Hill cipher: How to find an unknown key of unknown size How would you tackle the problem of finding the key (you don't know the length) to a Hill cipher when knowing only one 12-letter word of plaintext and its corresponding ciphertext?

CONVERSATION has been encoded as SQZHUSSUDYKP with standard alphabet (A=0, Z=25). The key, as I said, is unknown with unknown size. 

I am not asking for a solution, but for tips and guidance. Any help will be much appreciated.
Assuming that $2\times2$ matrix is used, and the encryption starts from the first letter of the plaintext, the key can be found by just calculating the "encryption" with size of $4$ plain- and cryptotext block.

For example, for CONV $\rightarrow$ SQZH, it would go as follows:
$$\begin{pmatrix} 
2 &amp; 14 \\
13 &amp; 21 
\end{pmatrix}\begin{pmatrix} 
a &amp; b \\
c &amp; d 
\end{pmatrix}=
\begin{pmatrix} 
18 &amp; 16 \\
25 &amp; 7 
\end{pmatrix}\pmod{26}$$

Then solving for $a,b,c,d$, the key $K$ is found.
As here the plaintext matrix is invertible, one can compute

$$\begin{pmatrix} 
a &amp; b \\
c &amp; d 
\end{pmatrix}=\begin{pmatrix} 
2 &amp; 14 \\
13 &amp; 21 
\end{pmatrix}^{-1}
\begin{pmatrix} 
18 &amp; 16 \\
25 &amp; 7 
\end{pmatrix}\pmod{26}$$