Explain proof better

1 files changed, 4 insertions, 4 deletions

diff --git a/games/games.tex b/games/games.tex
index ba0ed58..778f756 100644
--- a/games/games.tex
+++ b/games/games.tex
@@ -764,16 +764,16 @@ a non-negligible advantage for winning the unforgeability game
 %  \cite[Definition 3]{RSA-FDH-KTIvCTI} % or \cite[Definition 6.1]{OneMoreInversion}.
 % won by $\cal A$. 
 
-We let $C_{\ell+1}, \ldots, C_m$ denote all the spent coins arising
+We assume $\cal A$ made at most $l$ withdrawal and refresh oracle
+queries to obtain the $l+1$ coins $C_1, \ldots, C_\ell$ in the game.
+Also let $C_{\ell+1}, \ldots, C_m$ denote all the spent coins arising
 from the operation of $\cal A$. % Also let $C_{m+1}, ..., C_n$ denote
 % the unsigned planchets used by refresh oracle call. 
 % Now set $Y_i = FDA_N(C_i)$ for $0 \le i \le n$. 
 % DISCUSS: We could exploit some of the power of RSA-CTI to dispose
 % of these planchets.  I think this seems unnecessary, but maybe it
 % might refines our usage of ROM or something.
-We know $\cal A$ made at most $l$ withdrawal and refresh oracle
-queries to obtain the $l+1$ coins $C_1, \ldots, C_\ell$, so
-$\cal A$ made at most $m$ withdrawal and refresh oracle
+We now know $\cal A$ made at most $m$ withdrawal and refresh oracle
 queries to obtain the $m+1$ RSA signatures %, aka inversions,
  on the $Y_i := \textrm{FDH}_N(C_i)$ with $0 \le i \le m$. 
 %