Cryptography Reference
In-Depth Information
This value for
x
is an inverse of 7 modulo 26, and this is easily verified:
7
x
= 7(15) = 105
1 (mod 26).
Thus, to recover the plaintext from the ciphertext, we crank it through the deciphering
transformations:
C
15P
10
15
(8
10)
15
2
22 (mod 26)
C
15P
10
15
(10
10)
15
0
0 (mod 26)
C
15P
10
15
(25
10)
15
15
17 (mod 26)
C
15P
10
15
(9
10)
15
1
11 (mod 26)
C
15P
10
15
(4
10)
15
6
14 (mod 26)
C
15P
10
15
(6
10)
15
4
18 (mod 26)
C
15P
10
15
(13
10)
15
3
19 (mod 26)
which gives us
22 0 17 11 14 18 19
or
WARLO
ST.
5.4
WEAKNESSES OF AFFINE TRANSFORMATION CIPHERS
Clearly, affine ciphers are secret key ciphers, since if
m
and
b
in the enciphering transfor-
mation
C
mP
+
b
(mod
n
) are revealed, it is easy to compute the inverse of
m
modulo
n
,
and then decipher.
Ciphertext Only Attack-Frequency Analysis.
As with the Caesar cipher, break-
ing affine ciphers is easy. We may proceed as follows:
1.
Suppose the message is English text, and we are using the ordinary alphabet A = 00,
B = 01, . . . , Z = 25. (Of course, the message may not be English text, or even text at all,
but the principle remains the same.)
2.
Note that the most common letter appearing in English text is “E”(= 4), followed by
“T”(= 19).
3.
Examine as much ciphertext as possible. The character appearing most often is proba-
bly the character “E” enciphered, and the second most frequent character is probably
“T” enciphered.
4.
Knowing what “E” and “T” map to allows us to calculate
a
and
b,
and thus the mapping
of all the other letters.
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