From 0ee78397d5cf0cb1e7696324be717222df639e95 Mon Sep 17 00:00:00 2001
From: Florian Dold <florian.dold@gmail.com>
Date: Wed, 19 Sep 2018 10:40:41 +0200
Subject: typo

---
 taler-fc19/paper.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'taler-fc19/paper.tex')

diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex
index afcacc4..c415ec3 100644
--- a/taler-fc19/paper.tex
+++ b/taler-fc19/paper.tex
@@ -612,7 +612,7 @@ Hence we ensure that:
   \item if a coin was refreshed, the customer ``owns'' the resulting coins,
     even if the operation was aborted, and
   \item if the customer withdraws, they can always obtain a coin whenever the
-    exchange accounted for a withdrawl, even when protocol executions are
+    exchange accounted for a withdrawal, even when protocol executions are
     intermittently aborted.
 \end{itemize}
 
-- 
cgit v1.2.3


From 4d6bc3a5693e832935557b8b0f36481d5dad3b9c Mon Sep 17 00:00:00 2001
From: Florian Dold <florian.dold@gmail.com>
Date: Thu, 20 Sep 2018 00:22:58 +0200
Subject: typo

---
 taler-fc19/paper.tex | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

(limited to 'taler-fc19/paper.tex')

diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex
index 134d03f..ec868db 100644
--- a/taler-fc19/paper.tex
+++ b/taler-fc19/paper.tex
@@ -1338,7 +1338,7 @@ Our instantiation satisfies {weak income transparency}.
   \begin{equation*}
     \Exp{{p \over b + p} \middle| F \neq \emptyset}
 	= |F| \sum_{R_i\in F} {p_i \over b_i + p_i} 
-    = |F| \sum_{R_i\in F} {p_i \ovver \kappa p_i}
+    = |F| \sum_{R_i\in F} {p_i \over \kappa p_i}
 	= {1\over\kappa},
   \end{equation*}
   which yields the equality (\ref{eq:income-transparency-proof}).
-- 
cgit v1.2.3


From 08e10f3ea690c43d2249354e12dc5659679433bc Mon Sep 17 00:00:00 2001
From: Florian Dold <florian.dold@gmail.com>
Date: Thu, 20 Sep 2018 00:31:26 +0200
Subject: income transparency proof

---
 taler-fc19/paper.tex | 13 +++++++------
 1 file changed, 7 insertions(+), 6 deletions(-)

(limited to 'taler-fc19/paper.tex')

diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex
index ec868db..c39216e 100644
--- a/taler-fc19/paper.tex
+++ b/taler-fc19/paper.tex
@@ -1334,13 +1334,14 @@ Our instantiation satisfies {weak income transparency}.
     p_i &:= v\\
     b_i &= (\kappa - 1)v
   \end{align*}
-  and thus $\kappa p_i = b_i + p_i$.  Now
-  \begin{equation*}
+  The adversary will succeed in $1/\kappa$ runs ($p_i=v$) and looses in
+  $(\kappa-1)/\kappa$ runs ($p_i=0$). Hence:
+  \begin{align*}
     \Exp{{p \over b + p} \middle| F \neq \emptyset}
-	= |F| \sum_{R_i\in F} {p_i \over b_i + p_i} 
-    = |F| \sum_{R_i\in F} {p_i \over \kappa p_i}
-	= {1\over\kappa},
-  \end{equation*}
+        &= \frac{1}{|F|} \sum_{R_i\in F} {p_i \over b_i + p_i} \\
+        &= \frac{1}{\kappa |F|} \sum_{R_i\in F} {v \over 0 + v} + \frac{\kappa-1}{\kappa |F|} \sum_{R_i \in F} {0 \over v + 0} \\
+        &= {1\over\kappa},
+  \end{align*}
   which yields the equality (\ref{eq:income-transparency-proof}).
 
 As for $F = \emptyset$, the return value of the game must be $0$, we conclude
-- 
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