Cryptography Reference
In-Depth Information
Definition
A square matrix
A
is a transposition matrix if each column and row of
A
contain a sin-
gle 1; all other entries are 0.
E
XAMPLE
.
.
0010
0001
0100
A =
Note that an identity matrix is a transposition matrix (but one which we would never
use). These types of matrices do exactly what we want. Note that if we take the product
V
=
AX
where
is a transposition matrix, then
• since each row of
A
contains a single 1, each entry in
V
will merely be an entry from
X
,
and
• since each column of
A
contains a single 1, each entry of
V
will be a different entry from
X
.
Thus, the entries of
and
are column vectors, and
V
B
A
are merely a permutation of the entries of
.
V
X
E
XAMPLE
.
Suppose we have the following:
01000
00001
10000
00100
00010
A =
12
5
23
8
6
B =
and we take
V
=
BX
. Then we see that
01000
00001
10000
00100
00010
12
5
23
8
6
5
6
12
23
8
V =
=
.
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