Commit ef8cca2a by Stephane Glondu

### Specification: explain how to compute the election public key

parent 3485f613
Pipeline #54789 passed with stages
in 11 minutes and 42 seconds
 ... ... @@ -61,6 +61,20 @@ section~\ref{default-group}. \section{Parties} \newcommand{\pk}{\texttt{public\_key}} \newcommand{\sk}{\texttt{private\_key}} \newcommand{\proof}{\texttt{proof}} \newcommand{\iproof}{\texttt{iproof}} \newcommand{\ciphertext}{\texttt{ciphertext}} \newcommand{\pklabel}{\textsf{public\_key}} \newcommand{\pok}{\textsf{pok}} \newcommand{\challenge}{\textsf{challenge}} \newcommand{\response}{\textsf{response}} \newcommand{\alphalabel}{\textsf{alpha}} \newcommand{\betalabel}{\textsf{beta}} \newcommand{\Hash}{\mathcal{H}} \begin{itemize} \item $\mathcal{S}$: voting server \item $\mathcal{A}$: server administrator ... ... @@ -106,7 +120,10 @@ partial decryption. \item $\mathcal{A}$ checks $k_z$ \end{enumerate} \item $\mathcal{A}$ combines all the trustee public keys into the election public key $y$ public key $y$: $y=\prod_{z\in[1\dots m]}\pklabel(k_z)$ \end{enumerate} \subsubsection{Threshold decryption support} ... ... @@ -142,6 +159,10 @@ a partial decryption. \end{enumerate} \item $\mathcal{A}$ extracts encrypted decryption keys $K_1,\dots,K_m$ and \hyperref[threshold-params]{threshold parameters} \item $\mathcal{A}$ computes the election public key $y$: $y=\prod_{z\in[1\dots m]} \textsf{coefexps}(\textsf{message}(\textsf{coefexps}(P_z)))_0$ \end{enumerate} \subsection{Vote} ... ... @@ -208,20 +229,6 @@ $\textsf{field}(o)$ to access the field \textsf{field} of $o$. \subsection{Common structures} \label{common} \newcommand{\pk}{\texttt{public\_key}} \newcommand{\sk}{\texttt{private\_key}} \newcommand{\proof}{\texttt{proof}} \newcommand{\iproof}{\texttt{iproof}} \newcommand{\ciphertext}{\texttt{ciphertext}} \newcommand{\pklabel}{\textsf{public\_key}} \newcommand{\pok}{\textsf{pok}} \newcommand{\challenge}{\textsf{challenge}} \newcommand{\response}{\textsf{response}} \newcommand{\alphalabel}{\textsf{alpha}} \newcommand{\betalabel}{\textsf{beta}} \newcommand{\Hash}{\mathcal{H}} \begin{gather*} \proof=\left\{ \begin{array}{rcl} ... ... @@ -466,6 +473,11 @@ $s_{ij}=f_i(j)\mod q$ for $j=1,\dotsc,m$. $\mathcal{T}_i$ then fills the filled with $A_{i0},\dotsc,A_{it}$ \end{itemize} The public key of the election will be: $y=\prod_{z\in[1\dots m]}g^{f_z(0)}=\prod_{z\in[1\dots m]}A_{z0}$ \subsubsection{Vinputs} \label{vinputs} ... ...
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