Cryptography Reference
In-Depth Information
nothing about P
1
or P
2
; while AB reconstructs P
1
and A
B recovers P
2
where A
denotes the result of rotating A clockwise. Note that A
B
is equivalent to AB
. Intuitively, it is reasonable to choose circles as the
encoded shares since they ease the correct alignments between A and B as
well as A
and B pixel by pixel where 0
< < 360
.
They deliberately decomposed circle share A into 360
/ areas where each
area contains an equal amount of 2 2 sector blocks. Figure 3.4(a) shows
the four typical patterns for sector blocks, namely s
1
, s
1
, s
1
, and s
1
, used in
their approach. That is, the whole circle share A is composed by all these four
sector blocks. Note that s
1
(s
1
, s
1
, s
1
) can be consciously regarded as the
result of rotating s
1
(s
1
, s
1
, s
1
, respectively) 90
counterclockwise (or s
1
can
be consciously regarded as the result of rotating 90
clockwise). We say that
s
1
's (s
1
's, s
1
's, s
1
's) previous sector block is s
1
(s
1
, s
1
, s
1
, respectively) and
its next sector block is s
1
(s
1
, s
1
, s
1
, respectively) as summarized in Figure
3.4(b).
(a)
s
1
s
1
s
1
s
1
(b)
s
1
s
1
s
1
s
1
s
prev (s) s
1
s
1
s
1
s
1
next (s) s
1
s
1
s
1
s
1
FIGURE 3.4
22 sector blocks for A in Wu and Chang's approach: (a) 22 sector blocks
for A, (b) prev (s) and next (s) of sector block s.
Let the number of areas in circle share A be (= 360
=) and the number
of sector blocks in each area be . These areas are indexed clockwise. Let a
j
be the jth sector block in area k in A, 1 j and 1 k . At rst, the
sector blocks in the first area are randomly selected out of those in Figure
3.4(a). Then, sector blocks in area t are defined according to those in area
t1 by assigning a
j
as the next sector block of a
t
j
, i.e., a
j
= next(a
t
j
) (or
a
t
j
= prev(a
j
)) for 1 j and 2 t .
Given a pair of corresponding pixels p
1
and p
2
in P
1
and P
2
, respectively,
each sector block b
j
in B is determined by p
1
, p
2
, and the corresponding block
scheme.
Note that in Wu and Chen's scheme each extended block s
2
in S
2
would
be superimposed with s
1
and s
9
1
when s
1
is rotated 0
(or xed) and 90
counterclockwise, respectively. In Wu and Chang's scheme, each sector block
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