Cryptography Reference
In-Depth Information
Let S
1
be the matrix chosen by the dealer to share a black pixel. The
shares generated for participant 1 are s
1
= 100, s
1
= 010 and s
1
= 001,
whereas, the shares generated for the participant 2 are s
2
= 010, s
2
= 001
and s
2
= 100. During the reconstruction phase, the two participants stack
their shares and retrieve
1
= OR(s
1
;s
2
) = 110,
2
= OR(s
1
;s
2
) = 011, and
3
= O
R
(s
1
;s
2
) = 101. By computing = XOR(
1
;
2
;
3
) = 000 and its
reverse = 111 the two participants reconstruct a black pixel.
9.5 Conclusions
Visual cryptography schemes are characterized by two parameters: the pixel
expansion, i.e., the number of subpixels contained in each share and the con-
trast, which measures the difference between a black and a white pixel in the
reconstructed image. While it is possible to construct schemes with perfect re-
construction of black pixels (or white pixels, respectively), it has been shown
that a perfect reconstruction of both black and white pixels is infeasible. In
order to improve the contrast in VCSs, Viet and Kurosawa [13] introduced an
extra noncryptographic operation: the reversing operation. Specifically, they
showed how to construct VCSs with reversing where the reconstruction of
black (white, respectively) pixels is perfect, whereas, the reconstruction of
white (black, respectively) pixels is almost perfect. Afterwards, Cimato et
al. [6] showed how to construct VCSs with reversing where reconstruction of
both black and white pixels is perfect. Such schemes are said to have an ideal
contrast. In particular, Cimato et al. [6] proposed two different constructions.
One uses as a building block a VCS with perfect reconstruction of black pixels
while the other construction uses as a building block a binary secret sharing
scheme. Subsequently, new constructions for visual cryptography with revers-
ing have been described in [9, 14]. In particular, [9] considered the problem of
minimizing the number of the shares held by each participant while in [14] the
need of using as a building block a VCS with perfect reconstruction of black
pixels is removed.
Bibliography
[1] G. Ateniese, C. Blundo, A. De Santis, and D. R. Stinson. Visual cryp-
tography for general access structures.
Information and Computation,
129(2):86{106, 1996.
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