Abstract

Optical encryption methods based on double random phase encryption (DRPE) have been shown to be vulnerable to different types of attacks. The Fourier plane random phase mask (RPM), which is the most important key, can be cracked with a single impulse function attack. Such an attack is viable because the Fourier transform of a delta function is a unity function. Formation of a unity function can be avoided if RPMs are placed in front of both lenses in a 4-f optical setup, thereby protecting the DRPE from an impulse attack. We have performed numerical simulations to verify the proposed scheme. Resistance of this scheme is checked against the brute force and the impulse function attacks. The experimental results validate the feasibility of the scheme.

© 2009 Optical Society of America

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References

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    [CrossRef] [PubMed]
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    [CrossRef] [PubMed]
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    [CrossRef]
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    [CrossRef] [PubMed]
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    [CrossRef]

2009 (1)

2008 (3)

2007 (4)

2006 (3)

2005 (2)

2004 (2)

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

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

2000 (1)

1998 (1)

1997 (1)

D. Mendlovic, Z. Zalesvsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

1996 (1)

1995 (1)

Arcos, S.

Cai, L. Z.

Carnicer, A.

Castro, A.

Cheng, X. C.

Dong, G. Y.

Dorsch, R. G.

Dowling, T.

Feng, S.

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, “Known-plaintext attack on the double phase encoding and its implementation with parallel hardware,” Proc. SPIE 6837, 683703(2007).
[CrossRef]

Frauel, Y.

Gao, B. Z.

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, “Known-plaintext attack on the double phase encoding and its implementation with parallel hardware,” Proc. SPIE 6837, 683703(2007).
[CrossRef]

Garcia, J.

Gopinathan, U.

Hennelly, B. M.

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25, 2608-2617 (2008).
[CrossRef]

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

Javidi, B.

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] [PubMed]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Security analysis of optical encryption,” Proc. SPIE 5986, 598603(2005).
[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] [PubMed]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, and B. Javidi, “Strengths and weaknesses of optical encryption algorithms,” 18th Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE, 2005), pp. 951-952.

Joseph, J.

Juvells, I.

Konforti, N.

D. Mendlovic, Z. Zalesvsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Kumar, A.

Kumar, P.

Liu, H.

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, “Known-plaintext attack on the double phase encoding and its implementation with parallel hardware,” Proc. SPIE 6837, 683703(2007).
[CrossRef]

Mas, D.

Mendlovic, D.

D. Mendlovic, Z. Zalesvsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Meng, X. F.

Monaghan, D. S.

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122-5125 (2008).
[CrossRef]

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46, 5257-5262 (2007).
[CrossRef] [PubMed]

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641-6647 (2007).
[CrossRef] [PubMed]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181-3186(2006).
[CrossRef] [PubMed]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, and B. Javidi, “Strengths and weaknesses of optical encryption algorithms,” 18th Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE, 2005), pp. 951-952.

Montes-Usategui, M.

Naughton, T. J.

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122-5125 (2008).
[CrossRef]

T. J. Naughton, B. M. Hennelly, and T. Dowling, “Introducing secure modes of operation for optical encryption,” J. Opt. Soc. Am. A 25, 2608-2617 (2008).
[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] [PubMed]

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641-6647 (2007).
[CrossRef] [PubMed]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181-3186(2006).
[CrossRef] [PubMed]

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Security analysis of optical encryption,” Proc. SPIE 5986, 598603(2005).
[CrossRef]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, and B. Javidi, “Strengths and weaknesses of optical encryption algorithms,” 18th Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE, 2005), pp. 951-952.

Osten, W.

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122-5125 (2008).
[CrossRef]

Pedrini, G.

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122-5125 (2008).
[CrossRef]

Peng, X.

Refregier, P.

Shen, X. X.

Sheridan, J. T.

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122-5125 (2008).
[CrossRef]

D. S. Monaghan, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Key-space analysis of double random phase encryption technique,” Appl. Opt. 46, 6641-6647 (2007).
[CrossRef] [PubMed]

G. Situ, U. Gopinathan, D. S. Monaghan, and J. T. Sheridan, “Cryptanalysis of optical security systems with significant output images,” Appl. Opt. 46, 5257-5262 (2007).
[CrossRef] [PubMed]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, and J. T. Sheridan, “A known-plaintext heuristic attack on the Fourier plane encryption algorithm,” Opt. Express 14, 3181-3186(2006).
[CrossRef] [PubMed]

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

U. Gopinathan, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, and B. Javidi, “Strengths and weaknesses of optical encryption algorithms,” 18th Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE, 2005), pp. 951-952.

Singh, K.

Situ, G.

Unnikrishnan, G.

Wang, Y. R.

Wei, H.

Xu, X. F.

Yu, B.

Zalesvsky, Z.

D. Mendlovic, Z. Zalesvsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

Zhang, H.

Zhang, J.

Zhang, P.

