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Fixed some spelling mistakes, thanks Henrik. again

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Aaron Kaiser
2023-06-14 16:23:56 +02:00
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thesis/sections/mu_security_of_eddsa/mu-gamez_implies_mu-uf-nma.tex
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This section shows that MU-\igame implies MU-UF-NMA security of the EdDSA signature scheme using the Random Oracle Model. The section starts by first providing an intuition of the proof followed by the detailed security proof.
\paragraph{\underline{Introducing MU-\igame}} This game followed closely the definition of the \igame game. It again replaces the random oracle with the \ioracle oracle. The only difference to the \igame game is that the adversary gets access to $N$ public keys. The adversary again has to output a valid result for any commitment challenge pair generated by the \ioracle oracle for any of the public keys. The MU-\igame game is depicted in figure \ref{game:mu-igame}.
\paragraph{\underline{Introducing MU-\igame}} This game follows closely the definition of the \igame game. It again replaces the random oracle with the \ioracle oracle. The only difference to the \igame game is that the adversary gets access to $N$ public keys. The adversary again has to output a valid result for any commitment challenge pair generated by the \ioracle oracle for any of the public keys. The MU-\igame game is depicted in figure \ref{game:mu-igame}.
\begin{definition}[MU-\igame]
Let $n$ and $N$ be positive integers. For an adversary $\adversary{A}$, receiving $N$ public keys as input, we define its advantage in the MU-\igame as following: