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| -rw-r--r-- | doc/paper/taler.tex | 26 |
1 files changed, 17 insertions, 9 deletions
diff --git a/doc/paper/taler.tex b/doc/paper/taler.tex index 774300efa..eb06da588 100644 --- a/doc/paper/taler.tex +++ b/doc/paper/taler.tex @@ -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 double-spending. Then, the exchange generates a random $\gamma$ with $1 \le \gamma \le \kappa$ and - marks $C'_p$ as spent by persisting - $\langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$. + marks $C'_p$ as spent by persisting the \emph{refresh-record} + $\mathcal{F} = \langle C', \gamma, S_{C'}(\vec{B}, \vec{T_p}) \rangle$. Auditing processes should assure that $\gamma$ is unpredictable until this time to prevent the exchange from assisting tax evasion. \\ % @@ -1366,21 +1366,29 @@ The exchange can detect and prove double-spending. \end{lemma} \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} -\begin{lemma} -Merchants and customers can verify double-spending proofs. -\end{lemma} - -\begin{proof} -\end{proof} - +\begin{corollary} +Merchants and customers can verify double-spending proofs by verifying that the +signatures in the set of refresh-records and deposit-permissions are correct and +that the total value exceeds the coin's value. +\end{corollary} \begin{lemma} +% only holds given sufficient time Customers can either obtain proof-of-payment or their money back. \end{lemma} \begin{proof} + + \end{proof} \begin{lemma} |