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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