Cryptography Reference
In-Depth Information
TABLE 5.3
Values of for n = 5. The max over each row is in boldface and
1
and
2
denote very small values.
m
0
n`
0
;h
0
0,1
1,2
2,3
3,4
4,5
5,6
6,7
7,8 8,9 9,10
1
3/10
{
{
{
{
{
{
{
{
{
2
4=15
1=3
{
{
{
{
{
{
{
{
3
19=120 29=60 31=120
{
{
{
{
{
{
{
4
1=14
44=105 23=42 17=105
{
{
{
{
{
{
5
1=42
11=42 55=84 10=21
1=12
{
{
{
{
{
6
1
5=42
23=42 16=21
1=3
1=30
{
{
{
{
7
0
1=30
1=3
5=6
17=24 11=60
2
{
{
{
8
0
0
2=15
2=3
1
8=15 1=15
0
{
{
9
0
0
0
2=5
1
1
3=10
0
0
{
10
0
0
0
0
1
1
1
0
0
0
the table, a deterministic schemes is obtained from m
0
= 8 (in such a case,
by choosing `
0
= 4). Again the best probabilistic factor found is reported in
boldface.
5.7 Probabilistic Schemes with Boolean Operations
One of the peculiar characteristics of VCS is the fact that the reconstruction
of the secret image is done via the human visual system. This means that
representing a black pixel as `1' and the white pixel as `0,' the reconstruction
is performed via an "OR" operation of the superposed pixels contained in
the shares. Relaxing such an assumption, it is possible to obtain different
classes of VCS where the secret pixel is reconstructed after performing different
boolean operations on the subpixels contained in the shares. For example
XOR-based VCS have been proposed in [17]. As regards probabilistic VCS,
several proposals have been done [20, 18, 8], where the basic operation for the
reconstruction is no more based on the OR of the shared subpixels, and both
the distribution and the reconstruction phases are consequently modified.
5.7.1 (2,n) Scheme for Binary Images (Wang)
In [20], Wang et al. proposed a probabilistic (2;n)-VCS based on binary XOR
and AND operations, denoted with and &, respectively. The construction
is given in
Figure 5.3.
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