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Aaron Kaiser
2023-06-16 12:46:37 +02:00
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thesis/sections/security_of_eddsa/gamez_implies_uf-nma.tex
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This section shows that \igame implies the UF-NMA security of the EdDSA signature scheme using the random oracle model. The section begins with the introduction of an intermediate game \igame, followed by an intuition of the proof and the detailed security proof.
\paragraph{\underline{Introducing \igame}} The intermediate game \igame is introduced to create a separation between proofs in the random oracle model and the algebraic group model. This is achieved by replacing the random oracle with the \ioracle oracle, which takes a commitment and issues a challenge. This also removes the message and focuses on forging an arbitrary signature. The \igame game is shown in figure \ref{game:igame}.
\paragraph{\underline{Introducing \igame}} The intermediate game \igame is introduced to create a separation between proofs in the random oracle model and the algebraic group model. This is achieved by replacing the random oracle with the \ioracle oracle, which takes a commitment and issues a challenge. This also removes the message and focuses on forging an arbitrary signature. The \igame game is shown in figure \ref{game:igame}. The game has been inspired by the IDLOG game from \cite{C:KilMasPan16}.
\begin{definition}[\igame]
For an adversary $\adversary{A}$. The advantage of $\adversary{A}$ in the \igame game is defined as following: