Cryptography Reference
In-Depth Information
and the message is THE END, which we split into blocks of size 2 to get TH EE ND. To
encipher the plaintext TH, we use the vector
P
, which is
19
7
and crank it through the transformation
AP
+
B
C
(mod 26).
+
≡
517
415
19
7
5
2
11
1
(mod 26)
The number pair 11, 1 corresponds to the letter pair LB, and so this is the ciphertext. We now
encipher the pair EE
+
≡
517
415
4
4
5
2
15
0
(mod 26)
which yields the ciphertext PK. Finally, we encipher the pair ND
+
≡
517
415
13
3
5
2
17
21
(mod 26)
to get the ciphertext RV. Thus, the message sent is
LB
PA
RV.
To decipher, compute an inverse
A
of
A
modulo 26; verify that the following is such a
matrix.
17
5
18
23
P
A
C B
To decipher, crank the ciphertext through the inverse transformation
(
)
(mod 26). If we send the letter pair LB back through,
≡
17
5
11
−
5
1
−
2
19
7
(mod 26)
18
23
we note that we have the pair 19, 7 corresponding to the letter pair TH, the original plain-
text. You are invited to do the subsequent letter pairs.
Note that we can make the block size
m
as large as desired by choosing large
mm
encryption matrices. When
m
≥
10, cryptanalysis of such systems is quite difficult.
7.1
WEAKNESSES OF MATRIX CRYPTOSYSTEMS
Matrix cryptosystems, like the block affine system, are resistant to frequency analysis. In
general, when using the ordinary alphabet with blocks of size
, there are 26
n
different ways
n
to map an
n
is large quickly becomes infeasible. For example, when the enciphering matrix is 10 by 10,
that is, the block size
n
-block of text to another. Maintaining a frequency table of these blocks when
n
= 10, there are 26
10
1.4
10
14
possible blocks. A table of that size
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