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used uniform font for sets

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This commit is contained in:
Aaron Kaiser
2023-05-15 10:12:44 +02:00
parent 66ab947000
commit 048dd04b86
7 changed files with 31 additions and 31 deletions
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8
thesis/sections/mu_security_of_eddsa/omdl'_implies_mu-gamez.tex
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@@ -17,7 +17,7 @@ This section shows that \somdl implies MU-\igame using the Algebraic Group Model
\begin{algorithmic}[1]
\Statex \underline{\game \somdl}
\State \textbf{for} $i \in \{1,2,...,N\}$
\State \quad $a_i \randomsample \{ 2^{n-1}, 2^{n-1} + 8, ..., 2^{n} - 8 \}$
\State \quad $a_i \randomsample \{ 2^{n-1}, 2^{n-1} + 2^c, ..., 2^{n} - 2^c \}$
\State \quad $\groupelement{A_i} \assign a_i \groupelement{B}$
\State $I \assign 0$
\State $(a'_1, a'_2, ..., a'_N) \randomassign \adversary{A}^{DL(\inp)}(\groupelement{A_1}, \groupelement{A_2}, ..., \groupelement{A_N})$
@@ -58,7 +58,7 @@ This section shows that \somdl implies MU-\igame using the Algebraic Group Model
\State \quad $a_i \randomsample \{2^{n-1}, 2^{n-1} + 2^c, ..., 2^n - 2^c\}$
\State \quad $\groupelement{A_i} \assign a_i \groupelement{B}$
\State $s^* \randomsample \adversary{A}^{\ioracle(\inp)}(\groupelement{A_1}, \groupelement{A_2}, ..., \groupelement{A_N})$
\State \Return $\exists (\groupelement{R}^*, \ch^*) \in Q, i \in \{1,2,...,N\}: \groupelement{R}^* = 2^c s^* \groupelement{B} - 2^c \ch^* \groupelement{A_i}$
\State \Return $\exists (\groupelement{R}^*, \ch^*) \in \pset{Q}, i \in \{1,2,...,N\}: \groupelement{R}^* = 2^c s^* \groupelement{B} - 2^c \ch^* \groupelement{A_i}$
\end{algorithmic}
\vspace{2mm}
\begin{algorithmic}[1]
@@ -74,7 +74,7 @@ This section shows that \somdl implies MU-\igame using the Algebraic Group Model
\Comment{$G_2$}
\EndBox
\EndBox
\State $Q \assign Q \cup \{ (\groupelement{R}, \ch) \}$
\State $\pset{Q} \assign \pset{Q} \cup \{ (\groupelement{R}, \ch) \}$
\State \Return $\ch$
\end{algorithmic}
\hrule
@@ -129,7 +129,7 @@ This section shows that \somdl implies MU-\igame using the Algebraic Group Model
\State \textbf{If} $\exists i \in \{2,3,...,N+1\}: 2^c \ch \equiv -r_i \pmod L$ \textbf{then}
\State \quad $bad \assign true$
\State \quad $abort$
\State $Q \assign Q \cup \{ (\groupelement{R}, \ch) \}$
\State $\pset{Q} \assign \pset{Q} \cup \{ (\groupelement{R}, \ch) \}$
\State \Return $\ch$
\end{algorithmic}
\hrule