Abstract

We perform a numerical analysis on the double random phase encryption/decryption technique. The key-space of an encryption technique is the set of possible keys that can be used to encode data using that technique. In the case of a strong encryption scheme, many keys must be tried in any brute-force attack on that technique. Traditionally, designers of optical image encryption systems demonstrate only how a small number of arbitrary keys cannot decrypt a chosen encrypted image in their system. However, this type of demonstration does not discuss the properties of the key-space nor refute the feasibility of an efficient brute-force attack. To clarify these issues we present a key-space analysis of the technique. For a range of problem instances we plot the distribution of decryption errors in the key-space indicating the lack of feasibility of a simple brute-force attack.

© 2007 Optical Society of America

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2007 (1)

2006 (3)

2005 (3)

2004 (2)

T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
[CrossRef]

M. Liebling, T. Blu, and M. Unser, "Complex-wave retrieval from a single off-axis hologram," J. Opt. Soc. Am. A 21, 367-377 (2004).
[CrossRef]

2003 (3)

B. Hennelly and J. T. Sheridan, "Optical image encryption by random shifting in fractional Fourier domains," Opt. Lett. 28, 269-271 (2003).
[CrossRef]

B. H. Zhu, H. F. Zhao, and S. T. Liu, "Image encryption based on pure intensity random coding and digital holography technique," Optik 114, 95-99 (2003).

B. M. Hennelly and J. T. Sheridan, "Image encryption and the fractional Fourier transform," Optik 114, 251-265 (2003).

2000 (3)

1998 (1)

1995 (1)

1994 (1)

1987 (1)

C. A. Deavours, Cryptology Yesterday, Today and Tomorrow (Artech House, 1987).

1982 (1)

1976 (1)

W. Diffie and M. E. Hellman, "New directions in cryptography," IEEE Trans. Inf. Theory 22, 644-654 (1976).
[CrossRef]

1967 (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

1939 (1)

G. F. Gaines, Cryptanalysis: a Study of Ciphers and Their Solution (Dover, 1939).

1931 (1)

H. O. Yardley, The American Black Chamber (U.S. Naval Institute Press, 1931).

Arcos, S.

Bell, K. M.

Blu, T.

Bollaro, F.

Brackenbury, L. E. M.

Carnicer, A.

Castro, A.

Deavours, C. A.

C. A. Deavours, Cryptology Yesterday, Today and Tomorrow (Artech House, 1987).

Diffie, W.

W. Diffie and M. E. Hellman, "New directions in cryptography," IEEE Trans. Inf. Theory 22, 644-654 (1976).
[CrossRef]

Fienup, J. R.

Frauel, Y.

Gaines, G. F.

G. F. Gaines, Cryptanalysis: a Study of Ciphers and Their Solution (Dover, 1939).

Goodman, J. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Gopinathan, U.

Goudail, F.

Hellman, M. E.

W. Diffie and M. E. Hellman, "New directions in cryptography," IEEE Trans. Inf. Theory 22, 644-654 (1976).
[CrossRef]

Hennelly, B.

Hennelly, B. M.

B. M. Hennelly and J. T. Sheridan, "Optical encryption and the space bandwidth product," Opt. Commun. 247, 291-305 (2005).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, "Generalizing, optimizing, and inventing numerical algorithms for the fractional Fourier, Fresnel, and linear canonical transforms," J. Opt. Soc. Am. A 22, 917-927 (2005).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, "Image encryption and the fractional Fourier transform," Optik 114, 251-265 (2003).

Javidi, B.

Joseph, J.

Juptner, W.

Juvells, I.

Lawrence, R. W.

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

Liebling, M.

Liu, S. T.

B. H. Zhu, H. F. Zhao, and S. T. Liu, "Image encryption based on pure intensity random coding and digital holography technique," Optik 114, 95-99 (2003).

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Peng, X.

Refregier, P.

Schnars, U.

Sheridan, J. T.

Singh, K.

Tajahuerce, E.

Unnikrishnan, G.

Unser, M.

Wei, H. Z.

Yardley, H. O.

H. O. Yardley, The American Black Chamber (U.S. Naval Institute Press, 1931).

Yu, B.

Zhang, P.

Zhao, H. F.

B. H. Zhu, H. F. Zhao, and S. T. Liu, "Image encryption based on pure intensity random coding and digital holography technique," Optik 114, 95-99 (2003).

Zhu, B. H.

B. H. Zhu, H. F. Zhao, and S. T. Liu, "Image encryption based on pure intensity random coding and digital holography technique," Optik 114, 95-99 (2003).

Appl. Opt. (5)

Appl. Phys. Lett. (1)

J. W. Goodman and R. W. Lawrence, "Digital image formation from electronically detected holograms," Appl. Phys. Lett. 11, 77-79 (1967).
[CrossRef]

IEEE Trans. Inf. Theory (1)

W. Diffie and M. E. Hellman, "New directions in cryptography," IEEE Trans. Inf. Theory 22, 644-654 (1976).
[CrossRef]

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

Opt. Commun. (1)

B. M. Hennelly and J. T. Sheridan, "Optical encryption and the space bandwidth product," Opt. Commun. 247, 291-305 (2005).
[CrossRef]

Opt. Eng. (1)

T. J. Naughton and B. Javidi, "Compression of encrypted three-dimensional objects using digital holography," Opt. Eng. 43, 2233-2238 (2004).
[CrossRef]

Opt. Express (2)

Opt. Lett. (5)

Optik (2)

B. H. Zhu, H. F. Zhao, and S. T. Liu, "Image encryption based on pure intensity random coding and digital holography technique," Optik 114, 95-99 (2003).

B. M. Hennelly and J. T. Sheridan, "Image encryption and the fractional Fourier transform," Optik 114, 251-265 (2003).

Other (4)

http://sipi.usc.edu.database/.

C. A. Deavours, Cryptology Yesterday, Today and Tomorrow (Artech House, 1987).

G. F. Gaines, Cryptanalysis: a Study of Ciphers and Their Solution (Dover, 1939).

H. O. Yardley, The American Black Chamber (U.S. Naval Institute Press, 1931).

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