Cryptography Reference
In-Depth Information
is encoded as permute(s
btod(p
1
p
2
p
3
B
;
j
) where
j
is a random permutation for
1 j . It is noted that for a specic black b
j
in the first chord of B, when
A is rotated 0
, 120
, and 240
counterclockwise, the blocks that are super-
imposed onto b
j
are a
j
, a
j
, and a
j
, respectively where a
j
= permute(s
A
;
j
)
for 1 j and 1 k 3.
Now, consider a certain block b
j
in the second chord of B. When A
is rotated 0
, 120
, and 240
counterclockwise, the blocks that are super-
mula (3:2)). Thus, to recover a given set of (p
1
;p
2
;p
3
)
j
, we should assure
that s
2
A
s
B
, s
3
A
s
B
, and s
1
A
s
B
(or more precisely permute(s
2
A
;
j
)
permute(s
B
;
j
);permute(s
3
A
;
j
)permute(s
B
;
j
) and permute (s
1
A
;
j
)
permute(s
B
;
j
)) resconstruct (p
1
)
j
, (p
2
)
j
and (p
3
)
j
, respectively. Table 3.6
is designed for this principle.
TABLE 3.6
Encoding a set of corresponding pixels (p
1
;p
2
;p
3
)
j
into a
j
(a
j
and a
j
)
and b
j
in terms of s
2
A
(s
3
A
, s
1
A
, respectively) and s
B
in the first chords of
A and B, respectively for visual 3-secret sharing.
p
1
p
2
p
3
s
A
s
A
s
A
s
B
s
A
s
B
s
A
s
B
s
A
s
B
In fact, we can rearrange Table 3.6 to make the columns 4{10 exactly
the same as those in
Table 3.5.
Table 3.7
is such a consequence. Note that
Tables 3.5 and 3.7 are the same except for the headings of columns 1{3. From
Table 3.7, we observe that given a set of corresponding pixels (p
1
;p
2
;p
3
)
j
, the
elementary block of b
j
can be easily determined by s
btod(p
3
p
1
p
2
B
.
(;;) and
1
= (1; 2; 3; 4; 5; 6; ). Since btod(p
3
p
1
p
2
) = btod(011) = 3 b
1
is
encoded as permute(s
3
B
;
1
) (
) as show in
Figure 3.13.
It is easily seen that
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