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proof for lemma 1 and corrolary

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Florian Dold 2017-05-16 14:45:03 +02:00
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@ -1017,8 +1017,8 @@ than the comparable use of zk-SNARKs in ZeroCash~\cite{zerocash}.
to cover the value of the fresh coins to be generated and prevent to cover the value of the fresh coins to be generated and prevent
double-spending. Then, double-spending. Then,
the exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and the exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and
marks $C'_p$ as spent by persisting marks $C'_p$ as spent by persisting the \emph{refresh-record}
$\langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$. $\mathcal{F} = \langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$.
Auditing processes should assure that $\gamma$ is unpredictable until Auditing processes should assure that $\gamma$ is unpredictable until
this time to prevent the exchange from assisting tax evasion. \\ this time to prevent the exchange from assisting tax evasion. \\
% %
@ -1366,21 +1366,29 @@ The exchange can detect and prove double-spending.
\end{lemma} \end{lemma}
\begin{proof} \begin{proof}
A coin can only be spent by either running the deposit protocol or the refresh
protocol with the exchange. Thus every time a coin is spent, the exchange
obtains either a deposit-permission or a refresh-record, both of which
contain a signature made with the public key of coin to authorizing the
respective operation. If the exchange as a set of refresh-records and
deposit-permissions whose total value exceed the value of the coin, the
exchange can show this set to prove that a coin was double-spend.
\end{proof} \end{proof}
\begin{lemma} \begin{corollary}
Merchants and customers can verify double-spending proofs. Merchants and customers can verify double-spending proofs by verifying that the
\end{lemma} signatures in the set of refresh-records and deposit-permissions are correct and
that the total value exceeds the coin's value.
\begin{proof} \end{corollary}
\end{proof}
\begin{lemma} \begin{lemma}
% only holds given sufficient time
Customers can either obtain proof-of-payment or their money back. Customers can either obtain proof-of-payment or their money back.
\end{lemma} \end{lemma}
\begin{proof} \begin{proof}
\end{proof} \end{proof}
\begin{lemma} \begin{lemma}