Secure information display with limited viewing zone by use of multi-color visual cryptography

Hirotsugu Yamamoto; Yoshio Hayasaki; Nobuo Nishida

doi:10.1364/OPEX.12.001258

Optics Express
Vol. 12,
Issue 7,
pp. 1258-1270
(2004)
•https://doi.org/10.1364/OPEX.12.001258

Secure information display with limited viewing zone by use of multi-color visual cryptography

Hirotsugu Yamamoto, Yoshio Hayasaki, and Nobuo Nishida

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Hirotsugu Yamamoto, Yoshio Hayasaki, and Nobuo Nishida, "Secure information display with limited viewing zone by use of multi-color visual cryptography," Opt. Express 12, 1258-1270 (2004)

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Abstract

We propose a display technique that ensures security of visual information by use of visual cryptography. A displayed image appears as a completely random pattern unless viewed through a decoding mask. The display has a limited viewing zone with the decoding mask. We have developed a multi-color encryption code set. Eight colors are represented in combinations of a displayed image composed of red, green, blue, and black subpixels and a decoding mask composed of transparent and opaque subpixels. Furthermore, we have demonstrated secure information display by use of an LCD panel.

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Fig. 1. Schematic diagram of secure information display by use of visual cryptography.

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Fig. 2. Limitation of the viewing zone by use of a decoding mask.

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Fig. 3. Code set for encryption of eight-color images. The subpixel patterns of the displayed image are determined by the mask pattern and the pixel color. The white subpixels in the decoding mask pattern are transparent. R, G, B, C, M, Y, K, and W denote red, green, blue, cyan, magenta, yellow, black, and white, respectively, in the decoded image.

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Fig. 4. Examples of encryption for multi-color images. (a) A decoding mask, (b) a displayed image, (c) the decoded image, and (d) an unsuccessfully decoded image obtained by mis-overlaying of the decoding mask. Images (e) and (f) are another displayed image and the decoded image by overlaying the same decoding mask in (a).

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Fig. 5. Viewed images at the viewing position showing (a) red, green, and blue, (b) cyan, magenta, and yellow, (c) black, and (d) white.

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Fig. 6. Viewed images at different viewing points: (a) viewed image from the left side; (b) viewed image from relatively close to the ideal viewing position; (c) viewed image from the right side; (d) viewed image at close range; and (e) viewed image at long range.

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Tables (5)

Table 1. Assignment of subpixel values for multiple colors

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Table 2. Permutations of the red, green, and blue subpixels

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Table 3. Frequencies of obtained pixels values in combinations of each decoding mask pattern with the displayed image patterns. There are 120 different combinations for each mask pattern.

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Table 4. Frequencies of obtained pixel values in combinations of the displayed pattern for case number w with the decoding mask patterns. There are 20 different combinations for each displayed image pattern.

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Table 5. Extracted code set to encrypt multi-color images, where w denotes the case number.

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Equations (5)

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D = (\begin{matrix} d_{11} & d_{12} & d_{13} \\ d_{21} & d_{22} & d_{23} \end{matrix}), where {d_{11}, d_{12}, d_{13}, d_{21}, d_{22}, d_{23}} = {0, 0, 0, 1, 2, 4} .

M = (\begin{matrix} m_{11} & m_{12} & m_{13} \\ m_{21} & m_{22} & m_{23} \end{matrix}), where {m_{11}, m_{12}, m_{13}, m_{21}, m_{22}, m_{23}} = {0, 0, 0, 1, 1, 1} .

M^{T} D = \sum_{i = 1}^{2} (\begin{matrix} m_{i 1} d_{i 1} & m_{i 1} d_{i 2} & m_{i 1} d_{i 3} \\ m_{i 2} d_{i 1} & m_{i 2} d_{i 2} & m_{i 2} d_{i 3} \\ m_{i 3} d_{i 1} & m_{i 3} d_{i 2} & m_{i 3} d_{i 3} \end{matrix}),

M D^{T} = \sum_{j = 1}^{3} (\begin{matrix} m_{1 j} d_{1 j} & m_{1 j} d_{2 j} \\ m_{2 j} d_{1 j} & m_{2 j} d_{2 j} \end{matrix}) .

P_{0} = Tr (M^{T} D) = Tr (M D^{T}) = \sum_{i = 1}^{2} \sum_{j = 1}^{3} d_{ij} m_{ij},

Color	Pixel value	Subpixel values
Color	Pixel value	Red	Green	Blue
Black	0	0	0	0
Red	1	1	0	0
Green	2	0	2	0
Yellow	3	1	2	0
Blue	4	0	0	4
Magenta	5	1	0	4
Cyan	6	0	2	4
White	7	1	2	4

Case number w	a_w	b_w	c_w
1	1	2	4
2	1	4	2
3	2	1	4
4	2	4	1
5	4	1	2
6	4	2	1

Obtained pixel value	Frequency (total 120)
0 (black)	6
1 (red)	18
2 (green)	18
3 (yellow)	18
4 (blue)	18
5 (magenta)	18
6 (cyan)	18
7 (white)	6

Obtained pixel value	Frequency (total 20)
0	1
a_w	3
b_w	3
c_w	3
a_w +b_w	3
b_w +c_w	3
c_w +a_w	3
a_w +b_w +c_w	1

Pixel value
Mask	a_w	b_w	c_w	b_w +c_w	c_w +a_w	a_w +b_w	0	a_w +b_w +c_w
Mask	M ₁	$D_{5}^{w}$	$D_{6}^{w}$	$D_{4}^{w}$	$D_{2}^{w}$	$D_{3}^{w}$	$D_{7}^{w}$	$D_{8}^{w}$	$D_{1}^{w}$
M ₂	$D_{8}^{w}$	$D_{7}^{w}$	$D_{3}^{w}$	$D_{1}^{w}$	$D_{4}^{w}$	$D_{6}^{w}$	$D_{5}^{w}$	$D_{2}^{w}$
M ₃	$D_{7}^{w}$	$D_{8}^{w}$	$D_{2}^{w}$	$D_{4}^{w}$	$D_{1}^{w}$	$D_{5}^{w}$	$D_{6}^{w}$	$D_{3}^{w}$
M ₄	$D_{6}^{w}$	$D_{5}^{w}$	$D_{1}^{w}$	$D_{3}^{w}$	$D_{2}^{w}$	$D_{8}^{w}$	$D_{7}^{w}$	$D_{4}^{w}$
M ₅	$D_{1}^{w}$	$D_{4}^{w}$	$D_{6}^{w}$	$D_{8}^{w}$	$D_{7}^{w}$	$D_{3}^{w}$	$D_{2}^{w}$	$D_{5}^{w}$
M ₆	$D_{4}^{w}$	$D_{1}^{w}$	$D_{5}^{w}$	$D_{7}^{w}$	$D_{8}^{w}$	$D_{2}^{w}$	$D_{3}^{w}$	$D_{6}^{w}$
M ₇	$D_{3}^{w}$	$D_{2}^{w}$	$D_{8}^{w}$	$D_{6}^{w}$	$D_{5}^{w}$	$D_{1}^{w}$	$D_{4}^{w}$	$D_{7}^{w}$
M ₈	$D_{2}^{w}$	$D_{3}^{w}$	$D_{7}^{w}$	$D_{5}^{w}$	$D_{6}^{w}$	$D_{4}^{w}$	$D_{1}^{w}$	$D_{8}^{w}$

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Figures (6)

Tables (5)

Equations (5)

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