From 189932ef41248dfc16523feab1015514c7c95d43 Mon Sep 17 00:00:00 2001 From: Jeffrey Burdges Date: Fri, 9 Feb 2018 06:35:07 +0100 Subject: Grammar mostly --- games/games.tex | 9 +++++---- 1 file changed, 5 insertions(+), 4 deletions(-) (limited to 'games') diff --git a/games/games.tex b/games/games.tex index e60a756..12dc31e 100644 --- a/games/games.tex +++ b/games/games.tex @@ -790,15 +790,16 @@ $E[{b \over l-w}] \ge 1-{1\over\kappa}$. In our actual refresh operation, our commitment phase sends only the hash of the planchets to reduce bandwidth. We could however commit to the full planchets without damaging anything else, including -unforgeability. We may transform our our adversary $\cal A$ into +unforgeability. We may thus transform our our adversary $\cal A$ into any adversary for the protocol that commits to full planchets by rewinding $\cal A$ to try each $\gamma \in 1,\ldots,\kappa$ during each refresh operation to obtain all planchets. We observe a hash collision if this fails to provide the correct coins. We consider the degree one directed graph on coins induced by the -refresh protocol. It follows from unforgeability that any coin -must originate from some user's withdraw in this graph. +refresh protocol, thanks to assuming a single denomination. +It follows from unforgeability that any coin must originate from +some user's withdraw in this graph. Let $X$ denote the coins from $\{C_1,\ldots,C_\ell\}$ that originate from a non-corrupted user. So $\ell \leq w + |X|$. @@ -808,7 +809,7 @@ via the linking protocol, but no non-corrupted user could obtain the coin provided by the refresh, as otherwise $C$ gets marked as spend. In each $R_C$, we know $\cal A$ must submit a planchet for which the -linking protocol fails produce $C$ correctly. In this case, either +linking protocol fails to produce $C$ correctly. In this case, either \begin{enumerate} \item the planchet must be false outright, meaning either $C$ itself or the blinding factor does not arise form $t C'$, or else -- cgit v1.2.3