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Fixed equations in theorems

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This commit is contained in:
Aaron Kaiser
2023-05-15 09:41:48 +02:00
parent dd76d800fc
commit 66ab947000
5 changed files with 7 additions and 7 deletions
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thesis/sections/security_of_eddsa/uf-nma_implies_suf-cma.tex
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@@ -7,7 +7,7 @@ This section shows that the UF-NMA security of EdDSA implies the \cma security o
\label{theorem:adv_uf-nma}
Let $\adversary{A}$ be an adversary against $\cma$, making at most $\hashqueries$ hash queries and $\oraclequeries$ oracle queries. Then,
\[ \advantage{\adversary{A}}{\text{\cma}}(\secparamter) = \advantage{\adversary{B}}{\text{UF-NMA}}(\secparamter) - \frac{\oraclequeries \hashqueries}{2^{-\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}}. \]
\[ \advantage{\adversary{A}}{\text{\cma}}(\secparamter) \leq \advantage{\adversary{B}}{\text{UF-NMA}}(\secparamter) + \frac{\oraclequeries \hashqueries}{2^{-\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}}. \]
\end{theorem}
\paragraph{\underline{Proof Overview}} The UF-NMA security definition is close to the security definition of \cma but is missing the \Osign oracle. To show that UF-NMA security implies \cma security the reduction has to simulate the \Osign oracle without the knowledge of the private key.
@@ -184,7 +184,7 @@ This section shows that the UF-NMA security of EdDSA implies the EUF-CMA securit
\label{theorem:adv2_uf-nma}
Let $\adversary{A}$ be an adversary against EUF-CMA, making at most $\hashqueries$ hash queries and $\oraclequeries$ oracle queries. Then,
\[ \advantage{\adversary{A}}{\text{EUF-CMA}}(\secparamter) = \advantage{\adversary{B}}{\text{UF-NMA}}(\secparamter) - \frac{\oraclequeries \hashqueries}{2^{-\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}}. \]
\[ \advantage{\adversary{A}}{\text{EUF-CMA}}(\secparamter) \leq \advantage{\adversary{B}}{\text{UF-NMA}}(\secparamter) + \frac{\oraclequeries \hashqueries}{2^{-\log_2(\lceil \frac{2^{2b} - 1}{L} \rceil 2^{-2b})}}. \]
\end{theorem}
\paragraph{\underline{Formal Proof}}