Abstract

We analyze optical encryption systems using the techniques of conventional cryptography. All conventional block encryption algorithms are vulnerable to attack, and often they employ secure modes of operation as one way to increase security. We introduce the concept of conventional secure modes to optical encryption and analyze the results in the context of known conventional and optical attacks. We consider only the optical system “double random phase encoding,” which forms the basis for a large number of optical encryption, watermarking, and multiplexing systems. We consider all attacks proposed to date in one particular scenario. We analyze only the mathematical algorithms themselves and do not consider the additional security that arises from employing these algorithms in physical optical systems.

© 2008 Optical Society of America

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    [CrossRef]
  43. O. Matoba and B. Javidi, “Optical retrieval of encrypted digital holograms for secure real-time display,” Opt. Lett. 27, 321-323 (2002).
    [CrossRef]
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    [CrossRef]
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2008 (2)

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase keys in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808-3816 (2008).
[CrossRef] [PubMed]

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]

2007 (4)

2006 (3)

2005 (3)

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] [PubMed]

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

D. Woods and T. J. Naughton, “An optical model of computation,” Theor. Comput. Sci. 334, 227-258 (2005).
[CrossRef]

2004 (7)

W. C. Su and C. H. Lin, “Enhancement of the angular selectivity in encrypted holographic memory,” Appl. Opt. 43, 2298-2304 (2004).
[CrossRef] [PubMed]

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 123-128 (2004).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Random phase and shifting encryption in Fresnel domain,” Opt. Eng. (Bellingham) 43, 1-11 (2004).
[CrossRef]

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

N. K. Nischal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. (Bellingham) 42, 3566-3571 (2004).
[CrossRef]

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231-1280 (2004).
[CrossRef]

H.-Y. Lee, J.-P. Liu, C.-C. Chang, H.-F. Yau, and T.-C. Chang, “The decryption of random phase multiplexing encoding system,” Proc. SPIE 5560, 117-123 (2004).
[CrossRef]

2003 (3)

2002 (3)

O. Matoba and B. Javidi, “Optical retrieval of encrypted digital holograms for secure real-time display,” Opt. Lett. 27, 321-323 (2002).
[CrossRef]

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

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

2001 (3)

X. Tan, O. Matoba, T. Shimura, and K. Kuroda, “Improvement in holographic storage capacity by use of double-random phase encryption,” Appl. Opt. 40, 4721-4727 (2001).
[CrossRef]

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187, 57-63 (2001).
[CrossRef]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51-67 (2001).
[CrossRef]

2000 (8)

1999 (3)

1998 (1)

1997 (1)

1995 (1)

1984 (2)

A. Huang, “Architectural considerations involved in the design of an optical digital computer,” Proc. IEEE 72, 780-786 (1984).
[CrossRef]

A. A. Sawchuk and T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758-779 (1984).
[CrossRef]

Anderson, R.

R. Anderson, Security Engineering, 2nd ed. (Wiley, 2008).

Arcos, S.

Bashaw, M. C.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231-1280 (2004).
[CrossRef]

Bollaro, F.

Burnett, A.

A. Burnett, F. Byrne, T. Dowling, and A. Duffy, “A biometric identity based signature scheme,” Int. J. Netw. Secur. 5, 317-326 (2007).

Byrne, F.

A. Burnett, F. Byrne, T. Dowling, and A. Duffy, “A biometric identity based signature scheme,” Int. J. Netw. Secur. 5, 317-326 (2007).

Calabretta, N.

Carnicer, A.

Castro, A.

Caulfield, H. J.

H. J. Caulfield, D. Psaltis, and G. Sincerbox, Holographic Data Storage (Springer-Verlag, 2000).

Chang, C.-C.

H.-Y. Lee, J.-P. Liu, C.-C. Chang, H.-F. Yau, and T.-C. Chang, “The decryption of random phase multiplexing encoding system,” Proc. SPIE 5560, 117-123 (2004).
[CrossRef]

Chang, T.-C.

