Cryptography Reference
In-Depth Information
occurs, then the deciphering of up to
n
subsequent ciphertext digits may be
incorrect.
An example of a synchronous stream cipher is DES operating in OFB mode,
whereas an example of an asynchronous stream cipher is DES in CFB mode.
An example of a nonsynchronous cipher is given by reinterpreting an idea of
Vigenere.
The Autokey Vigenere Cipher
Let
n
=
|
A
|
where
A
is the alphabet of definition. We call
k
1
k
2
···
k
r
for 1
≤
r
n
a
primingkey
. Then given a plaintext message unit
m
=(
m
1
,m
2
,...,m
s
)
where
s
≤
≥
r
, we generate a keystream as follows:
k
=
k
1
k
2
···
k
r
m
1
m
2
···
m
s
−
r
.
Then we encipher via
E
k
j
(
m
j
)=
m
j
+
k
j
(mod
n
)=
c
j
for
j
=1
,
2
,...,r,
and
E
k
j
(
m
j
)=
m
j
+
m
j
−
r
(mod
n
)=
c
j
for
j>r,
and decipher via
D
k
j
(
c
j
)=
c
j
−
k
j
(mod
n
)=
m
j
for
j
=1
,
2
,...,r,
and
D
k
j
(
c
j
)=
c
j
−
m
j
−
r
(mod
n
)=
m
j
for
j>r.
This cipher is nonsynchronous since the plaintext serves as the key from the
(
r
+ 1)th position onward, with the simplest case being
r
= 1. Here is a simple
example.
Example 3.5
Given a priming key
k
=
k
1
k
2
=72
and
n
=26
in the autokey
Vigen`ere cipher, suppose we want to decrypt the Vigen`ere ciphertext
LPXEHGM
,
using Table 1.3 on page 11. Converting ciphertext to numerical equivalents, we
have
11
,
15
,
23
,
4
,
7
,
6
,
12
.
Thus, we compute the following:
m
1
=
c
1
−
k
1
=11
−
7=4
, m
2
=
c
2
−
k
2
=15
−
2=13
,
m
3
=
c
3
−
m
1
=23
−
4=19
, m
4
=
c
4
−
m
2
=4
−
13
≡
17(mod 26)
,
m
5
=
c
5
−
m
3
=7
−
19
≡
14(mod 26)
, m
6
=
c
6
−
m
4
=6
−
17
≡
15(mod 26)
,
and
m
7
=
c
7
−
m
5
=12
−
14
≡
24(mod 26)
.
Via Table 1.3, the letter equivalents give us
ENTROPY
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