diff options
| -rw-r--r-- | taler-fc19/paper.tex | 12 |
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}).
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