H.-Y. Lee, J.-P. Liu, C.-C. Chang, H.-F. Yau, and T.-C. Chang, “The decryption of random phase multiplexing encoding system,” Proc. SPIE 5560, 117-123 (2004).
[CrossRef]

Chiou, A. E. T.

de Waardt, H.

Dorren, H. J. S.

Dowling, T.

A. Burnett, F. Byrne, T. Dowling, and A. Duffy, “A biometric identity based signature scheme,” Int. J. Netw. Secur. 5, 317-326 (2007).

Duffy, A.

A. Burnett, F. Byrne, T. Dowling, and A. Duffy, “A biometric identity based signature scheme,” Int. J. Netw. Secur. 5, 317-326 (2007).

Frauel, Y.

Gavrilenko, K. V.

A. A. Vladimirov, K. V. Gavrilenko, and A. A. Mikhailovsky, Wi-Foo: The Secrets of Wireless Hacking (Addision, Wesley, 2004).

Glückstad, J.

Gopinathan, U.

Goudail, F.

Hennelly, B.

Hennelly, B. M.

B. M. Hennelly, T. J. Naughton, J. B. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060-1062 (2007).
[CrossRef] [PubMed]

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, “Random phase and shifting encryption in Fresnel domain,” Opt. Eng. (Bellingham) 43, 1-11 (2004).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).
[CrossRef]

Hesselink, L.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231-1280 (2004).
[CrossRef]

Hill, M. T.

Huang, A.

A. Huang, “Architectural considerations involved in the design of an optical digital computer,” Proc. IEEE 72, 780-786 (1984).
[CrossRef]

Huijskens, F. M.

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]

B. M. Hennelly, T. J. Naughton, J. B. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060-1062 (2007).
[CrossRef] [PubMed]

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

O. Matoba and B. Javidi, “Optical retrieval of encrypted digital holograms for secure real-time display,” Opt. Lett. 27, 321-323 (2002).
[CrossRef]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

B. Javidi, N. Towghi, N. Maghzi, and S. C. Verrall, “Error reduction techniques and error analysis for fully phase and amplitude based encryption,” Appl. Opt. 39, 4117-4130 (2000).
[CrossRef]

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28-30 (2000).
[CrossRef]

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

N. Towghi, B. Javidi, and Z. Luo, “Fully phase encrypted image processor,” J. Opt. Soc. Am. A 16, 1915-1927 (1999).
[CrossRef]

O. Matoba and B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288-7293 (1999).
[CrossRef]

F. Goudail, F. Bollaro, B. Javidi, and P. Refregier, “Influence of a perturbation in a double random phase encoding system,” J. Opt. Soc. Am. A 15, 2629-2638 (1998).
[CrossRef]

B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054-1058 (1997).
[CrossRef] [PubMed]

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]

Joseph, J.

N. K. Nischal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. (Bellingham) 42, 3566-3571 (2004).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
[CrossRef]

Juptner, W.

U. Schnars and W. Juptner, Digital Holography (Springer, 2005).

Juptner, W. P. O.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

Juvells, I.

Kelly, D. P.

Khoe, G. D.

Kuroda, K.

Lee, H.-Y.

H.-Y. Lee, J.-P. Liu, C.-C. Chang, H.-F. Yau, and T.-C. Chang, “The decryption of random phase multiplexing encoding system,” Proc. SPIE 5560, 117-123 (2004).
[CrossRef]

Li, J.

Lin, C. H.

Liu, J.-P.

H.-Y. Lee, J.-P. Liu, C.-C. Chang, H.-F. Yau, and T.-C. Chang, “The decryption of random phase multiplexing encoding system,” Proc. SPIE 5560, 117-123 (2004).
[CrossRef]

Liu, S.

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187, 57-63 (2001).
[CrossRef]

Liu, Y.

Luo, Z.

Maghzi, N.

Mao, W.

