I am pleased to offer this month's guest essay, written
by one of the newest members of the Quiller
Mailing List, Scryer. You might already have seen, on the
<QML>, Scryer's excellent decrypting of Quiller's intended message to
Control in The Warsaw Document, but if you've not been introduced
to the clarity of his thought, you're in for a treat!
For your convenience, I have reproduced at the bottom
of the page the cryptogram used by Scryer as
Rick Holt (Iron Mouth)
Quiller Puzzle Pages
As Rick points out in his essay on solving
Vigenere ciphers, the most important step is figuring out the period.
Kasiski is fine if there are substantial repeats, but is ambiguous or useless
if there are not. In the July Vigenere,
there was only one repeat of 3 letters, "UCE" at 0 and 90. This is
worth checking for periods 5, 6, 9, and 10, but isn't as definitive as
one would like. Happily, we have a stronger test called the Index
of Coincidence, discovered by William F. Friedman, the leader of the US
team that broke the Japanese Purple machine in World War 2.
The Index of Coincidence is a sensitive test that allows us to determine
(well, OK, guess) that a set of ciphertext characters comes from
a single alphabet. If they do, the IC will be about 0.065 (for English).
If the ciphertext characters are fairly random, the value will be about
To use it to determine the period, break the cipher up into each period
you would like to test; in this case, we may as well start with the four
we identified as likely from the Kasiski test. Write the cryptogram
four times, once in each period, then do a frequency count on each column.
For each one, add up the quantity f[i] * (f[i] - 1), where f[A] is the
frequency of ciphertext A and so on. Divide each of these results
by N * (N - 1), where N is the number of letters in that column.
This is simple to do by hand, and even simpler to do with a computer.
To test whether the July Vig is period 5, write it as period 5 and
calculate the IC on each column: it comes out as 0.0303 for the first column
(pretty random), 0.0563 for the second (not bad), 0.0433, 0.0476, and 0.0390
(pretty pathetic). Then take the average of these five numbers, and
we get the overall score for period five: 0.0433. This is not encouraging:
we want about 0.065.
Well, then let's try period 6: the average of these is 0.0487, still
not good. Period 9? 0.0455. Period 10? 0.0491.
The best of the lot (and it's not all that great) is period 10, 0.0491.
Usually the best value will show up much better than this, but occasionally
the cryptanalyst will have bad luck, especially with shortish cryptograms
such as this one. In any case, we have our candidate: try period
10 first, and start dragging your cribs through it looking for likely pieces
of the key to pop out the other side. If it doesn't work out, then
try period 6, and so on. The important thing is to keep trying stuff,
and don't be discouraged with failure: you can often solve something if
you just keep trying new ideas.
This is the July Vigenere cryptogram Scryer
refers to in his article:
Level of difficulty: High
Clue: For the Messiah's travel plans
UCEHH GSIEK NGADE
XBOLN JDCGY IOBNB WAOJA QSZRT IJDWW
ACGZX SELGJ PZIAW
GPIBP CUXBE NNESA
UITYT QPRLR TSXGH UCENP DIAGB RPFJH