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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 ...


CTR mode encryption, instantiated with a secure block cipher, is IND-CPA secure under the usual definition (Bellare et al., 1997; Rogaway, 2011). The term "mult-CPA" does not appear to be in widespread use, but it's found e.g. in these German lecture slides (Kiltz, 2011). In the slides, it is defined (on slide 66) in a similar way as ordinary IND-CPA ...

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