W. Mao, Modern Cryptography (Prentice Hall, 2004).

Matoba, O.

McDonald, J. B.

Mikhailovsky, A. A.

A. A. Vladimirov, K. V. Gavrilenko, and A. A. Mikhailovsky, Wi-Foo: The Secrets of Wireless Hacking (Addision, Wesley, 2004).

Mogensen, P. C.

Monaghan, D. S.

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]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase keys in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808-3816 (2008).
[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]

B. M. Hennelly, T. J. Naughton, J. B. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060-1062 (2007).
[CrossRef] [PubMed]

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]

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]

D. Woods and T. J. Naughton, “An optical model of computation,” Theor. Comput. Sci. 334, 227-258 (2005).
[CrossRef]

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

T. J. Naughton, “Continuous-space model of computation is Turing universal,” Proc. SPIE 4109, 121-128 (2000).
[CrossRef]

Nischal, N. K.

N. K. Nischal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. (Bellingham) 42, 3566-3571 (2004).
[CrossRef]

Nomura, T.

Orlov, S. S.

L. Hesselink, S. S. Orlov, and M. C. Bashaw, “Holographic data storage systems,” Proc. IEEE 92, 1231-1280 (2004).
[CrossRef]

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.

Psaltis, D.

H. J. Caulfield, D. Psaltis, and G. Sincerbox, Holographic Data Storage (Springer-Verlag, 2000).

Refregier, P.

Sawchuk, A. A.

A. A. Sawchuk and T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758-779 (1984).
[CrossRef]

Schnars, U.

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

U. Schnars and W. Juptner, Digital Holography (Springer, 2005).

Schneier, B.

B. Schneier, Applied Cryptography, 2nd ed. (Wiley, 1996), pp. 200-201.

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, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase keys in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808-3816 (2008).
[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]

B. M. Hennelly, T. J. Naughton, J. B. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060-1062 (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, “Optical encryption and the space bandwidth product,” Opt. Commun. 247, 291-305 (2005).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Random phase and shifting encryption in Fresnel domain,” Opt. Eng. (Bellingham) 43, 1-11 (2004).
[CrossRef]

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).
[CrossRef]

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

Shimura, T.

Sincerbox, G.

H. J. Caulfield, D. Psaltis, and G. Sincerbox, Holographic Data Storage (Springer-Verlag, 2000).

Singh, K.

N. K. Nischal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. (Bellingham) 42, 3566-3571 (2004).
[CrossRef]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51-67 (2001).
[CrossRef]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier domain encoding for optical security,” Opt. Eng. (Bellingham) 39, 2853-2859 (2000).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
[CrossRef]

Situ, 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]

D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase keys in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808-3816 (2008).
[CrossRef] [PubMed]

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 123-128 (2004).
[CrossRef]

Srivatsa, A.

Stallings, W.

W. Stallings, Cryptography and Network Security, 4th ed. (Prentice Hall, 2005).

Strand, T. C.

A. A. Sawchuk and T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758-779 (1984).
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S. H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Books, 2001).

Su, W. C.

Sun, C. C.

Tajahuerce, E.

Tan, X.

Tanno, N.

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

Towghi, N.

Trappe, W.

W. Trappe and L. C. Washington, Introduction to Cryptography with Coding Theory (Prentice Hall, 2001).

Unnikrishnan, G.

B. M. Hennelly, T. J. Naughton, J. B. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060-1062 (2007).
[CrossRef] [PubMed]

N. K. Nischal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. (Bellingham) 42, 3566-3571 (2004).
[CrossRef]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51-67 (2001).
[CrossRef]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier domain encoding for optical security,” Opt. Eng. (Bellingham) 39, 2853-2859 (2000).
[CrossRef]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
[CrossRef]

Vaudenay, S.

S. Vaudenay, “Security flaws induced by CBC padding,” in Advances in Cryptology--Proceedings of EUROCRYPT'02, Lecture Notes in Computer Science (Springer-Verlag, 2002), Vol. 2332, pp. 534-545.

