Abstract

We propose and analyze a dual encryption/decryption scheme, motivated by recent interest in polarization encoding. Compared to standard optical encryption methods, which are based on phase and amplitude manipulation, this encryption procedure relying on Mueller–Stokes formalism provides large flexibility in the key encryption design. The effectiveness of our algorithm is discussed, thanks to a numerical simulation of the polarization encryption/decryption procedure of a 256 gray-level image. Of additional special interest is the immunity of this encryption algorithm to brute force attacks.

© 2010 Optical Society of America

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References

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2009

2007

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

2006

G. Biener, N. Avi, V. Kleiner, and E. Hasman, Opt. Commun. 261, 5 (2006).
[CrossRef]

U. Gopinathan, T. J. Naughton, and J. T. Sheridan, Appl. Opt. 45, 5693 (2006).
[CrossRef] [PubMed]

2001

2000

P. C. Mogesen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[CrossRef]

B. Javidi and T. Nomura, Opt. Eng. 39, 2439 (2000).
[CrossRef]

U. Gopinathan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[CrossRef]

1999

1998

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

1995

1989

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

Alfalou, A.

Avi, N.

G. Biener, N. Avi, V. Kleiner, and E. Hasman, Opt. Commun. 261, 5 (2006).
[CrossRef]

Biener, G.

G. Biener, N. Avi, V. Kleiner, and E. Hasman, Opt. Commun. 261, 5 (2006).
[CrossRef]

Boumier, P.

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

Brosseau, C.

A. Alfalou and C. Brosseau, Adv. Opt. Photon. 1, 589 (2009).
[CrossRef]

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

Croin, O.

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

De Martino, A.

Dollfus, A.

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

Dreux, M.

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

Fauconnier, T.

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

Glückstad, J.

P. C. Mogesen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[CrossRef]

Gopinathan, U.

Hasman, E.

G. Biener, N. Avi, V. Kleiner, and E. Hasman, Opt. Commun. 261, 5 (2006).
[CrossRef]

Ide, M.

Javidi, B.

Kleiner, V.

G. Biener, N. Avi, V. Kleiner, and E. Hasman, Opt. Commun. 261, 5 (2006).
[CrossRef]

Kuroda, K.

Mansour, A.

Matoba, O.

Mogesen, P. C.

P. C. Mogesen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[CrossRef]

Naughton, T. J.

Nomura, T.

B. Javidi and T. Nomura, Opt. Eng. 39, 2439 (2000).
[CrossRef]

Okada-Shudo, Y.

Orlik, X.

Pohit, M.

U. Gopinathan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[CrossRef]

Pouchol, T.

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

Refregier, P.

Richert, M.

Sheridan, J. T.

Shimura, T.

Singh, K.

U. Gopinathan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[CrossRef]

Tan, X.

Wolf, E.

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

Adv. Opt. Photon.

Appl. Opt.

C. R. Acad. Sci. Paris Ser. II

A. Dollfus, T. Fauconnier, M. Dreux, P. Boumier, T. Pouchol, and O. Croin, C. R. Acad. Sci. Paris Ser. II 308, 19 (1989).

Opt. Commun.

U. Gopinathan, M. Pohit, and K. Singh, Opt. Commun. 185, 25 (2000).
[CrossRef]

G. Biener, N. Avi, V. Kleiner, and E. Hasman, Opt. Commun. 261, 5 (2006).
[CrossRef]

P. C. Mogesen and J. Glückstad, Opt. Commun. 173, 177 (2000).
[CrossRef]

Opt. Eng.

B. Javidi and T. Nomura, Opt. Eng. 39, 2439 (2000).
[CrossRef]

Opt. Express

Opt. Lett.

Other

C. Brosseau, Fundamentals of Polarized Light (Wiley, 1998).

E. Wolf, Introduction to the Theory of Coherence and Polarization of Light (Cambridge U. Press, 2007).

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Figures (2)

Fig. 1
Fig. 1

Experimental setup of polarization-encoded encryption system: target, object to be encrypted; key, random encrypting key; Ret(1), Ret(2), wave plate retarder; Pol(1), Pol(2), Pol(3), linear polarizers; BS, beam splitter; M, mirror; CCD, CCD camera.

Fig. 2
Fig. 2

Comparison of the different encrypted and decrypted images of the illustrative example chosen to validate our algorithm: (a) image to be encrypted, (b) key image, (c) encrypted image, (d) decrypted image encrypted with the procedure displayed in Fig. 1, (e) ciphered image after 500,000 trials, (f) MSE error as a function of the trial number.

Equations (2)

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I C ( i , j ) = I C 0 ( i , j ) = 1 4 ( 1 + cos ( 2 φ rand i , j ) ) [ S I 0 ( i , j ) + S k 0 ( i , j ) ] .
I decry ( i , j ) = M pol _ decry × ( 1 4 ( 1 + cos ( 2 φ rand i , j ) ) [ S I 0 ( i , j ) + S k 0 ( i , j ) ] 0 0 0 ) = 1 8 [ S I 0 ( i , j ) + S k 0 ( i , j ) ] × ( ( 1 + cos ( 2 φ rand i , j ) ) cos ( 2 φ decry i , j ) ( 1 + cos ( 2 φ rand i , j ) ) sin ( 2 φ decry i , j ) ( 1 + cos ( 2 φ rand i , j ) ) 0 ) = ( S 0 _ decryp S 1 _ decryp S 2 _ decryp S 3 _ decryp ) .

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