Try again on fairness game

1 files changed, 5 insertions, 11 deletions

diff --git a/games/games.tex b/games/games.tex
index c2d2b41..496ae02 100644
--- a/games/games.tex
+++ b/games/games.tex
@@ -425,20 +425,14 @@ Let \oraSet{Fair} stand for access to the oracles
   \item $C_0 \leftarrow {\cal A}^{\oraSet{Fair}}(pkExchange)$
   \item If $C_0$ is not a coin public key, return 0.
         Also let $U$ be the user that has $C_0$ in their wallet.  If no such $U$ exists, return 0.
-  \item Let $C_0, \dots, C_n$ be the coins reachable via \algo{Link} from $C_0$.
+  \item Let $C_0, \dots, C_n$ be the coins reachable via \algo{Link} from $C_0$.  
+        We note the user obtains unlinkable change through refreshes, which merely extend this list.
   \item Return 0 if either $U$ was corrupted or \ora{Share} was called with any of $C_0, \dots, C_n$.
   \item For each $C \in \{C_0, \dots, C_n\}$, do the following:
     \begin{enumerate}[label*=\arabic*.]
-      \item Let $v$ denote the residual value of $C$ expected by $U$, meaning
-            the value not consumed by contracts in $contractHashes[U]$ or
-            refreshed into coins in $C_0,\ldots, C_n$.
-            Let $v'$ be the closest under-approximation to $v$ reachable by denominations in $\V{pkE}$.
-      \item $R \leftarrow \algo{Refresh}(\prt{B}(skE, pkE), \prt{U}(U, C))$. \\
-            $R$ yields either new coins totaling $v'$, or error responses favoring the adversary.
-      \item Return 1 if $R$ indicates $C$ was spent on some contract $h \notin contractHashes[U]$ not known to $C$.
-      \item Return 1 if $R$ indicates existing refreshes (failed or succeeded) into coins not in $C_0, \dots, C_n$.
-      \comment{Discuss failed or succeeded}
-    \end{enumerate}
+      \item Return 1 if $\V{deposited}[C]$ contains a contract $h$ not appearing in the wallet's database $\V{acceptedContracts}[U]$.
+      \item Return 1 if the total value $r_E$ of attempted refreshes in $\V{refreshed}[C]$ exceeds the total value $r_U$ of coins in $C_0, \dots, C_n$ directly reachable in one link from $C$.  We note $r_E$ includes refreshes that failed due to dishonesty, but not refreshes that failed to authenticate as $C$.
+     \end{enumerate}
   \item Return 0 if this step is reached without an earlier return.
 \end{enumerate}