Verrall, S. C.

Vladimirov, A. A.

A. A. Vladimirov, K. V. Gavrilenko, and A. A. Mikhailovsky, Wi-Foo: The Secrets of Wireless Hacking (Addision, Wesley, 2004).

Wang, B.

Washington, L. C.

W. Trappe and L. C. Washington, Introduction to Cryptography with Coding Theory (Prentice Hall, 2001).

Wei, H.

Woods, D.

D. Woods and T. J. Naughton, “An optical model of computation,” Theor. Comput. Sci. 334, 227-258 (2005).
[CrossRef]

Yau, H.-F.

H.-Y. Lee, J.-P. Liu, C.-C. Chang, H.-F. Yau, and T.-C. Chang, “The decryption of random phase multiplexing encoding system,” Proc. SPIE 5560, 117-123 (2004).
[CrossRef]

Yu, B.

Yu, L.

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187, 57-63 (2001).
[CrossRef]

Zhang, G.

Zhang, J.

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 123-128 (2004).
[CrossRef]

Zhang, P.

Zhang, Y.

Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277-285 (2002).
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Y. Zhang, C. H. Zheng, and N. Tanno, “Optical encryption based on iterative fractional Fourier transform,” Opt. Commun. 202, 277-285 (2002).
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S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187, 57-63 (2001).
[CrossRef]

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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).
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D. S. Monaghan, G. Situ, U. Gopinathan, T. J. Naughton, and J. T. Sheridan, “Role of phase keys in the double random phase encoding technique: an error analysis,” Appl. Opt. 47, 3808-3816 (2008).
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B. Javidi, G. Zhang, and J. Li, “Encrypted optical memory using double-random phase encoding,” Appl. Opt. 36, 1054-1058 (1997).
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O. Matoba and B. Javidi, “Encrypted optical storage with angular multiplexing,” Appl. Opt. 38, 7288-7293 (1999).
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X. Tan, O. Matoba, T. Shimura, and K. Kuroda, “Improvement in holographic storage capacity by use of double-random phase encryption,” Appl. Opt. 40, 4721-4727 (2001).
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W. C. Su and C. H. Lin, “Enhancement of the angular selectivity in encrypted holographic memory,” Appl. Opt. 43, 2298-2304 (2004).
[CrossRef] [PubMed]

E. Tajahuerce and B. Javidi, “Encrypting three-dimensional information with digital holography,” Appl. Opt. 39, 6595-6601 (2000).
[CrossRef]

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A. Burnett, F. Byrne, T. Dowling, and A. Duffy, “A biometric identity based signature scheme,” Int. J. Netw. Secur. 5, 317-326 (2007).

J. Lightwave Technol. (1)

J. Opt. Soc. Am. A (2)

Meas. Sci. Technol. (1)

U. Schnars and W. P. O. Juptner, “Digital recording and numerical reconstruction of holograms,” Meas. Sci. Technol. 13, 85-101 (2002).
[CrossRef]

Opt. Commun. (6)

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]

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

S. Liu, L. Yu, and B. Zhu, “Optical image encryption by cascaded fractional Fourier transforms with random phase filtering,” Opt. Commun. 187, 57-63 (2001).
[CrossRef]

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

G. Situ and J. Zhang, “A lensless optical security system based on computer-generated phase only masks,” Opt. Commun. 232, 123-128 (2004).
[CrossRef]

G. Unnikrishnan and K. Singh, “Optical encryption using quadratic phase systems,” Opt. Commun. 193, 51-67 (2001).
[CrossRef]

Opt. Eng. (Bellingham) (4)

B. M. Hennelly and J. T. Sheridan, “Random phase and shifting encryption in Fresnel domain,” Opt. Eng. (Bellingham) 43, 1-11 (2004).
[CrossRef]

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

N. K. Nischal, G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption using a localized fractional Fourier transform,” Opt. Eng. (Bellingham) 42, 3566-3571 (2004).
[CrossRef]

