Can you break a Vigenere cipher with key length of 2 and message/cipher text length of 4? I am currently working on a problem where an attacker knows that a user's password is either &quot;pqrs&quot; or &quot;jmlo&quot; and also knows that the encryption scheme is using the Vigenere cipher with a key length of 2 (Obviously, the attacker also knows the ciphertext). I must either describe how to find out with 100% certainty that the password is either pqrs or jmlo, or describe why this cannot be broken.
After working through it, I cannot see how this would be broken. The plaintext is only 4 characters, so statistical analysis and Kasiskis method of searching for bigrams/trigrams wont work either. Is there anything you can do to crack this encryption scheme?
If I can prove there's no single key that can encrypt to both outputs I can prove with 100% certainty which message it is, but if not I can't.

&quot;pqrs&quot; or &quot;jmlo&quot;

You can identify which password it is by comparing each letter with the corresponding letter once encrypted. For example, compare $P-R$ with $J-L$ (treating each letter as a number

They look like variables in this notation but they're not.



P and R are 2 letters apart; J and L are also 2 letters apart so that's inconclusive.
Q and S are 2 letters apart. M and O are also 2 letters apart; so that's also inconclusive.

This means there exists a 2-character key mapping each password to the same ciphertext (the mathematical relations between the letters are insufficient to distinguish). As such, there's no way in this case to identify which password it is.