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Any good software should use PBKDF (a password based key derivation function) that uses a random salt. This salt is stored with the ciphertext and should be different for each ciphertext. As long as this is the case they key will be different for each ciphertext. The best way an attacker can then attack your ciphertext (when stored on disk) is to iterate ...


It really depends on you block cipher mode of operation and likeliness between your files. With any proper implementation, it should really not, but since you don't really give any details about your encryption scheme, it's hard to tell. (side-note: how do you derive the key from the password?)


Your subtracting two known solutions would be one way to eliminate $b$ from the equations and allow you to work only with $A$. However, you've already been told that $b = (0,0)$, and so we don't need to eliminate it. Instead, we know that the cipher satisfies the relations (omitting $b$ because that's known to be 0): $$\begin{gathered} A \times \left[ ...

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