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Added citation in definition 3.1

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Aaron Kaiser
2023-05-15 09:24:51 +02:00
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thesis/sections/preliminaries.tex
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@@ -10,17 +10,17 @@ During the proof these games are being modified until an adversary against the m
While modifying the games it has to be ensured that the advantage for an attacker to distinguish between the original and modified game is negligible. This can be achieved by constructing so called identical-until-bad games. While modifying the games it has to be ensured that the advantage for an attacker to distinguish between the original and modified game is negligible. This can be achieved by constructing so called identical-until-bad games.
\begin{definition}[identical-until-bad games] \begin{definition}[identical-until-bad games \cite{EC:BelRog06}]
Two games are called identical-until-bad games if they are syntactically equivalent except for instructions following the setting of a bad flag to true. Two games are called identical-until-bad games if they are syntactically equivalent except for instructions following the setting of a bad flag to true.
\end{definition} \end{definition}
\begin{lemma}[Fundamental lemma of game-playing] \begin{lemma}[Fundamental lemma of game-playing \cite{EC:BelRog06}]
Let G and H be identical-until-bad games and let $\adversary{A}$ be an adversary. Then, Let G and H be identical-until-bad games and let $\adversary{A}$ be an adversary. Then,
\[ Adv(G^{\adversary{A}}, H^{\adversary{A}}) = |\prone{G^{\adversary{A}}} - \prone{H^{\adversary{A}}}| \leq \Pr[bad] \] \[ Adv(G^{\adversary{A}}, H^{\adversary{A}}) = |\prone{G^{\adversary{A}}} - \prone{H^{\adversary{A}}}| \leq \Pr[bad] \]
\end{lemma} \end{lemma}
This means that the advantage to distinguish between two identical-until-bad games is bound by the probability of the bad flag being set. A proof for this lemma can be found in \cite{EC:BelRog06}. This means that the advantage to distinguish between two identical-until-bad games is bound by the probability of the bad flag being set.
\input{sections/notation} \input{sections/notation}