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I have read the Vigenère cipher is secure as long as the key length is the same as the length of the data to be ciphered.

Is this true in cases where the same key is used multiple times. In that case after how many uses would the key be considered insecure.

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If the key has the same length as the message and it used only once, then it is called a One-Time-Pad. And that is information theoretically secure. If you re-use the key, security is gone. And that's true for any key-length of Vigenere: Re-using a key means that security has left the building. – tylo Jul 24 '14 at 14:51
@tylo: I can't think of anything else anyone could add (except for possibly the mention of Venona as an example) -- why don't you convert your comment into an answer? – poncho Jul 24 '14 at 15:12
The key has to be perfectly random to be an one-time-pad. – Nova Jul 24 '14 at 15:13
@Nova To the attacker, anyway :P – Maarten Bodewes Jul 24 '14 at 20:13
It pretty much looks like this is a duplicate of… – e-sushi Jul 25 '14 at 15:56
up vote 1 down vote accepted

Forming my comment into an answer:

If the key has the same length as the message and is used only once, it is basically a One-Time-Pad. This means, that in theory you can match any ciphertext to any plaintext with $a key$. If this key has to match certain criteria (e.g. be a word of a certain language), the information theoretic aspect will be lost. It depends on the actual keyspace if this is a problem.

However, the re-usage is more tricky, because all security is lost in Vigenere once a key is reused. If you have two ciphertexts created by the same key, you can just combine them and have the key eliminated. Then you are left with the combination of the two plaintexts, which is easy to deal with by using frequency analysis.

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Fixed. Something came up when I was writing the answer earlier. – tylo Jul 28 '14 at 10:33

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