Abstract

In Visual Cryptography, several images, called “shadow images”, that separately contain no information, are overlapped to reveal a shared secret message. We develop a method to digitally register one printed shadow image acquired by a camera with a purely digital shadow image, stored in memory. Using Fourier techniques derived from Fourier Optics concepts, the idea is to enhance and exploit the quasi periodicity of the shadow images, composed by a random distribution of black and white patterns on a periodic sampling grid. The advantage is to speed up the security control or the access time to the message, in particular in the cases of a small pixel size or of large numbers of pixels. Furthermore, the interest of visual cryptography can be increased by embedding the initial message in two shadow images that do not have identical mathematical supports, making manual registration impractical. Experimental results demonstrate the successful operation of the method, including the possibility to directly project the result onto the printed shadow image.

© 2011 OSA

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References

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    [CrossRef]
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    [CrossRef]
  4. F. Liu, C. Wu, and X. Lin, “The alignment problem of visual cryptography schemes,” Designs Codes and Cryptography 50(2), 215–227 (2009).
    [CrossRef]
  5. D. Wang, L. Dong, and X. Li, “Towards Shift Tolerant Visual Secret Sharing Schemes,” Arxiv preprint arXiv:1004.2364.
  6. W. Yan, D. Jin, and M. Kankanhalli, “Visual cryptography for print and scan applications,” in Proceedings of the 2004 International Symposium on Circuits and Systems 5, Citeseer, 572–575 (2004).
  7. J. Weir and W.Q. Yan, “A comprehensive study of visual cryptography,” Transactions on data hiding and multimedia security V 6010, 70–105 (2010).
    [CrossRef]
  8. C. N. Yang and T. H. Chung, “A general multi-secret visual cryptography scheme,” Opt. Commun. 283(24), 4949–4960 (2010).
    [CrossRef]
  9. H. Yamamoto, Y. Hayasaki, and N. Nishida, “Securing information display by use of visual cryptography,” Opt. Lett. 28(17), 1564–1566 (2003).
    [CrossRef] [PubMed]
  10. H. Yamamoto, Y. Hayasaki, and N. Nishida, “Secure information display with limited viewing zone by use of multi-color visual cryptography,” Opt. Express 12(7), 1258–1270 (2004).
    [CrossRef] [PubMed]
  11. A. Maréchal and M. Francon, “Diffraction, structure des images. Influence de la cohérence de la lumière,” Masson, 1959.
  12. J. Goodman, “Introduction to Fourier optics,” Roberts & Company Publishers, (2005).
  13. L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24(4), 325–376 (1992).
    [CrossRef]
  14. B. Zitova and J. Flusser, “Image registration methods: a survey,” Image and Vision Computing 21 (11), 977–1000 (2003).
    [CrossRef]
  15. Q. Tian and M. N. Huhns, “Algorithms for subpixel registration,” Computer Vision Graphics, and Image Processing 35, 220–233 (1986).
    [CrossRef]

2010

J. Weir and W.Q. Yan, “A comprehensive study of visual cryptography,” Transactions on data hiding and multimedia security V 6010, 70–105 (2010).
[CrossRef]

C. N. Yang and T. H. Chung, “A general multi-secret visual cryptography scheme,” Opt. Commun. 283(24), 4949–4960 (2010).
[CrossRef]

2009

C. N. Yang, A. G. Peng, and T. S. Chen, “MTVSS: (M)isalignment (T)olerant (V)isual (S)ecret (S)haring on resolving alignment difficulty,” Signal Process. 89(8), 1602–1624 (2009).
[CrossRef]

F. Liu, C. Wu, and X. Lin, “The alignment problem of visual cryptography schemes,” Designs Codes and Cryptography 50(2), 215–227 (2009).
[CrossRef]

2004

W. Yan, D. Jin, and M. Kankanhalli, “Visual cryptography for print and scan applications,” in Proceedings of the 2004 International Symposium on Circuits and Systems 5, Citeseer, 572–575 (2004).

