New answers tagged perfect-secrecy
1
There is no mistake.
Just prefix your work with the observation that any scheme is secure for $\epsilon\ge 1/2$ because all probabilities are less than or equal to 1.
Then consider the case $0<\epsilon<1/2$. Repeat your argument, then note that $2(1-\epsilon)>1$ and so $\epsilon/2(1-\epsilon)<\epsilon$.
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