Code and ciphers: Julius Caesar, the Enigma and the internet

the message were known to relate to a vital matter of national security. It
has also been suggested that perhaps there is a secret ‘trapdoor’, or
Achilles heel, known to the designers of the DES that would enable those
who know it to find the key in a realistic time. This could be true, but
nobody has found any evidence that such a thing exists.
It has also been suggested that the DES should have been based upon a
longer key, 128 bits being the most popular choice. This would certainly
put its security beyond question and, since then, 128-bit encipherment
has been introduced in other systems, but in 1977 it was not thought to be
necessary.
An alternative to using 128-bit keys would seem to be using two 64-bit
keys in succession, but this can be shown to be only twice as secure as
using a single 64-bit key provided that a vast amount of computer
memory is available. The attack assumes that a known plaintext and its
cipher equivalent are available. The known plaintext is enciphered under
all possible 64-bit keys and the known cipher text is independently deciphered
under all possible 64-bit keys. The two sets of data are sorted and
compared. This means that 2 57 tests are required rather than 2 112 . When
two identical texts are found we have candidates for the two unknown
keys. Many false key pairs (about 2 48 in fact; see M27) will be found and
will have to be tested on further known plaintext–cipher text pairs. This
‘meet-in-the-middle’ attack is not practical at present and is unlikely to
be so in the foreseeable future.
The security of the DES is enormously increased however if we use
triple encipherment. Only two keys are required but they are employed as
follows:
(1) encipher with key 1;
(2) decipher with key 2;
(3) encipher with key 1.
Encipherment and the internet 185
The adversary now will have to try 2 112 possible pairs of keys and this is
considered to be impossible in any realistic time. This triple DES encipherment
is regarded as secure and is currently in use. This form of triple encipherment
has the additional advantage that it becomes identical to single
encipherment DES if the two keys are the same, for it would allow a user
with triple encipherment to communicate with a single encipherment
user, and vice versa. Another form of triple encipherment uses three different
keys in the three stages above. Once again compatibility with the
other forms is achieved by making two or more of the keys the same.