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Update 36_BulletProof.md
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ETAAcademy authored Jul 7, 2024
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2 changes: 1 addition & 1 deletion 36_BulletProof.md
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Expand Up @@ -84,7 +84,7 @@ $\vec{\alpha_R} = \vec{\alpha_L} - 1 \in \mathbb{Z}_{p}^{n \cdot m}$

$l(X) = (\vec{\alpha_L} - z \cdot \vec{1}^{n \cdot m}) + \vec{s}_{L} \cdot X \in \mathbb{Z}\_{p}^{n \cdot m}[X]$

$r(X) = y^{n\cdot m} \circ (\vec{a_R}+z \cdot \vec{1}^{n \cdot m} + \vec{s_R} \cdot X) +\sum\nolimits\_{j=1}^{m}z^{1+j}\cdot 0(j-1)n\Vert 2^{n}\Vert 0(m-j)n \tag{65}$
$r(X) = y^{n\cdot m} \circ (\vec{a_R}+z \cdot \vec{1}^{n \cdot m} + \vec{s_R} \cdot X) +\sum\nolimits\_{j=1}^{m}z^{1+j}\cdot \vec{0^{(j-1)n}} \Vert 2^{n} \Vert \vec{0^{(m-j)n}}$

$\begin{equation*} \delta (y, z)=-z^{2}\cdot\langle 1^{n\cdot m}, \mathbf{y}^{n\cdot m}\rangle-\sum\_{j=1}^{m}z^{j+2}\cdot\langle 1^{n}, 2^{n}\rangle \end{equation*}$

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