G. Unnikrishnan and K. Singh, “Double random fractional Fourier domain encoding for optical security,” Opt. Eng. (Bellingham) 39, 2853-2859 (2000).
[CrossRef]

Opt. Express (2)

Opt. Lett. (11)

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] [PubMed]

X. Peng, H. Wei, and P. Zhang, “Chosen-plaintext attack on lensless double-random phase encoding in the Fresnel domain,” Opt. Lett. 31, 3261-3263 (2006).
[CrossRef] [PubMed]

B. M. Hennelly, T. J. Naughton, J. B. McDonald, J. T. Sheridan, G. Unnikrishnan, D. P. Kelly, and B. Javidi, “Spread-space spread-spectrum technique for secure multiplexing,” Opt. Lett. 32, 1060-1062 (2007).
[CrossRef] [PubMed]

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] [PubMed]

G. Unnikrishnan, J. Joseph, and K. Singh, “Optical encryption by double random phase encoding in the fractional Fourier domain,” Opt. Lett. 25, 887-889 (2000).
[CrossRef]

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

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

B. Javidi and T. Nomura, “Securing information by use of digital holography,” Opt. Lett. 25, 28-30 (2000).
[CrossRef]

O. Matoba and B. Javidi, “Optical retrieval of encrypted digital holograms for secure real-time display,” Opt. Lett. 27, 321-323 (2002).
[CrossRef]

P. C. Mogensen and J. Glückstad, “Phase-only optical encryption,” Opt. Lett. 25, 566-568 (2000).
[CrossRef]

Optik (Stuttgart) (1)

B. M. Hennelly and J. T. Sheridan, “Image encryption and the fractional Fourier transform,” Optik (Stuttgart) 114, 251-265 (2003).
[CrossRef]

Proc. IEEE (3)

A. Huang, “Architectural considerations involved in the design of an optical digital computer,” Proc. IEEE 72, 780-786 (1984).
[CrossRef]

A. A. Sawchuk and T. C. Strand, “Digital optical computing,” Proc. IEEE 72, 758-779 (1984).
[CrossRef]

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[CrossRef]

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T. J. Naughton, “Continuous-space model of computation is Turing universal,” Proc. SPIE 4109, 121-128 (2000).
[CrossRef]

H.-Y. Lee, J.-P. Liu, C.-C. Chang, H.-F. Yau, and T.-C. Chang, “The decryption of random phase multiplexing encoding system,” Proc. SPIE 5560, 117-123 (2004).
[CrossRef]

Theor. Comput. Sci. (1)

D. Woods and T. J. Naughton, “An optical model of computation,” Theor. Comput. Sci. 334, 227-258 (2005).
[CrossRef]

Other (10)

U. Schnars and W. Juptner, Digital Holography (Springer, 2005).

R. Anderson, Security Engineering, 2nd ed. (Wiley, 2008).

S. H. Strogatz, Nonlinear Dynamics and Chaos (Perseus Books, 2001).

A. A. Vladimirov, K. V. Gavrilenko, and A. A. Mikhailovsky, Wi-Foo: The Secrets of Wireless Hacking (Addision, Wesley, 2004).

W. Mao, Modern Cryptography (Prentice Hall, 2004).

W. Stallings, Cryptography and Network Security, 4th ed. (Prentice Hall, 2005).

W. Trappe and L. C. Washington, Introduction to Cryptography with Coding Theory (Prentice Hall, 2001).

S. Vaudenay, “Security flaws induced by CBC padding,” in Advances in Cryptology--Proceedings of EUROCRYPT'02, Lecture Notes in Computer Science (Springer-Verlag, 2002), Vol. 2332, pp. 534-545.

B. Schneier, Applied Cryptography, 2nd ed. (Wiley, 1996), pp. 200-201.

H. J. Caulfield, D. Psaltis, and G. Sincerbox, Holographic Data Storage (Springer-Verlag, 2000).

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Figures (6)

Fig. 1
Fig. 1

General optical encryption/decryption setup for DRPE. OFT, optical Fourier transform; k, random phase mask represented on a SLM.

