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Added citation to OMDL

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Aaron Kaiser
2023-05-19 09:31:28 +02:00
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thesis/sections/security_notions.tex
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@@ -135,7 +135,7 @@ This thesis proves the security of the EdDSA signature scheme under two assumpti
The one-more discrete logarithm assumption is stronger than the discrete logarithm assumption. In this assumption the adversary is supplied with $N$ group elements and an oracle to obtain the discrete logarithm of up to $N-1$ group elements. The task of the adversary is to output the discrete logarithm for all supplied group elements. The one-more discrete logarithm assumption is stronger than the discrete logarithm assumption. In this assumption the adversary is supplied with $N$ group elements and an oracle to obtain the discrete logarithm of up to $N-1$ group elements. The task of the adversary is to output the discrete logarithm for all supplied group elements.
\begin{definition}[One-More Discrete Logarithm Problem] \begin{definition}[One-More Discrete Logarithm Problem \cite{JC:BNPS03}]
Let $\group{G}$ be a cyclic group of order $L$ with a generator $\groupelement{B}$. Let the one-more discrete logarithm game be defined in figure \ref{game:om-dlog}. The advantage of an adversary $\adversary{A}$ is defined by its ability to win the one-more discrete logarithm game. Let $\group{G}$ be a cyclic group of order $L$ with a generator $\groupelement{B}$. Let the one-more discrete logarithm game be defined in figure \ref{game:om-dlog}. The advantage of an adversary $\adversary{A}$ is defined by its ability to win the one-more discrete logarithm game.
\[ \advantage{\group{G}, \adversary{A}}{OM-Dlog} \assign \prone{\text{OM-Dlog}^{\adversary{A}}} \] \[ \advantage{\group{G}, \adversary{A}}{OM-Dlog} \assign \prone{\text{OM-Dlog}^{\adversary{A}}} \]