-Before we move on to the OAEP+ security results, we state and prove the
-following lemma, due (I believe) to Victor Shoup.
-
-\begin{lemma}[Shoup]
- \label{lem:shoup}
- If $X$, $Y$ and $F$ are events, and
- \[ \Pr[X \land \lnot F] = \Pr[Y \land \lnot F] \]
- then
- \[ |{\Pr[X]} - \Pr[Y]| \le \Pr[F]. \]
-\end{lemma}
-\begin{proof}
- We have:
- \begin{eqnarray*}[rll]
- \Pr[X] &= \Pr[X \land F] &+ \Pr[X \land \lnot F] \\
- \Pr[Y] &= \Pr[Y \land F] &+ \Pr[Y \land \lnot F]
- \end{eqnarray*}
- Subtracting gives
- \[ |{\Pr[X]} - \Pr[Y]| = |{\Pr[X \land F]} - \Pr[Y \land F]| \le \Pr[F] \]
- as required.
-\end{proof}
-