Finding Vigenere's keys with part of decrypted text? I have a text that was encrypted twice with two Vigenere keys.
However, I know the seven first characters of the decrypted text.

I have already implemented a function displaying for the five first characters the two keys that were possibly used but there are so many possibilities (265 if I am correct)...

I think the answer is no but I'd like be sure. Is there a way of finding the two keys that were used ? Can I use a statistical method even if I don't know the lengths of the keys ?

P.S.: The text is not in English but in German (not very important but for statistical methods, it obviously depends on the language of the text you analyze)

UPDATE: According to the analysis of the text, the LCM of lengths of the keys seems to be equal to 12. If the two keys have 12 characters then it is as if the author had used only one key with 12 characters right ? So if two characters are separated by 11 characters, then they have the same Caesar's shift, don't they ? And if the two keys have different lengths, does it mean that the lengths are either (4,6) or (2,12) or (3,4) ?
The key lengths are important, also if it's the Vigenère cipher is applied twice its the same as once with a different keyword. If the two keys are the same length then the new key is that length, if the two keys are different lengths then the new key is sometimes = k1 length * k2 length. If the key length is longer than the message there isn't much analysis you can do.