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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 $n\times n$).

pkotvan
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    It would be useful if you could tell us what you have tried. This helps us to understand what you already know so we can better focus our help. Also, people around here get touchy when people just post a question without motivation etc. as they are unwilling to simply do others homework for them, moreover they dislike it when a third party steps in and does the homework for them anyway so questions like this which merely states a question tend to get closed (pending adding more info). Adding in what you have tried and where you came across it will stop your question getting closed in this way. – user1729 Oct 21 '13 at 19:52
  • Thank you for suggestions. I certainly do not want anybody to completely solve it for me. Any hints would be fine. I will edit the question. – pkotvan Oct 21 '13 at 19:58

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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).

user35603
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