Abstract

A hybrid heuristic attack scheme that combines the hill climbing algorithm and the simulated annealing algorithm is proposed to speed up the search procedure and to obtain a more accurate solution to the original key in the Fourier plane encryption algorithm. And a unit cycle is adopted to analyze the value space of the random phase. The experimental result shows that our scheme can obtain more accurate solution to the key that can achieve better decryption result both for the selected encrypted image and another unseen ciphertext image. The searching time is significantly reduced while without any exceptional case in searching procedure. For an image of 64×64 pixels, our algorithm costs a comparatively short computing time, about 1 minute, can retrieve the approximated key with the normalized root mean squared error 0.1, therefore, our scheme makes the known-plaintext attack on the Fourier plane image encryption more practical, stable, and effective.

© 2009 Optical Society of America

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References

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  1. Ph. Réfrégier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995)
    [CrossRef] [PubMed]
  2. L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. 35, 2459-2463 (1996).
    [CrossRef]
  3. O. Matoba and B. Javidi, "Encrypted optical memory system using three-dimensional keys in the Fresnel domain," Opt. Lett. 24, 762-764 (1999).
    [CrossRef]
  4. O. Matoba and B. Javidi, "Encrypted optical storage with wavelength-key and random phase codes," Appl. Opt. 38, 6785-6790 (1999).
    [CrossRef]
  5. E. Tajahuerce and B. Javidi, "Encrypting three-dimensional information with digital holography," Appl. Opt. 39, 6595-6601 (2000).
    [CrossRef]
  6. 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]
  7. 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]
  8. J. Ohtsubo and A. Fujimoto, "Practical image encryption and decryption by phase-coding technique for optical security systems," Appl. Opt. 41, 4848-4855 (2002).
    [CrossRef] [PubMed]
  9. G. Situ and J. Zhang, "Double random-phase encoding in the Fresnel domain," Opt. Lett. 29, 1584-1586 (2004).
    [CrossRef] [PubMed]
  10. H. Suzuki, M. Yamaguchi, M. Yachida, N. Ohyama, H. Tashima, and T. Obi, "Experimental evaluation of fingerprint verification system based on double random phase encoding," Opt. Express 14, 1755-1766 (2006). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-5-1755.
    [CrossRef] [PubMed]
  11. R. Tao, Y. Xin, and Y. Wang, "Double image encryption based on random phase encoding in the fractional Fourier domain," Opt. Express 15, 16067-16079 (2007). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-15-24-16067.
    [CrossRef] [PubMed]
  12. X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, "Security enhancement of double-random phase encryption by amplitude modulation," Opt. Lett. 33, 1575-1577 (2008).
    [CrossRef] [PubMed]
  13. P. Kumar, A. Kumar, J. Joseph, and K. Singh, "Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions," Opt. Lett. 34, 331-333 (2009)
    [CrossRef] [PubMed]
  14. W. Stallings, Cryptography and Network Security: Principles and Practice, 3rd ed. (Prentice Hall, 2004).
  15. A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, "Vulnerability to chosen-ciphertext attacks of optical encryption schemes based on double random phase keys," Opt. Lett. 30, 1644-1646 (2005).
    [CrossRef] [PubMed]
  16. 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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-14-8-3181.
    [CrossRef] [PubMed]
  17. 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]
  18. 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]
  19. 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). http://www.opticsexpress.org/abstract.cfm?URI=OPEX-15-16-10253.
    [CrossRef] [PubMed]
  20. S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
    [CrossRef] [PubMed]
  21. S. Nahar, S. Sahni, and E. Shragowitz, "Simulated annealing and combinatorial optimization," in Proceedings of ACM/IEEE Conference on Design Automation (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 293-299.
  22. M. Nieto-Vesperinas, R. Navarro, and F. J. Fuentes, "Performance of a simulated annealing algorithm for phase retrieval," J. Opt. Soc. Am. A 5, 30-38 (1988).
    [CrossRef]
  23. F. J. O. Martinez, J. S. Gonzalez, and I. Stojmenovic, "A parallel hill climbing algorithm for pushing dependent data in clients-providers-servers systems," in Proceedings of IEEE International Symposium on Computers and Communications (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 611-616.

2009 (1)

2008 (1)

2007 (2)

2006 (4)

2005 (1)

2004 (1)

2002 (1)

2001 (1)

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]

2000 (2)

1999 (2)

1996 (1)

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. 35, 2459-2463 (1996).
[CrossRef]

1995 (1)

1988 (1)

1983 (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Arcos, S.

Cai, L. Z.

Carnicer, A.

Castro, A.

Cheng, X. C.

Dong, G. Y.

Frauel, Y.

Fuentes, F. J.

Fujimoto, A.

Gelatt, C. D.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Gopinathan, U.

Javidi, B.

Joseph, J.