H. Yamamoto, Y. Hayasaki, and N. Nishida, “Secure information display with limited viewing zone by use of multi-color visual cryptography,” Opt. Express 12(7), 1258–1270 (2004).
[CrossRef] [PubMed]

2003

H. Yamamoto, Y. Hayasaki, and N. Nishida, “Securing information display by use of visual cryptography,” Opt. Lett. 28(17), 1564–1566 (2003).
[CrossRef] [PubMed]

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image and Vision Computing 21 (11), 977–1000 (2003).
[CrossRef]

1995

M. Naor and A. Shamir, “Visual cryptography,” Lecture Notes in Computer Science 950(01), 1–12 (1995).
[CrossRef]

1992

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24(4), 325–376 (1992).
[CrossRef]

1987

1986

Q. Tian and M. N. Huhns, “Algorithms for subpixel registration,” Computer Vision Graphics, and Image Processing 35, 220–233 (1986).
[CrossRef]

Brown, L. G.

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24(4), 325–376 (1992).
[CrossRef]

Chen, T. S.

C. N. Yang, A. G. Peng, and T. S. Chen, “MTVSS: (M)isalignment (T)olerant (V)isual (S)ecret (S)haring on resolving alignment difficulty,” Signal Process. 89(8), 1602–1624 (2009).
[CrossRef]

Chung, T. H.

C. N. Yang and T. H. Chung, “A general multi-secret visual cryptography scheme,” Opt. Commun. 283(24), 4949–4960 (2010).
[CrossRef]

Dong, L.

D. Wang, L. Dong, and X. Li, “Towards Shift Tolerant Visual Secret Sharing Schemes,” Arxiv preprint arXiv:1004.2364.

Flusser, J.

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image and Vision Computing 21 (11), 977–1000 (2003).
[CrossRef]

Francon, M.

A. Maréchal and M. Francon, “Diffraction, structure des images. Influence de la cohérence de la lumière,” Masson, 1959.

Goodman, J.

J. Goodman, “Introduction to Fourier optics,” Roberts & Company Publishers, (2005).

Hayasaki, Y.

Huhns, M. N.

Q. Tian and M. N. Huhns, “Algorithms for subpixel registration,” Computer Vision Graphics, and Image Processing 35, 220–233 (1986).
[CrossRef]

Jin, D.

W. Yan, D. Jin, and M. Kankanhalli, “Visual cryptography for print and scan applications,” in Proceedings of the 2004 International Symposium on Circuits and Systems 5, Citeseer, 572–575 (2004).

Kafri, O.

Kankanhalli, M.

W. Yan, D. Jin, and M. Kankanhalli, “Visual cryptography for print and scan applications,” in Proceedings of the 2004 International Symposium on Circuits and Systems 5, Citeseer, 572–575 (2004).

Keren, E.

Li, X.

D. Wang, L. Dong, and X. Li, “Towards Shift Tolerant Visual Secret Sharing Schemes,” Arxiv preprint arXiv:1004.2364.

Lin, X.

F. Liu, C. Wu, and X. Lin, “The alignment problem of visual cryptography schemes,” Designs Codes and Cryptography 50(2), 215–227 (2009).
[CrossRef]

Liu, F.

F. Liu, C. Wu, and X. Lin, “The alignment problem of visual cryptography schemes,” Designs Codes and Cryptography 50(2), 215–227 (2009).
[CrossRef]

Maréchal, A.

A. Maréchal and M. Francon, “Diffraction, structure des images. Influence de la cohérence de la lumière,” Masson, 1959.

Naor, M.

M. Naor and A. Shamir, “Visual cryptography,” Lecture Notes in Computer Science 950(01), 1–12 (1995).
[CrossRef]

Nishida, N.

Peng, A. G.

C. N. Yang, A. G. Peng, and T. S. Chen, “MTVSS: (M)isalignment (T)olerant (V)isual (S)ecret (S)haring on resolving alignment difficulty,” Signal Process. 89(8), 1602–1624 (2009).
[CrossRef]

Shamir, A.

