Cryptography Reference
In-Depth Information
Compared to the naive solution, the scheme introduces some computational
overhead by requiring additional stacking and reversing operations.
In the distribution phase, for each qualified set X in
0
and each par-
ticipant i 2 X the dealer generates the subtransparency t
X;i
resulting by
applying the XOR-(jXj;jXj)-VCS on the set of participants X. For each
set X in
0
such that the participant i does not belong to X, the dealer
generates the subtransparency t
X;i
consisting of all ones. Each participant
i receives a transparency ti
i
corresponding to the concatenation of its sub-
transparency according to an ordering over the qualified sets in
0
. Hence, let
X
1
;:::;X
j
0
j
be the qualified sets in
0
, each participant i receives the trans-
parency t
i
= t
X
1
;i
:::t
X
j
0
j
;i
, where denotes the concatenation between
transparencies. Each participant i also receives an additional transparency
t
0
i
of the same size as t
i
such that each subtransparency t
0
X;i
has all ones if
the participant i does not belong to the qualified set X whereas it (to re-
peat the subject that is each sub transparency) has all zeros, otherwise. The
construction is described in Figure 9.4.
Let (
Qual
;
Forb
) be an access structure on a set of n participants.
Distributionphase.For each qualied set X 2
0
the dealer has to:
execute
the
XOR-(jXj;jXj)-VCS
on X to
generate
the
sub-
transparency t
X;i
for each participant i 2 X;
for each i 62 X, generate the subtransparency t
X;i
consisting of all
ones;
for each i 2 X, generate a subtransparency t
0
X;i
of the same size of
the original image, having all zeros;
for each i 62 X, generate a subtransparency t
0
X;i
of the same size of
the original image, having all ones;
distribute to participant i the transparencies ti
i
= t
X
1
;i
:::t
X
j
0
j
;i
and t
0
i
= t
0
X
1
;i
:::t
0
X
j
0
j
;i
.
Reconstructionphase. Let X = fi
1
;:::;i
p
g be a qualied set in
Qual
. Participants in X reconstruct the original image by computing:
T = XOR(t
i
1
;:::;t
i
p
);
T
0
= OR(t
0
i
1
;:::;t
0
i
p
);
U = OR(T;T
0
);
U
0
= XOR(U;T
0
), which corresponds to the original image.
FIGURE 9.4
Hu and Tzeng's ideal contrast VCS with reversing.
It is easy to see that the i-th qualified set obtains the original image in place
of the i-th subtransparency of U
0
while all other subtransparencies contains
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