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simplified equations

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This commit is contained in:
Aaron Kaiser
2023-07-12 22:11:02 +02:00
parent a75f324d8f
commit 8d6f37310c
10 changed files with 48 additions and 48 deletions
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18
thesis/sections/security_notions.tex
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@@ -19,7 +19,7 @@ A common security notion for digital signature schemes is the existential unforg
\begin{definition}[MU-EUF-CMA]
Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme and $N$ be an integer. Let the N-MU-EUF-CMA game be defined in figure \ref{game:mu-euf-cma}. $SIG$ is N-MU-EUF-CMA secure if for all ppt adversaries $\adversary{A}$, we have
\[ \advantage{SIG,\adversary{A}}{\textsf{N-MU-EUF-CMA}}(\secparamter) \assign \prone{\textsf{N-MU-EUF-CMA}^{\adversary{A}}} \leq negl(\secparamter). \]
\[ \advantage{SIG,\adversary{A}}{\textsf{$N$-MU-EUF-CMA}}(\secparamter) \assign \prone{\textsf{$N$-MU-EUF-CMA}^{\adversary{A}}} \leq negl(\secparamter). \]
\end{definition}
\begin{figure}[h]
@@ -27,7 +27,7 @@ A common security notion for digital signature schemes is the existential unforg
\normalsize
\vspace{1mm}
\begin{algorithmic}
\Statex \underline{\game $\text{N-MU-EUF-CMA}$}
\Statex \underline{\game $\text{$N$-MU-EUF-CMA}$}
\State \textbf{for} $i \in \{1,2,...,N\}$
\State \quad $(\pubkey_i, \privkey_i) \randomassign \keygen(1^\secparamter)$
\State $(\m^*, \signature^*) \randomassign \adversary{A}^{\sign(\inp, \inp)}(\pubkey_1, \pubkey_2, ..., \pubkey_n)$
@@ -41,14 +41,14 @@ A common security notion for digital signature schemes is the existential unforg
\State \Return $\signature$
\end{algorithmic}
\hrule
\caption{N-MU-EUF-CMA Security Game}
\caption{$N$-MU-EUF-CMA Security Game}
\label{game:mu-euf-cma}
\end{figure}
\begin{definition}[MU-SUF-CMA]
Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme and $N$ be an integer. Let the MU-SUF-CMA game be defined in figure \ref{game:mu-suf-cma}. $SIG$ is MU-SUF-CMA secure if for all ppt adversaries $\adversary{A}$, we have
\[ \advantage{SIG,\adversary{A}}{\textsf{N-MU-SUF-CMA}}(\secparamter) \assign \prone{\textsf{N-MU-SUF-CMA}^{\adversary{A}}} \leq negl(\secparamter). \]
\[ \advantage{SIG,\adversary{A}}{\textsf{$N$-MU-SUF-CMA}}(\secparamter) \assign \prone{\textsf{$N$-MU-SUF-CMA}^{\adversary{A}}} \leq negl(\secparamter). \]
\end{definition}
\begin{figure}[h]
@@ -56,7 +56,7 @@ A common security notion for digital signature schemes is the existential unforg
\normalsize
\vspace{1mm}
\begin{algorithmic}
\Statex \underline{\game $\text{N-MU-SUF-CMA}$}
\Statex \underline{\game $\text{$N$-MU-SUF-CMA}$}
\State \textbf{for} $i \in \{1,2,...,N\}$
\State \quad $(\pubkey_i, \privkey_i) \randomassign \keygen(1^\secparamter)$
\State $(\m^*, \signature^*) \randomassign \adversary{A}^{\sign(\inp, \inp)}(\pubkey_1, \pubkey_2, ..., \pubkey_n)$
@@ -70,7 +70,7 @@ A common security notion for digital signature schemes is the existential unforg
\State \Return $\signature$
\end{algorithmic}
\hrule
\caption{N-MU-SUF-CMA Security Game}
\caption{$N$-MU-SUF-CMA Security Game}
\label{game:mu-suf-cma}
\end{figure}
@@ -79,21 +79,21 @@ The MU-EUF-NMA security game is similar to the MU-EUF-CMA game. The only differe
\begin{definition}[MU-EUF-NMA]
Let $SIG = (\keygen, \sign, \verify)$ be a digital signature scheme and $N$ be an integer. Let the N-MU-EUF-NMA game be defined in figure \ref{game:mu-uf-nma}. $SIG$ is N-MU-EUF-NMA secure if for all ppt adversaries $\adversary{A}$, we have
\[ \advantage{SIG,\adversary{A}}{\textsf{N-MU-EUF-NMA}}(\secparamter) \assign \prone{\textsf{N-MU-EUF-NMA}^{\adversary{A}}} \leq negl(\secparamter). \]
\[ \advantage{SIG,\adversary{A}}{\textsf{$N$-MU-EUF-NMA}}(\secparamter) \assign \prone{\textsf{$N$-MU-EUF-NMA}^{\adversary{A}}} \leq negl(\secparamter). \]
\end{definition}
\begin{figure}[h]
\hrule
\vspace{1mm}
\begin{algorithmic}
\State \underline{\game $\text{N-MU-EUF-NMA}$}
\State \underline{\game $\text{$N$-MU-EUF-NMA}$}
\State \textbf{for} $i \in \{1,2,...,N\}$
\State \quad $(\pubkey_i, \privkey_i) \randomassign \keygen(1^\secparamter)$
\State $(\m^*, \signature^*) \randomassign \adversary{A}(\pubkey_1, \pubkey_2, \pubkey_n)$
\State \Return $\exists i \in \{1,2,...,N\}: \verify(\pubkey_i, \m^*, \signature^*) \test 1$
\end{algorithmic}
\hrule
\caption{N-MU-EUF-NMA Security Game}
\caption{$N$-MU-EUF-NMA Security Game}
\label{game:mu-uf-nma}
\end{figure}