27 lines
1.1 KiB
TeX
27 lines
1.1 KiB
TeX
\subsection{\igame $=>$ UF-NMA (ROM)}
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This section shows that \igame implies the UF-NMA security if the EdDSA signature scheme using the Algebraic Group Model. The section starts by first providing an intuition if the proof followed by the detailed security proof.
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\begin{figure}
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\hrule
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\begin{multicols}{2}
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\large
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\begin{algorithmic}[1]
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\Statex \underline{\game \igame}
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\State \quad $a \randomsample \{2^{n-1}, 2^{n-1} + 8, ..., 2^n - 8\}$
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\State \quad $\groupelement{A} \assign a \groupelement{B}$
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\State \quad $s^* \randomsample \adversary{A}^{\ioracle(\inp)}(\groupelement{A})$
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\State \quad \Return $\exists \groupelement{R}^*, \ch^*: \groupelement{R}^* = 2^c (s^* \groupelement{B} - \ch^* \groupelement{A}) \wedge (\groupelement{R}^*, \ch^*) \in Q$
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\end{algorithmic}
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\columnbreak
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\begin{algorithmic}[1]
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\Statex \underline{\oracle \ioracle($\groupelement{R_i} \in \group{G}$)}
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\State \quad $\ch_i \randomsample \{0,1\}^{2b}$
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\State \quad $Q \assign Q \cup \{ (\groupelement{R}_i, \ch_i) \}$
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\State \quad \Return $\ch_i$
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\end{algorithmic}
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\end{multicols}
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\hrule
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\caption{\igame}
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\label{game:igame}
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\end{figure} |