Cheating Prevention in Visual Cryptography - Visual Cryptography and Secret Image Sharing - page 287

10.4 Analysis of Cheating Prevention Schemes
We begin with a general discussion of the advantages and disadvantages of the
share authentication approach and blind authentication approach. The advan-
tages of share-authentication-based cheating prevention approach are twofold.
One is that checking the authenticity of shares is optional. It can be done only
when someone is suspected of cheating. The other is that the generation of
verification shares is done after the generation of secret shares. Therefore, any
conventional visual secret sharing schemes (for any access structures) can be
turned into a cheating prevention scheme. The quality of the reconstructed se-
cret image is not affected. The disadvantages of this approach are also twofold.
One is that additional shares for verification purpose are needed. The other
is that these schemes lack a formal proof of security.
The advantages of blind-authentication-based cheating prevention ap-
proach are twofold. One is that no additional shares are required. The other is
that we can formally prove the security. We can formally argue that the prob-
ability of changing a black pixel (or white pixel) by the cheaters is less than 1.
The disadvantages of this approach are also twofold. One is that this approach
is only suitable for threshold visual secret sharing schemes. The other is that
the quality of the reconstructed secret image is degraded.
The comparisons of different cheating prevention schemes are illustrated
in Table 10.1. With respect to the total number of subpixels for sharing a
pixel, TCH requires the least subpixels for sharing a pixel. HCL1 requires
2n 2 subpixels, since an extra transparency is used to verify the correctness
of other transparencies. HT requires 2n(n + 2) subpixels because this scheme
also needs verification transparencies and each original transparency is en-
larged. Finally, HCT2 needs 2(n + l) 2 subpixels. With respect to prevention
of shares against cheating, the following schemes are all designed according
to authentic conditions (AC). PS and HT both prevent all blocks of each
transparency from cheating. HCT1 only prevents these blocks within the
corresponding verification logo. And HCT2 only prevents blocks that were
created for presenting black pixels. The share-authentication-based cheating
prevention approach can be applied to general access structures. Whereas
blind-authentication-based cheating prevention approach is more suitable for
threshold access structures, with respect to the method for share generation,
HT uses a modified VC by the basis matrices T 0 and T 1 . HCL1 and HCL2
use the share construction method of traditional VC. Finally, TCH uses GA
for share generation. With respect to security, all schemes are designed for
preventing a known secret cheating attack. However, HCL1, HT, and TCH
are not formally proved to be secure.