rixxc/masterthesis
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

More more more

Browse Source
This commit is contained in:
Aaron Kaiser
2023-05-01 17:38:55 +02:00
parent cf19ceb0fe
commit 419018dec3
7 changed files with 171 additions and 34 deletions
Download Patch File Download Diff File Expand all files Collapse all files

14
thesis/sections/mu_security_of_eddsa/omdl'_implies_mu-gamez.tex
View File

@@ -109,7 +109,7 @@ This section shows that \somdl implies MU-\igame using the Algebraic Group Model
\State $s^* \randomassign \adversary{A}^{\ioracle(\inp)}(\groupelement{A_1}, \groupelement{A_2}, ..., \groupelement{A_N})$
\State \textbf{If} $\nexists (\agmgroupelement{R^*}{r^*}, \ch^*) \in Q, i \in \{1,2,...,N\}: \groupelement{R^*} = 2^c s^* \groupelement{B} - 2^c \ch^* \groupelement{A_i}$ \textbf{then}
\State \quad $abort$
\State Let $\groupelement{R^*} = r_1 \groupelement{B} + r_2 \groupelement{A_1} + ... + r_{N+1} \groupelement{A_N}$
\State Let $\groupelement{R^*} = r^*_1 \groupelement{B} + r^*_2 \groupelement{A_1} + ... + r^*_{N+1} \groupelement{A_N}$
\State $r_b \assign r_1$
\State \textbf{for} $j \in \{1,2,...,N\} \backslash \{i\}$
\State \quad $a_j \assign \textit{DL}(\groupelement{A_j})$
@@ -121,15 +121,15 @@ This section shows that \somdl implies MU-\igame using the Algebraic Group Model
\end{algorithmic}
\vspace{2mm}
\begin{algorithmic}[1]
\Statex \underline{\oracle \ioracle($\agmgroupelement{R_i}{r_i} \in \group{G}$)}
\Statex \underline{\oracle \ioracle($\agmgroupelement{R}{r} \in \group{G}$)}
\vspace{1mm}
\State Let $\groupelement{R}_i = r_1 \groupelement{B} + r_2 \groupelement{A_1} + ... + r_{N+1} \groupelement{A_N}$
\State $\ch_i \randomsample \{0,1\}^{2b}$
\State \textbf{If} $\exists i \in \{2,3,...,N+1\}: 2^c \ch_i \equiv -r_i \pmod L$ \textbf{then}
\State Let $\groupelement{R} = r_1 \groupelement{B} + r_2 \groupelement{A_1} + ... + r_{N+1} \groupelement{A_N}$
\State $\ch \randomsample \{0,1\}^{2b}$
\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 $Q \assign Q \cup \{ (\groupelement{R}_i, \ch_i) \}$
\State \Return $\ch_i$
\State $Q \assign Q \cup \{ (\groupelement{R}, \ch) \}$
\State \Return $\ch$
\end{algorithmic}
\hrule
\caption{Adversary $\adversary{B}$ breaking \somdl}