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-rw-r--r--doc/paper/taler.tex38
1 files changed, 25 insertions, 13 deletions
diff --git a/doc/paper/taler.tex b/doc/paper/taler.tex
index eb06da588..ea096ba6f 100644
--- a/doc/paper/taler.tex
+++ b/doc/paper/taler.tex
@@ -1361,16 +1361,16 @@ protocol is never used.
\subsection{Exculpability arguments}
-\begin{lemma}
+\begin{lemma}\label{lemma:double-spending}
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
+A coin can only be spent by 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
+respective operation. If the exchange has 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}
@@ -1383,33 +1383,45 @@ that the total value exceeds the coin's value.
\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, even
+when the merchant is faulty.
\end{lemma}
\begin{proof}
-
-
+When the customer sends the deposit-permission for a coin
+to a correct merchant, the merchant will pass it on to the
+exchange, and pass the exchange's response, a deposit-confirmation, on
+to the customer. If a faulty merchant deposits the coin
+but does not pass the deposit-confirmation to the customer,
+the customer will receive the deposit-confirmation as an error
+response from the refreshing protocol. Otherwise if the merchant
+doesn't deposit the coin, the customer can get a new, unlinkable
+coin by running the refresh protocol.
\end{proof}
-\begin{lemma}
-If a customer paid for a contract, they can prove it.
-\end{lemma}
-
-\begin{proof}
-\end{proof}
+\begin{corollary}
+If a customer paid for a contract, they can prove it by showing
+the deposit permissions for all coins.
+\end{corollary}
\begin{lemma}
The merchant can issue refunds, and only to the original customer.
\end{lemma}
\begin{proof}
+Since the refund only increases the balance of a coin that the original
+customer owns, only the original customer can spend the refunded coin again.
\end{proof}
-
\begin{theorem}
The protocol prevents double-spending and provides exculpability.
\end{theorem}
+\begin{proof}
+ Follows from Lemma \ref{lemma:double-spending} and the assumption
+ that the exchange can't forge signatures to obtain an incriminating
+ set of deposit-permissions and/or refresh-records.
+\end{proof}