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152 CHAPTER 8. POLYALPHABETIC CIPHERS
Using mathematics similar to that used in Friedman’s Index of Coincidence,
given enough text any Auto Key cipher can be broken. To perhaps explain
how, notice that the plaintext-key pairs (t,O), (n,I), (s, N) and (i, D) all give
rise to the ciphertext letter V. But this is the only way of creating V from two
high-frequency letters. So if we suspect that an Auto Key Cipher with priming
keyword of length 1 was used, then we can try each of these as the possible
plaintext–key pair on each V’s in the ciphertext. By probability, we very quickly
will find one that gives the correct decipherment. Similarly, the pairs re and
er will occur often in the plaintext, producing a large number of W’s in the
ciphertext. Thus an Auto Key cipher with a priming key of length 1 is not
secure.
Likewise, every the in a Auto Key cipher of keylength two will give many
e’s enciphered by t’s into Y’s. In general, the etaoinshr letters so frequently
encipher one another they give each other away, leading to a decryption of the
cipher.
To summarize, we broke the Vigenère Cipher by exploiting the pattern of
its repeating keyword. The Auto Key Cipher can be broken by exploiting the
usual frequency patterns of English. Removing all such patterns must be our
next goal.
8.6 Perfect Secrecy
All the ciphers we’ve studied so far depend, eventually, on some sort of pattern,
and this pattern eventually gives them away. What is needed is a cipher system
whose keyword is both endless and and senseless. The need for endless should
be clear after our work with Vigenère ciphers. Once a keyword starts to be
repeated, the cipher is in danger of being broken. Hence, for perfect secrecy we
can never allow the it to be repeated, i.e., it must be endless. The reason for
senseless is nearly the same: an extremely long keyword that is not senseless
has some pattern to it. And a pattern is not much different from a repeating
keyword. As Kahn puts it, the perfect cipher must “avoid the Scylla of repetition
and the Charybdis of intelligibility.”
Joseph O. Mauborgne (1881–1971) had the idea of “endless”. Mauborgne
had a long and very distinguished career in cryptography. In 1914 he gave the
first recorded solution of a Playfair cipher. (We will study these in Chapter 9.)
He eventually rose to the post of Chief Signal Officer in October 1937 and as a
Major General built the cryptanalytic abilities of the Signal Corps to the extent
that it was reading a flood of Japanese ciphers by his retirement in 1941.
Gilbert S. Vernam (1890-1960) had the idea of “senseless”. Vernam was an
employee of AT&T when in 1917 he proposed the use of “stream cipher devices”
for automatic encryption and decryption of telegram messages. Vernam received
65 patents in the areas of cryptography and telephone switching systems and
was well known for his cleverness – supposedly he asked himself “What can I