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Fixed GameZ

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This commit is contained in:
Aaron Kaiser
2023-03-02 14:02:35 +01:00
parent 5183fd3bb1
commit 8925f7c66c
2 changed files with 640 additions and 9 deletions
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15
thesis/Abschlussarbeit.tex
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@@ -10,7 +10,7 @@ listof=totoc,
]{scrartcl}
\usepackage{thesisstyle}
\usepackage{algpseudocodex}
\usepackage[noend]{algpseudocodex}
\usepackage{xcolor}
\usepackage{tikz}
\usepackage{multicol}
@@ -302,8 +302,7 @@ This section shows that \igame implies the UF-NMA security if the EdDSA signatur
\end{algorithmic}
\columnbreak
\begin{algorithmic}[1]
\Procedure{\ioracle}{$\agmgroupelement{R_i}{r_i}$}
\State $\groupelement{R}_i = r_1 \groupelement{B} + r_2 \groupelement{A}$
\Procedure{\ioracle}{$\groupelement{R_i} \in \group{G}$}
\State $c_i \randomsample \{0,1\}^{2b}$
\State $Q \assign Q \cup \{ (\groupelement{R}_i, c_i) \}$
\State \Return $c_i$
@@ -370,11 +369,10 @@ Assuming that $r_2 + 2^c c$ is invertible in $\field{L}$ (not equal to $0$) we c
\State $c_i \randomsample \{0,1\}^{2b}$
\BeginBox[draw=blue]
\State \textbf{If} $2^c c_i \equiv -r_2 \pmod L$ \textbf{then}
\State \text{ } $bad \assign true$
\State \quad $bad \assign true$
\BeginBox[draw=red,dashed]
\State \text{ } $abort$
\State \quad $abort$
\EndBox
\State \textbf{endIf}
\EndBox
\State $Q \assign Q \cup \{ (\groupelement{R}_i, c_i) \}$
\State \Return $c_i$
@@ -436,9 +434,8 @@ Game $G_0$ is defined in Figure \ref{fig:igamewithabort} by ignoring all boxes.
\State $\groupelement{R}_i = r_1 \groupelement{B} + r_2 \groupelement{A}$
\State $c_i \randomsample \{0,1\}^{2b}$
\State \textbf{If} $2^c c_i \equiv -r_2 \pmod L$ \textbf{then}
\State \text{ } $bad \assign true$
\State \text{ } $abort$
\State \textbf{endIf}
\State \quad $bad \assign true$
\State \quad $abort$
\State $Q \assign Q \cup \{ (\agmgroupelement{R_i}{r_i}, c_i) \}$
\State \Return $c_i$
\EndProcedure