Cryptography Reference
In-Depth Information
value for sufficiently long, different texts in the
same language
. This is quite
amazing, but the reason is clear: in the first approximation, the characters
of long texts have a certain distribution based on probability theory, which
depends on the language used. Moreover, the pairs of letters written above
one another are statistically somewhat independent in long texts. Therefore,
the kappa expected is the square sum of all character probabilities. Whether or
not you can reproduce this in detail is not important — just remember this:
the
kappa results from the common distribution of single characters in two texts
.
We shift the entire text block by four characters to the right and form the kappa
of the shifted text onto itself (and simply cut off ends that jut out):
is the first text
this is the first
*
We can see that roughly the same kappa as for long texts occurs here too.
Though superimposed characters are no longer entirely independent (especially
when moved by one position only), the effect is still there. Had I used English
text with all the blanks and line breaks removed from it, I would have obtained
a kappa of approximately 5.5 %.
Let's use this function for a special case: a plaintext, represented by the
character string
(p
i
)i
=
1
,
2
,
3
...
, is to be Vigenere-encrypted with a key
(
s
1
,s
2
,...,s
N
) of length
N
, to produce ciphertext
(c
i
)i
=
1
,
2
,
3
,...
:
p
1
p
2
p
3
... p
N
p
N
+
1
p
N
+
2
...
s
1
s
2
s
3
... s
N
s
1
s
2
...
c
1
c
2
c
3
... c
N
c
N
+
1
c
N
+
2
...
with
⊕
⊕
c
1
=p
1
s
1
,c
2
=p
2
s
2
, ...
We can see instantly that
c
i
=
p
N
+
i
, since both cipher-
text characters were encrypted with the same key characters (whereas different
key characters produce different ciphertext characters). So we conclude:
c
N
+
i
exactly when
p
i
=
The kappa of the ciphertext shifted by N positions against itself equals the kappa
of the plaintext calculated in the same manner.
If the ciphertext is shifted against itself by an amount smaller than
N
, then the
result will be a different kappa, namely one in the order of magnitude of a kappa
