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64 3.2.1 Disjoint Visual Cryptography
3.3 Embedding a Share of Visual Cryptography in a Halftone Image
Using halftone and colour images as a base or cover for multiple secret sharing is an interesting topic. Techniques proposed within [117] allow for a smaller set of shares (which can be unique) to be hidden with these meaningful colour images. Using the idea of a master key is capable of recovering all the secrets which have been generated using the outlined scheme, it is used to cover the halftone or colour image in order to reveal the secrets. The secret shares in this case are embedded within the cover images, this helps to remove suspicion that any encryption has taken place or, that the image has even been altered in any specific noticeable way.
Image hiding based on IE’s select function provides the basis to hide the shares of visual cryptography in a halftone image. Fig. 3.6 shows the two shares of an image “Q”. Being able to hide these shares inside a halftone image without any noticeable changes in the base image would be highly desirable in terms of secret sharing.
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(a) (b) (c)
Figure 3.6: The \Q” image and its corresponding shares. © Weir & Yan 2009
Figure 3.7: Flowchart of secret hiding using visual cryptography. © Weir & Yan 2009
Fig. 3.7 depicts the halftone scheme and illustrates how to embed a share of visual cryptography into a halftone image. The halftone image is created using dispersed-dot ordered dithering [64]. Dispersed dots were chosen because they usually have a square shape, this corresponds to the square nature of the VC shares allowing a share to be inserted into a halftone image with minimal changes to the overall image. With one of the shares in Fig. 3.6, a similar region on the given image is searched for and the similar regions are employed to embed the share into this image using the even and odd scan lines. This merging combines the odd scan line from the share, the even scan lines from the public halftone image or visa versa. The merged image includes the secret, when another share of visual cryptography is overlapped on the regions, the secret can be revealed.
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Given the shares width W and height H, appropriate areas W × H are located within the base image. This involves working out the relative pixel densities with the shares Dsi , s1 and s2 and the corresponding W
× H area within the base image DcW×H. If the densities fall within a specific threshold (T > 0), then that is a potential area, suitable for hiding a share.
The difference at these locations is not noticeable because of the fact that only the odd lines from the share are written to the halftone image. This allows the halftone image to keep part of its pattern and shape and allows the shares to blend in. That means the even lines from the halftone image fill in the missing lines from the embedded share. This has the potential to distort the recovered secret, however during most of our tests, this tends not to be the case. This is due to the threshold that is chosen. Because it leaves little room for error, any anomalous pixels recovered are not generally noticeable by the human visual system. When the comparison is done between the lines that get replaced in the halftone image by the lines in the shares, they appear quite similar. Fig. 3.8 illustrates this minimal difference between the original and embedded image.
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(a) (b)
Figure 3.8: Comparison of pre (a) and post (b) share embedding. © Weir & Yan 2009
Given a halftone image and a number of shares, using the proposed halftone embedding scheme the shares are inserted into the image as best as possible. The most appropriate locations within the halftone images are selected. After the merging process is complete, the halftone image should be as unchanged as possible. After the embedding process is complete, the key share is used to recover one secret at a time. The results are detailed in Figure 3.9.
(a) Original image. (b) Embedded share at location 1.
(c) Embedded share at location 2.
(d) Embedded share at location 3.
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Summary
From the previous visual cryptography schemes proposed and demonstrated, it is possible to see that being able to hide secrets within images can prove to be highly advantageous. The most interesting results are gained when using a key that is the same size as the final share which may contain a number of different images. This makes it harder to determine whether the shares have actually been encrypted with just one hidden secret or with a large number of secrets.
The same is true when it comes to hiding visual cryptography shares inside halftone images. This new scheme greatly improves the overall robustness of traditional visual cryptography because the halftone and colour images have very minimal changes after the adjustments have been made. Due to the fact that one of the schemes uses colour images, this gives it the potential for a wider range of applications.