003).

[CrossRef]

X. Wang, H. Zhai, Z. Li, and Q. Ge, “Double random phase encoding based on discrete quaternion Fourier transforms,” Optik 122, 1856–1859 (2011).

[CrossRef]

R. Horstmeyer, B. Judkewitz, I. M. Vellekoop, S. Assawaworrarit, and C. Yang, “Physical key-protected one-time pad,” Sci. Rep. 3, 3543 (2013).

[CrossRef]

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[CrossRef]

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