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Removed line numbers in figures

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This commit is contained in:
Aaron Kaiser
2023-06-12 11:53:44 +02:00
parent 9ba0bc2ef3
commit 3df7ccbfe4
10 changed files with 82 additions and 61 deletions
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12
thesis/sections/security_of_eddsa/gamez_implies_uf-nma.tex
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@@ -14,7 +14,7 @@ This section shows that \igame implies the UF-NMA security of the EdDSA signatur
\hrule
\begin{multicols}{2}
\large
\begin{algorithmic}[1]
\begin{algorithmic}
\Statex \underline{\game \igame}
\State $a \randomsample \{2^{n-1}, 2^{n-1} + 2^c, ..., 2^n - 2^c\}$
\State $\groupelement{A} \assign a \groupelement{B}$
@@ -22,7 +22,7 @@ This section shows that \igame implies the UF-NMA security of the EdDSA signatur
\State \Return $\exists (\groupelement{R}^*, \ch^*) \in \pset{Q}: \groupelement{R}^* = 2^c s^* \groupelement{B} - 2^c \ch^* \groupelement{A}$
\end{algorithmic}
\columnbreak
\begin{algorithmic}[1]
\begin{algorithmic}
\Statex \underline{\oracle \ioracle($\groupelement{R_i} \in \group{G}$)}
\State $\ch_i \randomsample \{0,1\}^{2b}$
\State $\pset{Q} \assign \pset{Q} \cup \{ (\groupelement{R}_i, \ch_i) \}$
@@ -49,7 +49,7 @@ This section shows that \igame implies the UF-NMA security of the EdDSA signatur
\hrule
\begin{multicols}{2}
\large
\begin{algorithmic}[1]
\begin{algorithmic}
\State \underline{\game $G_0$}
\State $(h_0, h_1, ..., h_{2b-1}) \randomsample \{0,1\}^{2b}$
\State $s \leftarrow 2^n + \sum_{i=c}^{n-1} 2^i h_i$
@@ -58,7 +58,7 @@ This section shows that \igame implies the UF-NMA security of the EdDSA signatur
\State \Return $\verify(\groupelement{A}, \m^*,\signature^*)$
\end{algorithmic}
\columnbreak
\begin{algorithmic}[1]
\begin{algorithmic}
\Statex \underline{\oracle $H(m \in \{0,1\}^*)$}
\State $\textbf{if } \sum[m] = \bot \textbf{ then}$
\State \quad $\sum[m] \randomsample \{0,1\}^{2b}$
@@ -88,13 +88,13 @@ This section shows that \igame implies the UF-NMA security of the EdDSA signatur
\vspace{1mm}
\begin{multicols}{2}
\large
\begin{algorithmic}[1]
\begin{algorithmic}
\Statex \underline{\textbf{Adversary} $\adversary{B}^{\ioracle(\inp)}(\groupelement{A})$}
\State $(\m^*, \signature^* \assign (\encoded{R}, S)) \randomassign \adversary{A}^{H(\inp)}(\groupelement{A})$
\State \Return $S$
\end{algorithmic}
\columnbreak
\begin{algorithmic}[1]
\begin{algorithmic}
\Statex \underline{\oracle $H(m \in \{0,1\}^*)$}
\State $\textbf{if } \sum[m] = \bot \textbf{ then}$
\State \quad $\textbf{if } \encoded{R} | \encoded{A} | m' \assign m \wedge \groupelement{R} \in \curve \textbf{ then}$