Abstract

An encryption and verification method with multiple encrypted keys based on interference principle is proposed. The encryption process is realized on computer digitally and the verification process can be completed optically or digitally. Two different images are encoded into three diffractive phase elements (DPEs) by using two different incident wavelengths. Three DPEs have different distances from output plane. The two wavelength parameters and three distance parameters can be used as encryption keys, which will boost security degree of this system. Numerical simulation proves that the proposed encryption method is valid and has high secrecy level.

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References

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2009

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

2008

2007

Z. J. Liu and S. T. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (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(16), 10253–10265 (2007).
[CrossRef] [PubMed]

2006

2005

2004

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235(4-6), 253–259 (2004).
[CrossRef]

2002

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).
[CrossRef]

2001

2000

1999

O. Matoba and B. Javidi, “Encrypted optical memory system using three-dimensional keys in the Fresnel domain,” Opt. Lett. 24(11), 762–764 (1999).
[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kin, “Optical image encryption based on XOR operations,” Opt. Eng. (Bellingham) 38(1), 47–54 (1999).
[CrossRef]

J. W. Han, S. H. Lee, and E. S. Kin, “Optical key bit stream generator,” Opt. Eng. (Bellingham) 38(1), 33–38 (1999).
[CrossRef]

1996

P. K. Wang, L. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. (Bellingham) 35(9), 2464–2469 (1996).
[CrossRef]

1995

Arcos, S.

Cai, L. Z.

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

Carnicer, A.

Castro, A.

Chatwin, C.

P. K. Wang, L. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. (Bellingham) 35(9), 2464–2469 (1996).
[CrossRef]

Frauel, Y.

Gao, Z.

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

Gopinathan, U.

Han, J. W.

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kin, “Optical image encryption based on XOR operations,” Opt. Eng. (Bellingham) 38(1), 47–54 (1999).
[CrossRef]

J. W. Han, S. H. Lee, and E. S. Kin, “Optical key bit stream generator,” Opt. Eng. (Bellingham) 38(1), 33–38 (1999).
[CrossRef]

Javidi, B.

Joseph, J.

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235(4-6), 253–259 (2004).
[CrossRef]

Juvells, I.

Kin, E. S.

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kin, “Optical image encryption based on XOR operations,” Opt. Eng. (Bellingham) 38(1), 47–54 (1999).
[CrossRef]

J. W. Han, S. H. Lee, and E. S. Kin, “Optical key bit stream generator,” Opt. Eng. (Bellingham) 38(1), 33–38 (1999).
[CrossRef]

Kreske, K.

Lee, S. H.

J. W. Han, S. H. Lee, and E. S. Kin, “Optical key bit stream generator,” Opt. Eng. (Bellingham) 38(1), 33–38 (1999).
[CrossRef]

Li, A. M.

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

Li, Y.

Liu, S. T.

Z. J. Liu and S. T. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[CrossRef]

S. T. Liu, Q. L. Mi, and B. H. Zhu, “Optical image encryption with multistage and multichannel fractional Fourier-domain filtering,” Opt. Lett. 26(16), 1242–1244 (2001).
[CrossRef]

Liu, Z. J.

Z. J. Liu and S. T. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[CrossRef]

Matoba, O.

Meng, X. F.

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

Mi, Q. L.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Nishchal, N. K.

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235(4-6), 253–259 (2004).
[CrossRef]

Nomura, T.

Park, C. S.

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kin, “Optical image encryption based on XOR operations,” Opt. Eng. (Bellingham) 38(1), 47–54 (1999).
[CrossRef]

Peng, X.

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

Refregier, P.

Rosen, J.

Ryu, D. H.

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kin, “Optical image encryption based on XOR operations,” Opt. Eng. (Bellingham) 38(1), 47–54 (1999).
[CrossRef]

Sheridan, J. T.

Singh, K.

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235(4-6), 253–259 (2004).
[CrossRef]

Tanno, N.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).
[CrossRef]

Wang, B.

Wang, P. K.

P. K. Wang, L. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. (Bellingham) 35(9), 2464–2469 (1996).
[CrossRef]

Wang, Y. R.

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

Watson, L. A.

P. K. Wang, L. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. (Bellingham) 35(9), 2464–2469 (1996).
[CrossRef]

Zhang, Y.

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

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).
[CrossRef]

Zheng, C. H.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).
[CrossRef]

Zhu, B. H.

Appl. Opt.

J. Opt. A, Pure Appl. Opt.

X. F. Meng, X. Peng, L. Z. Cai, A. M. Li, Z. Gao, and Y. R. Wang, “Cryptosystem based on two-step phase-shifting interferometry and the RSA public-key encryption algorithm,” J. Opt. A, Pure Appl. Opt. 11(8), 085402 (2009).
[CrossRef]

Opt. Commun.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202(4-6), 277–285 (2002).
[CrossRef]

Z. J. Liu and S. T. Liu, “Double image encryption based on iterative fractional Fourier transform,” Opt. Commun. 275(2), 324–329 (2007).
[CrossRef]

N. K. Nishchal, J. Joseph, and K. Singh, “Securing information using fractional Fourier transform in digital holography,” Opt. Commun. 235(4-6), 253–259 (2004).
[CrossRef]

Opt. Eng. (Bellingham)

P. K. Wang, L. A. Watson, and C. Chatwin, “Random phase encoding for optical security,” Opt. Eng. (Bellingham) 35(9), 2464–2469 (1996).
[CrossRef]

J. W. Han, C. S. Park, D. H. Ryu, and E. S. Kin, “Optical image encryption based on XOR operations,” Opt. Eng. (Bellingham) 38(1), 47–54 (1999).
[CrossRef]

J. W. Han, S. H. Lee, and E. S. Kin, “Optical key bit stream generator,” Opt. Eng. (Bellingham) 38(1), 33–38 (1999).
[CrossRef]

Opt. Express

Opt. Lett.

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Figures (5)

Fig. 1
Fig. 1

Schematic of the verification optical system

Fig. 2
Fig. 2

Encryption results. (a) The first original image for encryption, (b) the second original image for encryption, (c) and (d) two reconstructed images with correct encryption keys, (e) and (f) two reconstructed images with incorrect encryption keys.

Fig. 3
Fig. 3

Height distributions of three encrypted DPEs

Fig. 4
Fig. 4

(a) Dependence of RE on wavelength difference Δ λ 1 and Δ λ 2 , (b) decryption result with Δ λ 1 = 1 × 10 4 n m , (c) decryption result with Δ λ 2 = 1 × 10 4 n m .

Fig. 5
Fig. 5

(a) Dependence of RE on distance difference Δ l and Δ l 3 , (b) decryption result with Δ l = 2 n m , (c) decryption result with Δ l 3 = 2 n m .

Equations (1)

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h 1 ( x , y ) = Φ 1 λ 1 ( x , y ) + 2 P ( x , y ) π 2 π ( n ( λ 1 ) 1 ) λ 1 Φ 1 λ 2 ( x , y ) + 2 Q ( x , y ) π 2 π ( n ( λ 2 ) 1 ) λ 2

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