Fariness proof updates

1 files changed, 3 insertions, 3 deletions

diff --git a/games/games.tex b/games/games.tex
index 12fb0a8..bd6af06 100644
--- a/games/games.tex
+++ b/games/games.tex
@@ -737,10 +737,10 @@ satisfies \emph{Fairness}.
 \begin{proof}
 We replace coin public keys with signing public keys from the EUF-CMA
 challenger, unless the coins are withdrawn by corrupted users.
-Signature operations with these public keys are replaces with calls to the signing \ora{Sign} oracle of the EUF-CMA challenger.
+Signature operations with these public keys are replaced with calls to the signing \ora{Sign} oracle of the EUF-CMA challenger.
 
-If the adversary wins in step 6.2, there must be a valid deposit permission over a contract not signed by the user,
-and thus not send to \ora{Sign}.   If the adversary wins in step 6.3, there must be a refresh request not signed
+If the adversary wins in step 6.1, there must be a valid deposit permission over a contract not signed by the user,
+and thus not send to \ora{Sign}.   If the adversary wins in step 6.2, there must be a refresh request not signed
 by the user.  In either case, we can extract a forged signature and use \prt{A} to construct an adversary against EUF-CMA.
 \end{proof}