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@ -129,6 +129,7 @@ h_i =
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\end{cases}
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$$
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\adv{B} then sets $\alpha = y_0 \cdot a^{n+1}$. $PK$ is then defined as the scheme dictates where the only oddity is $e(g,g)^\alpha$, which can be computed as $e(g^a,g^{a^{n}})^{y_0}$ due to the definition of $\alpha$. $PK$ is sent to \adv{A}.
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% TODO: Finish this proof
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\section{Implementation of Schemes}
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\subsection{Identity-Based Encryption}
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