Relationship among secrecy-constant, key space and message space Here scheme $\Pi$ is $\epsilon $ -
perfectly secret.
Given that encryption scheme $\Pi$ =  $(\mathrm{Gen}, \mathrm{Enc}, \mathrm{Dec})$ over $(\mathcal K,\mathcal M,\mathcal C)$ is called $\epsilon $ -
perfectly secret if for any distribution over $\mathcal M$, any $m \in  M $ and any $ c \in C$,
$|Pr[M=m|C=c] - Pr[M=m]|&lt;\epsilon$
then how to prove that ,
$|\mathcal K|\geq (1 - \epsilon)|\mathcal M|$
I am not getting idea how to proceed as here $\epsilon$ can be anything i.e non-negligible or negligible both.
HINT: here you can prove the above thing by contradiction. Start with the reverse of what needs to be proved and see you can arrive at contradiction or not. Treat $\epsilon$ as a parameter any, by the way, you are right it can be anything negligible or non-negligible.