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Assume for the sake of contradiction that $|K|<(1-\epsilon)|M|$. We will define an adversary which has semantic advantage greater than $\epsilon$. Let $S=\{D(k,c)|k\in K\}$, where D is the decryption function of our cipher $\mathcal{E}$. We define our adversary A with the following characteristics: $m_0,m_1\in M$ are chosen randomly The predicate $\phi$ ...


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