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100 CHAPTER 6. DECRYPTING MONOALPHABETIC CIPHERS
the same letter. That is the goal of our next chapter. We end this chapter with a
couple of ways that can make monoalphabetic ciphers harder to decrypt. (These
tricks can actually be used with most of the ciphers we will see.)
Homophones. When a substitution alphabet has multiple substitutions for a
given letter these substitutes are called homophones. For instance, we may
decide that every other e will be replaced by a z before the message is enciphered.
Since z is so uncommon, our partner should be able to figure out we’ve replaced
some e’s by z’s without prior warning. But to the enemy who intercepts the
ciphertext, the tall 12% peak of e’s will be split into two far less visible 6%
bumps. This would make the frequency analysis of our adversary a bit harder.
Homophones are more commonly used when one is sending the ciphertext in
numerical form. For example, consider the replacement list in a cipher of Henri
IV of Navarre of France, c. 1600. [Pratt, page 64.]
plaintext a b c d e f g h i l n o p r s t u w x y z
ciphertextA 31 26 27 28 31 29 3 33 12 14 44 15 16 17 9 20 21 22 23 24 25
ciphertextB 34 35 36 37 38 39 30 41 42 43 67 18 46 47 19 50 51 52 76 54 55
ciphertextC 37 59 60 61 62 40 64 65 66 85 45 69 70 49 73 74 75 77 78
ciphertextD 80 81 82 68 83 72 84 86 87
(Most of the unassigned numbers stood for common words: 10 = le, 39 = mon.)
To encipher a letter choose one of the numbers beneath it. So tres might
be enciphered as 20-17-31-9 or as 50-70-38-49. These multiple substitutes
flatten the frequency chart, making it much harder for our adversary to decide
which number(s) represent which letter.
To make this effective we would probably want several homophones for each
letter, and then somehow force ourselves to pick the homophones at random.
We might have six homophones for each letter and then to encipher a letter
we would roll a die and if the die comes up with a 4, then pick the fourth
homophone as the cipherletter. Unfortunately, homophones make enciphering
and deciphering much slower.
Further, if the message is thousands of letters long frequency analysis will
still win out. A handwritten page will have approximately 500 characters on it
(about 25 characters per line and 20 lines per page) and a typewritten page can
easily consist of 3000 characters (70 characters per line and 45 lines per page).
For our die-homophone example, the cipher-numerals standing for uvwxyz still
would very seldom be used, while those standing for e would be popular, and
often occur paired with those standing for t and h. So while homophones are
helpful, they cannot make monoalphabetic ciphers secure.
Nulls. Extra meaningless symbols that added to a text only to confuse the
enemy analysts are known as nulls. One could spread a number of unpopular
letters randomly throughout the plaintext. Itz yisx xnot jtooquk qdifficult
wtowq jread ax meksskage cbontgainuing nzullys, but it is harder to cryptanalize
it. However, it is a bother to add (and later, remove) such letters, and they make