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The adversary $\mathcal A$ is an entity (think of a computer program) designed to participate in the experiment $\operatorname{PrivK}^{\text{eav}}_{A,\Pi}$. So the adversary produces two messages, then is given the encryption of one of them, and has to guess which one it was. Of course, you can give the adversary other "ciphertexts" too, but this wouldn't ...

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