Cryptography Reference
In-Depth Information
CRYPTANALYSIS OF THE PLAYFAIR CIPHER
Is the Playfair Cipher a secure cryptosystem? The first thing to check is
the size of the keyspace. The key is an arrangement of the letters A to Z
(excluding J) in a square. Since every arrangement of these letters corresponds
to a different key, the number of possible keys is the number of possible
arrangements. This is the number of possible permutations of 25 letters, which
is approximately 10
25
. Thus the keyspace is very large, being slightly smaller
than that of the Simple Substitution Cipher, but significantly more than that
of DES (see Section 2.1.2). A determined attacker with a great deal of money,
time and computing resources could search this keyspace, but it would be a
mammoth task.
Neither is single letter frequency analysis an option for an attacker. Continuing
our example, there are three occurrences of the letter A in the plaintext
NATTERJACK TOAD, but these are encrypted to the ciphertext letters N, C
and T, respectively. This means that frequency analysis of single letters will not
be effective.
There is, however, an alternative frequency analysis that will succeed against
the Playfair Cipher. A cryptanalyst could generalise the single letter technique to
look at frequencies of bigrams. This works in a similar way to letter frequency
analysis but is more complex to conduct, for three reasons:
1. There are 25
600 possible Playfair bigrams, hence frequency analysis
will be more complex than for single letters, notwithstanding the need to
compute accurate bigram statistics. However, bigram frequencies can be very
revealing. For example, in English plaintext the bigram TH is by far the most
common, so it should be relatively simple to detect this bigram if we have
enough ciphertext.
2. A considerable amount of ciphertext will be needed before these bigram
statistics can be used to conduct an effective bigram frequency analysis of a
Playfair ciphertext. It is likely that thousands, rather than hundreds, of ciphertext
letters will be needed.
3. The last two difficulties are enhanced by the fact that two letters next to one
another in the original plaintext are not necessarily encrypted together, since
they may occur in adjacent bigrams. For example, in the plaintext THE MOTH,
the bigram TH occurs twice in the plaintext, but only the first occurrence is
encrypted as a TH, since this plaintext gets split into bigrams TH EM OT HZ
during preprocessing.
×
24
=
Breaking the Playfair Cipher is thus feasible, but is a rather tedious task that
requires a considerable amount of data processing. This is why the Playfair Cipher
was regarded as secure at the start of the 20th century. However, that same century
saw the development of computers, which thrive on the routine processing of vast
volumes of data. Thus the Playfair Cipher is now regarded as an insecure cipher,
and 'easy' to break given sufficient ciphertext.