M. Naor and A. Shamir, “Visual cryptography,” Lecture Notes in Computer Science 950(01), 1–12 (1995).
[CrossRef]

Tian, Q.

Q. Tian and M. N. Huhns, “Algorithms for subpixel registration,” Computer Vision Graphics, and Image Processing 35, 220–233 (1986).
[CrossRef]

Wang, D.

D. Wang, L. Dong, and X. Li, “Towards Shift Tolerant Visual Secret Sharing Schemes,” Arxiv preprint arXiv:1004.2364.

Weir, J.

J. Weir and W.Q. Yan, “A comprehensive study of visual cryptography,” Transactions on data hiding and multimedia security V 6010, 70–105 (2010).
[CrossRef]

Wu, C.

F. Liu, C. Wu, and X. Lin, “The alignment problem of visual cryptography schemes,” Designs Codes and Cryptography 50(2), 215–227 (2009).
[CrossRef]

Yamamoto, H.

Yan, W.

W. Yan, D. Jin, and M. Kankanhalli, “Visual cryptography for print and scan applications,” in Proceedings of the 2004 International Symposium on Circuits and Systems 5, Citeseer, 572–575 (2004).

Yan, W.Q.

J. Weir and W.Q. Yan, “A comprehensive study of visual cryptography,” Transactions on data hiding and multimedia security V 6010, 70–105 (2010).
[CrossRef]

Yang, C. N.

C. N. Yang and T. H. Chung, “A general multi-secret visual cryptography scheme,” Opt. Commun. 283(24), 4949–4960 (2010).
[CrossRef]

C. N. Yang, A. G. Peng, and T. S. Chen, “MTVSS: (M)isalignment (T)olerant (V)isual (S)ecret (S)haring on resolving alignment difficulty,” Signal Process. 89(8), 1602–1624 (2009).
[CrossRef]

Zitova, B.

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image and Vision Computing 21 (11), 977–1000 (2003).
[CrossRef]

ACM Comput. Surv.

L. G. Brown, “A survey of image registration techniques,” ACM Comput. Surv. 24(4), 325–376 (1992).
[CrossRef]

Computer Vision Graphics, and Image Processing

Q. Tian and M. N. Huhns, “Algorithms for subpixel registration,” Computer Vision Graphics, and Image Processing 35, 220–233 (1986).
[CrossRef]

Designs Codes and Cryptography

F. Liu, C. Wu, and X. Lin, “The alignment problem of visual cryptography schemes,” Designs Codes and Cryptography 50(2), 215–227 (2009).
[CrossRef]

Image and Vision Computing

B. Zitova and J. Flusser, “Image registration methods: a survey,” Image and Vision Computing 21 (11), 977–1000 (2003).
[CrossRef]

Lecture Notes in Computer Science

M. Naor and A. Shamir, “Visual cryptography,” Lecture Notes in Computer Science 950(01), 1–12 (1995).
[CrossRef]

Opt. Commun.

C. N. Yang and T. H. Chung, “A general multi-secret visual cryptography scheme,” Opt. Commun. 283(24), 4949–4960 (2010).
[CrossRef]

Opt. Express

Opt. Lett.

Proceedings of the 2004 International Symposium on Circuits and Systems

W. Yan, D. Jin, and M. Kankanhalli, “Visual cryptography for print and scan applications,” in Proceedings of the 2004 International Symposium on Circuits and Systems 5, Citeseer, 572–575 (2004).

Signal Process.

