Perfect secrecy of hill cryptosystem Let $H_{n\times n}$ matrix be a key for Hill cryptosystem over English alphabet. How can be proved that Hill cryptosystem is not perfectly secure? (Assuming that all messages are sent with the same probability.) What is the sufficient condition for plaintext blocks so that cryptosystem is perfectly secure?
Thanks for help.
We know that cryptosystem is perfectly secure if $p_p(w|c)=p_p(w)$ if and only if $w \in P$ and $c \in C$. Plaintext and cryptotext space sizes are $|P|=|C|=26^n$. I am not sure if we can use the formula since $|K|$ depends on its size (number of all invertible matrix of size $n\times n$).

Hint: Take the ciphertext $aaaaaa...$ (or $0000...$ if you'll encode it by numbers from $\mathbb{Z}/26\mathbb{Z}$). Then you can specify a plaintext that is most probable for this ciphertext (for any key taken randomly).
