Cryptography Reference
In-Depth Information
Certainly, 25! seems like a huge number (and it is), but even these generalized charac-
ter-to-character mappings are vulnerable to the same frequency analysis used on Caesar
ciphers. If enough ciphertext is examined, we can determine what most letters map to, then
can fill out the rest of the letters by simply guessing.
5.5
THE VIGENERE CIPHER
As described in Chapter 1, the Vigenere cipher maps characters to characters based on a key
which specifies multiple shifts. A key of length
n
represents a series of shifts
s
0
,
s
1
, . . . ,
s
n
1
.
The enciphering transformation maps the
i
th character of the plaintext message
P
=
p
0
,
p
1
,
. . . ,
p
t
1
to the
i
th ciphertext character of the ciphertext message
C
=
c
0
,
c
1
, . . . ,
c
t
1
in this
way:
c
i
p
i
+
s
r
(mod
m
)
(0
≤
c
i
<
m
, 0
≤
i
<
t
)
where
r
i
(mod
n
)
(0
≤
r
<
n
).
E
XAMPLE
.
For convenience in the following example, we provide a table of character-to-
number associations for the ordinary alphabet. (See Table 5.5.)
We will use the ordinary alphabet, and the keyword SPACE representing the shifts
s
0
=
18,
s
1
= 15,
s
2
= 0,
s
3
= 2, and
s
4
= 4. The plaintext message is
DANGER WILL ROBINSON.
So using the Vigenere transformation, we compute the following (see Table 5.6).
Thus, the ciphertext message (grouped in blocks of 5 characters) is
VPNII
JLINP
JDBKR
KDN
Vigenere ciphers fall prey to frequency analysis, just like monoalphabetic substitution
ciphers. See Chapter 1 to see how this is done.
To get around the weaknesses posed by ciphers which map single characters to single char-
acters, we may wish to construct mappings that deal with entire blocks of characters. There
are certainly many more ways to construct such a mapping; these are called block ciphers.
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
V
W
X
Y
Z
0
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
TABLE 5.5
Table of character-to-number associations for the ordinary
alphabet
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