\documentclass{article}
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\begin{document}
\section*{تحليل}
[
r = {0, 1}
]
[
v = 1 \quad (A, b) \leftarrow \mathcal{W} E{m, m, q, \chi}
]
[
v = 0 \quad (A, b) \leftarrow \mathbb{Z}q^n \times \mathbb{Z}_q^n
]
[
\begin{array}{|c|c|c|}
\hline
\beta & (A, b) & A \
\hline
v' = 1 & {0, 1} & \
& (A, b) \leftarrow \mathcal{W} E{m, m, q, \chi} & \
\hline
& C1 = A & \
& C2 = b + \left[\frac{y}{z}\right] \mu, \mu1 & C1, C2 \
\hline
\end{array}
]
[
v' = 1 \quad \Rightarrow \quad v^{(1)}, v^{(2)}
]
[
v' = 0 \quad \Rightarrow \quad v^{(1)} \neq v^{(2)}
]
[
pr {v' = v''} = pr {v = 1, v' = 1} + pr {v = 0, v' = 0}
]
[
= \frac{1}{2} pr {v = 1, v' = 1} + \frac{1}{2} p_r {v = 0, v' = 0}
]
[
= \frac{1}{2} + \frac{1}{2} \left( pr {v = 1 | v' = 1} - pr {v = 1 | v' = 0} \right)
]
[
= \frac{1}{2} + \frac{1}{2} \left( \Pr{\text{IK}}(A{\Pi}) \left( v = 1 | v' = 0 \right) - \frac{1}{2} \right)
]
[
\approx \text{negl}
]
\end{document}
