Cryptography Reference
In-Depth Information
4
1
2
1
3
2
3
Figure 11.4. Example for an access structure term.
as drawn in Fig. 11.4. We start by attaching S to the whole expression
. It is written as
1 2 )
1 3 ) and (
2 3 )
4 . So we attach S to both terms.
a
between (
(
Similarly, in the former term, we attach S to
1 2 and
1 3 . We have thus three
terms to which S is attached. For the first one
1 2 , we attach W to
1 and S
W
to
2 . For the second one
1 3 , we attach X to
1 and S
X to
3 . For the third
one (
2 3 )
4 we attach Y to
2 3 and S
Y to
4 . It thus remains to attach
Z to
2 and Y
Z to
3 . To summarize, we have two occurrences of
1 to which
are attached W and X , we have two occurrences of
2 to which are attached S
W
and Z , we have two occurrences of
3 to which are attached S
X and Y
Z , and
we have one occurrence of
4 to which is attached S
Y . Therefore we define the
share
S 1 =
,
( W
X )
S 2 =
,
( S
W
Z )
S 3 =
( S
X
,
Y
Z )
S 4 =
S
Y
where W
Z are independent uniformly distributed random variables. We can,
for instance, check that P 1 and P 2 can reconstruct S because they have W and S
,
X
,
Y
,
W .
But P 2 and P 3 , for instance, cannot reconstruct S because ( S
W
,
Z
,
S
X
,
Y
Z )
is equivalent to ( S
W
,
X
W
,
Y
,
Z ) which gives no clue about S .
11.3
Special Purpose Digital Signatures
In this section we list a few important variants of digital signature schemes.
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