Appl. Opt. (4)

J. Mod. Opt. (1)

D. Mendlovic, Z. Zalesvsky, and N. Konforti, “Computation considerations and fast algorithms for calculating the diffraction integral,” J. Mod. Opt. 44, 407-414 (1997).
[CrossRef]

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

Opt. Commun. (1)

G. Situ, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, G. Pedrini, and W. Osten, “Collision in double random phase encoding,” Opt. Commun. 281, 5122-5125 (2008).
[CrossRef]

Opt. Eng. (1)

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 (2)

Opt. Lett. (8)

Proc. SPIE (2)

Y. Frauel, A. Castro, T. J. Naughton, and B. Javidi, “Security analysis of optical encryption,” Proc. SPIE 5986, 598603(2005).
[CrossRef]

H. Wei, X. Peng, H. Liu, S. Feng, and B. Z. Gao, “Known-plaintext attack on the double phase encoding and its implementation with parallel hardware,” Proc. SPIE 6837, 683703(2007).
[CrossRef]

Other (2)

B.Javidi, ed., Optical and Digital Techniques for Information Security, Vol. 1 of Advanced Science and Technologies for Security Applications (Springer, 2005).
[CrossRef]

U. Gopinathan, D. S. Monaghan, T. J. Naughton, J. T. Sheridan, and B. Javidi, “Strengths and weaknesses of optical encryption algorithms,” 18th Annual Meeting of the IEEE Lasers and Electro-Optics Society (IEEE, 2005), pp. 951-952.

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Figures (10)

Fig. 1
Fig. 1

Schematic diagram with the RPMs placed in front of lens L 1 : I ( x , y ) , image; R 1 ( x , y ) and R 2 ( x 1 , y 1 ) , RPMs; L 1 , spherical lens of focal length f; U f ( u , v ) , transformed image (random function).

Fig. 2
Fig. 2

Transform U f ( u , v ) of the impulse function: (a) 2D representation of magnitude, (b) mesh diagram for the normalized magnitude variation with pixel number.

Fig. 3
Fig. 3

Schematic diagram of the proposed encryption scheme: R 1 , R 2 , R 3 , and R 4 , RPMs; I, original image to be encrypted; E, encrypted image; L 1 and L 2 , lenses of focal length f each.

Fig. 4
Fig. 4

Results of numerical simulation: (a) original image to be encrypted, (b) encrypted image, and (c) decrypted image.

Fig. 5
Fig. 5

Results of brute force attack for the decryption of images encrypted with 16-phase level RPMs; decryption by means of RPMs with phase levels: (a), (b) 16; (c), (d) 4; (e), (f) 3; and (g), (h) 2.

Fig. 6
Fig. 6

Brute force attack with partial window size of RPMs; decryption with RPMs reduced by (a), (b) 10%; (c), (d) 20%; (e), (f) 30%; (g), (h) 40%; and (i), (j) 50%.

Fig. 7
Fig. 7

Results of brute force attack with 30% reduced window size of RPMs; decryption with phase levels (a), (b) 4; and (c), (d) 3.

Fig. 8
Fig. 8

Decryption under different conditions when the Fourier plane RPM is obtained with an impulse attack: (a) using classical DRPE setup, (b) when only R 4 is known, and (c) when only R 2 is known.

Fig. 9
Fig. 9

Experimental setup for the proposed scheme: BE, beam expander; BS, beam splitter; M, mirror; I, image; R 1 and R 2 , random phase masks; L 1 and L 2 , spherical lenses of focal length 20 cm each; L 3 , imaging lens; and Li Nb O 3 , photorefractive crystal.

Fig. 10
Fig. 10

Experimental results: (a) original image, (b) encrypted image, (c) correctly decrypted image, (d) decrypted image when R 4 is replaced with an incorrect RPM, and (e) decrypted image when R 2 is replaced with an incorrect RPM.

Equations (7)

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E ( x , y ) = FT 1 [ ( FT [ I ( x , y ) R 1 ( x , y ) ] ) R 3 ( u , v ) ] .
E ( x , y ) = FT 1 [ ( FT [ δ ( 0 , 0 ) R 1 ( x , y ) ] ) R 3 ( u , v ) ] .
U f ( u , v ) = 1 i λ f exp { i k 2 f ( 1 d 2 f ) ( u 2 + v 2 ) } FT [ ( FRT λ , d 1 [ δ ( 0 , 0 ) R 1 ( x , y ) ] ) R 2 ( x 1 , y 1 ) ] ,
U f ( u , v ) = 1 i λ f exp { i k 2 f ( 1 d 2 f ) ( u 2 + v 2 ) } FT [ ( FRT λ , d 1 [ I ( x , y ) R 1 ( x , y ) ] ) R 2 ( x 1 , y 1 ) ] .
E ( x E , y E ) = 1 i λ f exp { i k 2 f ( 1 d 4 f ) ( x E 2 + y E 2 ) } FT [ ( FRT λ , d 3 [ U f ( u , v ) R 3 ( u , v ) ] ) R 4 ( u 1 , v 1 ) ] .
u f ( u , v ) = 1 i λ f exp { i k 2 f ( 1 d 2 f ) ( u 2 + v 2 ) } FT [ ( FRT λ , d 1 [ δ ( 0 , 0 ) R 1 ( x , y ) ] ) R 2 ( x 1 , y 1 ) ] ,
E ( x E , y E ) = 1 i λ f exp { i k 2 f ( 1 d 4 f ) ( x E 2 + y E 2 ) } FT [ ( FRT λ , d 3 [ U f ( u , v ) R 3 ( u , v ) ] ) R 4 ( u 1 , v 1 ) ] .

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