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Fabrice Mouhartem 2018-05-17 14:15:14 +02:00
parent 793d532abc
commit a904f4fcb3
1 changed files with 4 additions and 4 deletions
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8
chap-sigmasig.tex
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@ -125,8 +125,8 @@ Moreover, we show that their scheme remains unforgeable under the $\SXDH$ assump
\setlength{\arraycolsep}{0.3em}\def\arraystretch{1.3} \setlength{\arraycolsep}{0.3em}\def\arraystretch{1.3}
\left(\begin{array}{c|c|c|c} \left(\begin{array}{c|c|c|c}
g & \mathbf{1}_{{}_{\ell+1}} & \mathbf{1}_{{}_{\ell+1}} & h \\ \hline g & \mathbf{1}_{{}_{\ell+1}} & \mathbf{1}_{{}_{\ell+1}} & h \\ \hline
\vec{v}^\top & g^{\mathbf{I}_{\ell+1}} & h^{\mathbf{I}_{\ell+1}} \vec{v}^T & g^{\mathbf{I}_{\ell+1}} & h^{\mathbf{I}_{\ell+1}}
& \mathbf{1}_{{}_{\ell+1}}^\top & \mathbf{1}_{{}_{\ell+1}}^T
\end{array}\right) , \end{array}\right) ,
\end{equation} \end{equation}
where $\mathbf{1}_{{}_{\ell+1}}=(1_{\GG},\ldots,1_{\GG})\in\GG^{\ell+1}$. where $\mathbf{1}_{{}_{\ell+1}}=(1_{\GG},\ldots,1_{\GG})\in\GG^{\ell+1}$.
@ -403,8 +403,8 @@ If DDH holds in $\GG$, for each $k \in
\def\arraystretch{1.5} \def\arraystretch{1.5}
\begin{array}{c|c} \begin{array}{c|c}
\mathbf{I}_{\ell+1} & a \cdot \mathbf{I}_{\ell + 1}\\ \hline \mathbf{I}_{\ell+1} & a \cdot \mathbf{I}_{\ell + 1}\\ \hline
\boldsymbol{0}_{\ell + 1}^{\top} & ac \cdot( m_1 | \cdots | m_\ell | 1) \\ \hline \boldsymbol{0}_{\ell + 1}^{T} & ac \cdot( m_1 | \cdots | m_\ell | 1) \\ \hline
\boldsymbol{0}_{\ell + 1}^{\top} & a s_1 \cdot( m_1^\star | \cdots | m_\ell^\star | 1) \boldsymbol{0}_{\ell + 1}^{T} & a s_1 \cdot( m_1^\star | \cdots | m_\ell^\star | 1)
\end{array} \end{array}
\egroup \egroup
\right) \cdot \right) \cdot