Juvells, I.

Kirkpatrick, S.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Kumar, A.

Kumar, P.

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]

Matoba, O.

Meng, X. F.

Monaghan, D. S.

Montes-Usategui, M.

Naughton, T. J.

Navarro, R.

Neto, L. G.

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. 35, 2459-2463 (1996).
[CrossRef]

Nieto-Vesperinas, M.

Obi, T.

Ohtsubo, J.

Ohyama, N.

Peng, X.

Réfrégier, Ph.

Shen, X. X.

Sheng, Y.

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. 35, 2459-2463 (1996).
[CrossRef]

Sheridan, J.T.

Singh, K.

Situ, G.

Suzuki, H.

Tajahuerce, E.

Tao, R.

Tashima, H.

Unnikrishnan, G.

Vecchi, M. P.

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Wang, Y.

Wang, Y. R.

Wei, H.

Xin, Y.

Xu, X. F.

Yachida, M.

Yamaguchi, M.

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, H.

Zhang, J.

Zhang, P.

Zhu, B.

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]

Appl. Opt. (3)

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

Opt. Commun. (1)

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]

Opt. Eng. (1)

L. G. Neto and Y. Sheng, "Optical implementation of image encryption using random phase encoding," Opt. Eng. 35, 2459-2463 (1996).
[CrossRef]

Opt. Express (4)

Opt. Lett. (9)

X. C. Cheng, L. Z. Cai, Y. R. Wang, X. F. Meng, H. Zhang, X. F. Xu, X. X. Shen, and G. Y. Dong, "Security enhancement of double-random phase encryption by amplitude modulation," Opt. Lett. 33, 1575-1577 (2008).
[CrossRef] [PubMed]

P. Kumar, A. Kumar, J. Joseph, and K. Singh, "Impulse attack free double-random-phase encryption scheme with randomized lens-phase functions," Opt. Lett. 34, 331-333 (2009)
[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]

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]

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

A. Carnicer, M. Montes-Usategui, S. Arcos, and I. Juvells, "Vulnerability to chosen-ciphertext 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]

Ph. Réfrégier and B. Javidi, "Optical image encryption based on input plane and Fourier plane random encoding," Opt. Lett. 20, 767-769 (1995)
[CrossRef] [PubMed]

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

Science (1)

S. Kirkpatrick, C. D. Gelatt, and M. P. Vecchi, "Optimization by Simulated Annealing," Science 220, 671-680 (1983).
[CrossRef] [PubMed]

Other (3)

S. Nahar, S. Sahni, and E. Shragowitz, "Simulated annealing and combinatorial optimization," in Proceedings of ACM/IEEE Conference on Design Automation (Institute of Electrical and Electronics Engineers, New York, 1986), pp. 293-299.

F. J. O. Martinez, J. S. Gonzalez, and I. Stojmenovic, "A parallel hill climbing algorithm for pushing dependent data in clients-providers-servers systems," in Proceedings of IEEE International Symposium on Computers and Communications (Institute of Electrical and Electronics Engineers, New York, 2002), pp. 611-616.

W. Stallings, Cryptography and Network Security: Principles and Practice, 3rd ed. (Prentice Hall, 2004).

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Figures (8)

Fig. 1.
Fig. 1.

Unit circle of the random phase.

Fig. 2.
Fig. 2.

Errors of single pixel perturbation.

Fig. 3.
Fig. 3.

Errors of multi-pixels perturbed by the value chosen randomly.

Fig. 4.
Fig. 4.

Errors of multi-pixels perturbed by the same perturbation value.

Fig. 5.
Fig. 5.

Block diagram of the hybrid heuristic algorithm.

Fig. 6.
Fig. 6.

(a) Original plaintext image A with 64×64 pixels, (b) the real part and (c) the imaginary part of the complex-valued encrypted image of A, (d) the decrypted image with an NRMS error of 0.1, (e) the plaintext B, (f) the real part and (g) the imaginary part of the complex-valued encrypted image of B, (h) the decrypted image B with an NRMS error of 0.1193, (i) Original plaintext image C with 64×64 pixels, (j) the decrypted image with an NRMS error of 0.0916, (k) Original plaintext image D, (l) the decrypted image with an NRMS error of 0.0952.

Fig. 7.
Fig. 7.

Time cost of estimating the key used to encrypt image of A and with an NRMS error of 0.1 in the cases of three different perturbation values.

Fig. 8.
Fig. 8.

NRMS error to decrypt the encrypted image of B using the same key that decrypts the encrypted image of A with NRMS error of 0.1.

Equations (3)

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Ψ(x)={f(x)R1}*R̂2
NRMS=i=1Mj=1NId(i,j)I(i,j)2i=1Mj=1NI(i,j)2
MSTD={1ni=1n(xix̅)2}12x̅,x̅=1ni=1nxi

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