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Update 36_BulletProof.md
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ETAAcademy authored Jul 8, 2024
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Expand Up @@ -86,6 +86,8 @@ $l(X) = (\vec{\alpha_L} - z \cdot \vec{1}^{n \cdot m}) + \vec{s}_{L} \cdot X \in

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

$\tau_{x} = \tau_1x + \tau_2x^2 + \sum\nolimits\_{j=1}^{m}(z^{1+j} \gamma_j)$

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

$g^{t}h^{\tau_{x}}\mathop{=}^{?}g^{\delta (y,z)+z\langle 1^{n\cdot m},\mathbf{y}^{n\cdot m}\rangle}\cdot \mathbf{V}^{z^{3}\mathbf{z}^{m}}\cdot T_{1}^{x}\cdot T\_{2}^{x^{2}}$
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