I am currently working on a problem where an attacker knows that a user's password is either "pqrs" or "jmlo" 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?