Test around Fairness

1 files changed, 11 insertions, 8 deletions

diff --git a/games/games.tex b/games/games.tex
index dd731ec..d69a0b0 100644
--- a/games/games.tex
+++ b/games/games.tex
@@ -339,10 +339,16 @@ allowing them to talk to themselves does not make sense.
 %at receipts and the coin doesn't even need to be valid directly.
 
 \subsection{Fairness}
-Intuition: An adversarial merchant wins if a non-corrupted user can't obtain a proof-of-spending or unlinkable change.
 
-Let \oraSet{Fair} stand for access to the oracles \ora{AddClient}, \ora{WithdrawAsExchange}, \ora{Spend},
-\ora{RefreshAsExchange}, \ora{Share}, \ora{CorruptClient}
+Inuitively, an adversarial merchant wins if a non-corrupted user
+cannot obtain a proof-of-spending or unlinkable change, including
+if the deposit receipt from the exchange is forged by the merchant. 
+We have auditors to address adversarial exchanges who attempt to defraud
+users, but only with weaker legal security assurances.  
+
+Let \oraSet{Fair} stand for access to the oracles
+ \ora{AddClient}, \ora{WithdrawAsExchange}, \ora{Spend},
+ \ora{RefreshAsExchange}, \ora{Share}, \ora{CorruptClient}.
 
 \bigskip
 \noindent $\mathit{Exp}_{\cal A}^{fair}(1^\lambda, \kappa)$:
@@ -351,10 +357,9 @@ Let \oraSet{Fair} stand for access to the oracles \ora{AddClient}, \ora{Withdraw
   \setlength\itemsep{0em}
   \item $(skE, pkE) \leftarrow \mathrm{EKeygen}()$ 
   \item $C_0 \leftarrow {\cal A}^{\oraSet{Fair}}(pkExchange)$
-  \item If $C_0$ is not a coin public key, return 0.  Let $U$ be the user that has $C_0$ in their wallet.  If no such $U$ exists, return 0.
-    \comment{Note however that $C_0$ is not required to be fresh or unspent.}
+  \item If $C_0$ is not a coin public key, return 0.  Let $U$ be the user that has $C_0$ in their wallet.  If no such $U$ exists, return 0.  $C_0$ need not unspent or unrefreshed.
   \item Let $C_0, \dots, C_n$ be the coins reachable via \algo{Link} from $C_0$.
-    \comment{When $C_0$ was not refreshed, $n=0$ and $C_n = C_0$}
+  \footnote{In particular $n=0$ if $C_0$ is unrefreshed.}
   \item If $U$ was corrupted or \ora{Share} was called with any of $C_0, \dots, C_n$, return 0.
   \item $R \leftarrow \algo{Refresh}(\prt{B}(skE, pkE), \prt{U}(U, C_n))$
   \item If $R$ indicates a successful refresh, return $0$.
@@ -362,8 +367,6 @@ Let \oraSet{Fair} stand for access to the oracles \ora{AddClient}, \ora{Withdraw
     Otherwise return 1.
 \end{enumerate}
 
-\paragraph{Note:}  This also covers the case where the deposit receipt from the exchange is forged by the merchant.
-
 
 \subsection{Unforgability} % Exculpability?