Cryptography Reference
In-Depth Information
word and can even determine whether a columnar transposition is likely,
except for the two columns in which the 'E' of the probable word occurs.
•
Consecutive letters statistically depend on one another in a certain way,
because language has a structure. In this way, sufficiently long ciphertexts
that came into being by transposing equally long groups of characters can
be statistically tested for dependent (but now torn apart) pairs. We proceed
as follows:
- To determine the length,
N
, of the groups, we can use character coin-
cidence (Section 3.6.1), for example.
- We look at all
N
∗
(N
−
1
)/
2 possible pairs in positions
i
and
j
in the
=
1
,
2
,...,N)
. For each pair of positions, we analyze the
common distribution of the pertaining characters in the ciphertext at
these places.
- If the plaintext is normal language, then pairs of successive characters
have a typical distribution (see Table 2.1). Non-adjacent characters are
statistically less dependent and have a different distribution.
- We apply this to the pairs of positions mentioned in the previous point.
With some pairs, but not with others, we will find the typical digram
distribution of the plaintext. We will call pairs with numbers from 1
through
N
distinguished pairs
.
- Among the distinguished pairs, we try to find chains with the following
form:
groups (
i, j
(n1,n2), (n2,n3), (n3,n4), ...
Such a chain of length
N
, in which all
n
i
are different, could already
be the permutation (i.e., transposition) we are looking for.
- If we don't find such a chain, or if no meaningful decryption results
are produced, then we try to join chain links; we will have to guess
missing members. Digrams that virtually never occur could be helpful.
It is certainly an attractive task to write and expand a corresponding
program (that would be an elegant practical training course for high
schools).
The major drawback of this method is the large amount of plaintext it
requires.
