# How we can said a crypto system have perfect secrecy?

For example: I have 3 plaintexts ($a$, $b$, $c$) and 4 keys ($K_1$, $K_2$, $K_3$, $K_4$), making a table map to the cipher text, key as row and plaintext as column

$\begin{matrix} \ \ \ \ \ \ \ \ \ \ \ \ a\ \ \ \ b\ \ \ \ c\\ \\ K_1\ \ \ \ \ \ \ A\ \ \ C\ \ \ B\\ K_2\ \ \ \ \ \ \ B\ \ \ A\ \ \ C\\ K_3\ \ \ \ \ \ \ B\ \ \ C\ \ \ A\\ K_4\ \ \ \ \ \ \ C\ \ \ A\ \ \ B\\ \end{matrix}$

This is not a perfect secrecy system, because if we know cipher text not $B$, then plaintext confirm not $b$. to avoid this, we need distribute cipher text at least each $A$, $B$, $C$ in each columnâ€¦ am I correct?

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It's not clear what you're asking here - you're correct that the cipher is not perfectly secret, but that doesn't match the title, which seems to ask how one can demonstrate that a cipher has perfect secrecy... – archie Apr 13 '14 at 9:49
@archie sorry of that, but i want to know both, 1st how we can determine a cipher is perfect secrecy, 2nd my explanation is correct or not? – atom2ueki Apr 13 '14 at 10:39