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In order to use this extended visual cryptography scheme, a general construction needs to be defined. Ateniese et al. [4] have devised a mechanism by which we can generate the shares for the scheme. A stronger security model for EVCS is one in which the shares associated with a forbidden subset can be inspected by the user, meaning that the secret image will still remain totally hidden even if all n shares are previously known by the user. A systematic approach to fully address a general (k,n) problem was also proposed [5].
For each set of access structures, let P =–1, · · · , n} represent the set of elements called participants, and let 2P denote the set of all subsets of P. Let
(a) Secret (192×192). (b) Base image 1 (192×192). (c) Base image 2 (192×192).
(d) Extended share 1 (384×
384).
(e) Extended share 2 (384×
384).
(f) Recovered secret after su- perimposing share 2 atop share 1 (384×384).
Figure 2.1: The results of (2, 2)-EVCS encryption process.
ΓQual/ΓForb be the collection of qualified / forbidden sets. The pair is called the access structure of the scheme. Any qualified set can recover the shared image by stacking its participants transparencies, while any forbidden set has no information on the shared image. This extension generalizes the original secret sharing problem by [84]. In [5], the authors propose a new technique to realize (k, n)-VCS, which is better with respect to the pixel expansion than the one proposed by Naor and Shamir. Schemes for improving the contract are discussed later.
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Improving the shares quality [128] to that of a photo realistic picture has also been examined within extended visual cryptography. This is achieved using gray subpixels rather than black and white pixels in the form of halftoning. Figure 2.2 provides an example of a grayscale image which has been converted to binary using halftone techniques. The difference between these types of image is also shown within this figure. The same area has been zoomed on each image to illustrate this difference.
The use of high quality halftone images to further improve the quality of the
(a) Grayscale image (b) Halftone image
(c) Zoomed 8×grayscale image. (d) Zoomed 8×halftone image.
Figure 2.2: Comparison between grayscale and halftone images.
extended visual cryptography schemes has proved to be a worthwhile effort. Many high quality halftone schemes have been detailed, in both single and multiple secret sharing schemes.
2.2
Halftone Visual Cryptography
This method of secret sharing expands on Naor and Shamir’s original findings in the 2-out-of-2 secret sharing scheme. It also takes extended visual cryptography a step further. The halftoning technique that is used can be applied to colour and grayscale images. Halftoning simulates a continuous tone through the use of dots, varying either in size or in spacing [14].
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Based on the idea of extended visual cryptography, Zhou et al. [142] set about improving these techniques by proposing halftone grayscale images which carry significant visual information. Traditional VC produces random patterns of dots with no visual meaning until the shares are superimposed. This raises the suspicion of data encryption. Halftoning attempts to alleviate this suspicion by having visually pleasing attributes. This means creating halftone shares that carry one piece of information, such as another image, while having the secret hidden until both shares are superimposed. This gives no indication that any encryption has been performed on both shares. This in itself drastically improves the security model for visual cryptography. Along with Zhou, [81, 82, 114] present novel techniques by which halftone images can be shared with significant visual meaning which have a higher quality than those presented within [6] by employing error diffusion techniques [71]. These error diffusion techniques spread the pixels as homogeneously as possible to achieve the improvements in the shares overall quality.
A halftone scheme [83] was proposed in which the quality of the shares is improved by using contrast enhancement techniques. However the problem with this scheme is that it is not perfectly secure. By using a space-filling curve ordered dithering technique [141], grayscale images can be converted into an approximate binary image. This allows encryption and decryption of the gray-level images using traditional visual cryptography methods [74].
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– You have to be proactive and open-minded as a newcomer and make it clear to your colleagues what you are able to cope. The pharmaceutical fi eld is new to me. But busy as they are, most of my colleagues fi nd the time to teach me, and they also trust me. Even though it was a bit hard at fi rst, I can feel over time that I am beginning to be taken seriously and that my contribution is appreciated.