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One can't "get rid of" the factor 2. However, there might be a way to replace it with $\:2\hspace{-0.03 in}-\hspace{-0.03 in}o(1)\:$ where that depends on $q$ and the advantage. $||$ is concatenation. Start with some encryption scheme $\mathcal{E}'\hspace{-0.04 in}$, and for any integer $n$ and probability $p$, let $\mathcal{E}_{\hspace{.02 ...



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