Fig. 2
Fig. 2

Flow chart for (a) DRPE encryption E k and (b) DRPE decryption D k . FT, Fourier transform; IFT, inverse Fourier transform. The conjugate of the phase key k 2 is used in the decryption process. The symbol * denotes complex conjugation.

Fig. 3
Fig. 3

Illustrations of DRPE operation: (a) Sequence of plaintext inputs (in white) is encrypted to ciphertext outputs (shaded). (b) In ECB and CBC modes, if attackers obtain the key they can immediately decrypt the entire sequence. (c) In CFB mode, if attackers approximate the key with a single plaintext–ciphertext pair, only subsequent images can be decrypted because function f 1 is not reversible. (d) In both CFB and OFB modes, careful choice of f 1 can mean that the propagation of errors from an attack that only approximates the key will mean that only a very small number of subsequent images will be decrypted.

Fig. 4
Fig. 4

Flow chart for CBC mode. (a) Encryption, where the two phase mask products and two FTs represent the E k operation. (b) Decryption, where the two phase mask products and two IFTs represent the D k operation. The flow chart does not show that at i = 1 , the initial feedback image is C 0 = IV .

Fig. 5
Fig. 5

Flow chart for CFB mode. (a) Encryption, where the two phase mask products and two FTs represent the E I operation. (b) Decryption, where the two phase mask products and two IFTs represent the D I operation. Function * denotes the application of complex conjugation. The flow chart does not show that at i = 1 , I i = k 2 .

Fig. 6
Fig. 6

Flow chart for OFB mode. (a) Encryption, where the two phase mask products and two FTs represent the E I operation. (b) Decryption, where the two phase mask products and two IFTs represent the D I operation. Function * denotes the application of complex conjugation. The flow chart does not show that at i = 1 , I i = k 2 .

Tables (1)

Tables Icon

Table 1 List of Attacks on DRPE

Equations (31)

Equations on this page are rendered with MathJax. Learn more.

C ( x ) = E ( P ( x ) ) ,
E ( P ( x ) ) = { P ( x ) exp [ j 2 π k 1 ( x ) ] } h ( x ) ,
F { h ( x ) } = exp [ j 2 π k 2 ( x ) ] .
P ( x ) = D ( C ( x ) ) ,
D ( C ( x ) ) = { C ( x ) h ( x ) } exp [ j 2 π k 1 ( x ) ] ,
C i = E k ( P i ) , 1 i m .
P i = D k ( C i ) , 1 i m .
C 0 = I V ,
C i = E k ( P i C i 1 ) , 1 i m ,
P i = D k ( C i ) C i 1 , 1 i m .
C i = E k ( f ( P i , C i 1 ) ) , 1 i m ,
P i = f 1 ( D k ( C i ) , C i 1 ) , 1 i m .
I 1 = I V ,
I i = C i 1 , 2 i m ,
C i = P i E k ( I i ) , 1 i m ,
P i = C i E k ( I i ) , 1 i m .
I i = f 1 ( I i 1 , C i 1 ) , 2 i m ,
C i = f 2 ( P i , I i ) , 1 i m ,
P i = f 2 1 ( C i , I i ) , 1 i m .
I 1 = k 2 ,
I i = f 1 ( I i 1 , C i 1 ) , 2 i m ,
C i = E I i ( P i ) , 1 i m ,
P i = D I i ( C i ) , 1 i m .
I 1 = I V ,
I i = E k ( I i 1 ) , 2 i m ,
C i = P i I i , 1 i m ,
P i = C i I i , 1 i m .
I 1 = k 2 ,
I i = f 1 ( I i 1 ) , 2 i m ,
C i = E I i ( P i ) , 1 i m ,
P i = D I i ( C i ) , 1 i m .

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