C. N. Yang, A. G. Peng, and T. S. Chen, “MTVSS: (M)isalignment (T)olerant (V)isual (S)ecret (S)haring on resolving alignment difficulty,” Signal Process. 89(8), 1602–1624 (2009).
[CrossRef]

Transactions on data hiding and multimedia security V

J. Weir and W.Q. Yan, “A comprehensive study of visual cryptography,” Transactions on data hiding and multimedia security V 6010, 70–105 (2010).
[CrossRef]

Other

D. Wang, L. Dong, and X. Li, “Towards Shift Tolerant Visual Secret Sharing Schemes,” Arxiv preprint arXiv:1004.2364.

A. Maréchal and M. Francon, “Diffraction, structure des images. Influence de la cohérence de la lumière,” Masson, 1959.

J. Goodman, “Introduction to Fourier optics,” Roberts & Company Publishers, (2005).

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Figures (11)

Fig. 1
Fig. 1

(a) The six types of 2 × 2 shares. The shares are denoted : V0, V1 and D1 (top left to right), D0, H1 and H0 (bottom left to right), respectively. (b) An example of the coding of one bit when V0 was selected (at random) for the 0-bit: left to right: the initial bits, the SI1 share (V0), the SI2 share, the two SI’s overlaid.

Fig. 2
Fig. 2

(a) One single shadow image (SI) composed of 128×128 subpixels. Overlay of two SI’s sharing a 64 × 64 secret image for different horizontal shift values: (b) zero subpixel, (c) 0.5 subpixel and (d) 1.5 subpixels.

Fig. 3
Fig. 3

Processing a digitized SI : (a) Edge detection, (b) Amplitude of its Fourier transform. Peaks along the two axes at frequencies ± 1 2 wand ± 1 w can be seen (black circles), as well as at the center, where w is the length of the (square) subpixel sides.

Fig. 4
Fig. 4

(a) Morphological gradient on all possible shares (those on Fig. (1)), (b) Horizontal profile of the share D0 along the marked horizontal segment (lower left hand part of (a)) and (c) amplitude of its Fourier transform

Fig. 5
Fig. 5

(a) Signal randomly composed by shares and (b) The amplitude of its Fourier transform

Fig. 6
Fig. 6

Processing a digitized SI : (a) Edge detection, (b) Amplitude of its Fourier transform. Peaks along the two axes at frequencies ± 1 w 1 and ± 1 w 2 can be seen (black circles), as well as at the center.

Fig. 7
Fig. 7

Result of the superimposition of the printed SI1 and the suitably scaled shifted and rotated and projected SI2. The calibration of the video projector with the digital camera is not perfect and some slight distortions appears on the top.

Fig. 8
Fig. 8

Result of the superimposition of the digitized SI1 and the suitably scaled shifted and rotated SI2. The secret message is revealed with slight distortions on the right side due to a slight defect of flatness of SI1. The illustration shown is typical of many cases that we tried. The subpixels are either square (a–c) or rectangular (d). Comparison (a) with Fig. 2(c) indicates a registration accuracy better than half a subpixel.

Fig. 9
Fig. 9

Automatic registration of SI’s with non identical mathematical support. First column (a,d,g) the SI2 support is modified with respect to that of SI1. Second column (b,e,h) the automatic superposition shows accurate registration. Third column (c,f,i) with a one subpixel shift, no indication that the registration is close is visible.

Fig. 10
Fig. 10

The secret message (a) is revealed (b) by the suitably modified SI2 superposed with the acquired SI1. If a spurious symbol “K” is added to the message (c), typically by modifying a few pixels of SI1, the spurious symbol also appears in the revealed message (d). The support of SI2 has been reduced to a set of non overlapping windows (e). With this mathematical support, only “VC2011” is revealed whereas the spurious symbol is masked out (or, in other cases, it could just making the result unreadable, providing evidence that counterfeiting has occurred) (f).

Fig. 11
Fig. 11

Evolution of the maximum of the cross-correlation for messages with different ratio of black and white pixels

Equations (2)

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f ˜ D 0 ( ν ) = N ( w 2 t ) sinc [ π ν ( w 2 t ) ] exp ( i π ν w ) + N w sinc ( π ν w ) exp ( 3 i π ν w )
g ( x , y ) = f ( sx cos ( θ ) + sy sin ( θ ) , sx cos ( θ ) + sy sin ( θ ) ) g ˜ ( μ , ν ) = 1 s 2 f ˜ ( μ s cos ( θ ) + ν s sin ( θ ) , μ s cos ( θ ) + ν s sin ( θ ) )

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