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I. Breaking the Vigenere Cipher
The first key piece of information we would need in order to break this cipher is the
length of the keyword. Once we know this, we can group the letters in accordance to
which were shifted with the same key.
Two ways to get the length of the key word:
a) Kasiski test
b) Index of Coincidence
Kasiski test  you look for repeated strings of ciphertext of length 3 or greater. If this
occurs, it's likely that they were encrypted with the same keys. Now, just count the
number of characters in between the starting of the first string and the starting of the
second string. Often times, this length will be a multiple of the keylength. For example, if
this length were 85, we could be fairly certain that the keylength was 5. (17 is probably
unlikely since that would be a very long keyword!)
Index of Coincidence  This is defined for a probability distribution for characters. It is
the probability that two random characters are the same. This seems like a strange item to
measure, but notice that if we want to maximize a sum of products of this sort, we can do
so by measuring this quantity. The more skewed the distribution is, the higher the Index
of Coincidence for it is.
The IoC of English is about 0.065 and it is about 0.038 for a completely random
distribution. So here's what you do: guess the keyword length, then try out each group's
IoC. They should all be high, around 0.065. If they aren't try the next length.
..
Now, once you are reasonably sure you have the keylength.
..
You could cycle through all the possibilities, but this is still a pain. In fact, it's just as
much of a pain as cycling through all of them.
..
But, you can get relative shifts using the mutual index of coincidence.
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 Summer '09

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