Cryptography Reference
In-Depth Information
8
Visual Cryp
tography and Contrast Bounds
Andreas Klein
Ghent University, Belgium
CONTENTS
8.1
Introduction :::::::::::::::::::::::::::::::::::::::::::::::::::::: 223
8.2
Preliminaries ::::::::::::::::::::::::::::::::::::::::::::::::::::: 225
8.3
Approximate Inclusion Exclusion :::::::::::::::::::::::::::::::: 227
8.4
Designs and Codes ::::::::::::::::::::::::::::::::::::::::::::::: 232
8.5
Optimal 3-out-of-n Schemes ::::::::::::::::::::::::::::::::::::: 236
8.6
Asymptotic Optimal k-out-of-n Schemes :::::::::::::::::::::::: 241
8.7
Contrast Trade-Offs for Extended Visual Cryptography
Schemes :::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 244
8.8
Enhancing the Contrast by Nonstandard Models ::::::::::::::: 251
8.9
Conclusion :::::::::::::::::::::::::::::::::::::::::::::::::::::::: 251
8.1 Introduction
To describe a visual cryptography scheme we encode the encryption of a pixel
by Boolean matrices. The rows represent the slides and the columns represent
the different subpixels.
For example, the encoding illustrated in
Figure 8.1
is described by
0
1
0
1
0
1
@
A
:
M =
0
0
1
1
0
1
1
0
To describe the random decision, which must be made when encoding a
pixel, we use multisets that contain all possible choices with the right fre-
quency.
This leads to the formal definition of a visual cryptography scheme.
Denition 1 Let be any access structure for n persons. A visual cryptog-
raphy scheme is a pair of multisetsM
b
andM
w
of Boolean nm matrices.
Which satisfy:
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