sync

1 files changed, 6 insertions, 6 deletions

diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex
index 48c127b..7ba662c 100644
--- a/taler-fc19/paper.tex
+++ b/taler-fc19/paper.tex
@@ -1327,22 +1327,22 @@ Our instantiation satisfies {weak income transparency}.
   For any $R_i$, there are $\kappa$ game runs identical up through the

   commitment phase of $R_i$ and exhibit different outcomes based on the

   challenger's random choice of $\gamma$.

-  If $v$ is the financial value of the coin resulting from refresh operation

-  $R_i$ then one of the possible runs adds $v$ to $p$, while the remaining

-  $\kappa-1$ runs add $v$ to $b$.

+  If $v_i$ is the financial value of the coin resulting from refresh operation

+  $R_i$ then one of the possible runs adds $v_i$ to $p$, while the remaining

+  $\kappa-1$ runs add $v_i$ to $b$.

 

   We define $p_i$ and $b_i$ to be these contributions summed over the $\kappa$ possible

   runs, i.e.

   \begin{align*}

-    p_i &:= v\\

-    b_i &= (\kappa - 1)v

+    p_i &:= v_i\\

+    b_i &= (\kappa - 1)v_i

   \end{align*}

   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}

         &= \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} \\

+        &= \frac{1}{\kappa |F|} \sum_{R_i\in F} {v_i \over 0 + v_i} + \frac{\kappa-1}{\kappa |F|} \sum_{R_i \in F} {0 \over v_i + 0} \\

         &= {1\over\kappa},

   \end{align*}

   which yields the equality (\ref{eq:income-transparency-proof}).