Cryptography Reference
In-Depth Information
set of 2 3 (2 x) chord blocks. Let the number of 2 3 blocks in each
chord be . Let a
j
and b
j
denote block j of chord k in A and B, respectively,
1 j and 1 k 3(= x). The chords are indexed clockwise and the
divided blocks in A and B are indexed as shown in
Figures 3.5(a)
and (b),
respectively. We call a
j
and b
j
the corresponding blocks in A and B.
3.4.1.2 Encoding Circle Share A
We rst dene three 23 elementary blocks, namely s
1
A
, s
2
A
, and s
3
A
, for circle
share A as shown in
Figure 3.6.
That is, these elementary blocks are the basic
constituents of A and there are one white and five black subpixels in each of
the elementary blocks.
In order to guarantee the randomness when using s
A
as a constituent of
A for 1 k 3, we permute the subpixels within s
A
before assigning s
A
as
a constituent block in A. Let = (
1
;
2
;
3
;
4
;
5
;
6
) be a permutation of
1; 2; 3; 4; 5; 6 (in which 6 = 2x = 23). We dene a function permute(s, ) re-
arranging the subpixels in elementary block s by permutation .
Figure 3.7(a)
shows a certain typical ordering of the subpixels in a 23 elementary block s
and Figure 3.7(b) shows the result of permute(s, ) with = (3; 5; 1; 6; 2; 4).
Note that the order of the subpixels in the elementary block s can be defined
arbitrarily.
We call the set of three blocks (a
j
, a
j
, a
j
) the related blocks of the three
chords in A for 1 j . Obviously, there are totally sets of the related
blocks in A. For a certain set of related blocks (a
j
, a
j
, a
j
), we generate one
permutation, denoted as
j
, and assign a
j
to be permute(s
A
;
j
) for 1 k
3 and 1 j . That is,
(a
j
;a
j
;a
j
) = (permute(s
1
A
;
j
);permute(s
s
A
;
j
);permute(s
3
A
;
j
))
(3.1)
for 1 j .
For the purpose of illustration, we show how the first set of the related
particular
1
permute(s
A
;
1
) = s
A
for 1 k 3. In real implementation,
a new random permutation
j
is adopted when encoding (a
j
;a
j
;a
j
) in A for
each j; 1 j . Figures 3.8(b) and (c) show the results of A
120
and A
240
,
respectively.
Let [k;j] denote the absolute location with respect to block j of chord k in
A
(i.e., the results of rotating A counterclockwise) where 1 k 3 (= x),
1 j and = 120
(= 360
=3)(A
0
[k;j] = A[k;j]). The relationship
among the related blocks is easily seen from Figures 3.8 and 3.9:
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