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author committer Florian Dold 2018-09-21 19:45:43 +0200 Florian Dold 2018-09-21 19:45:43 +0200 5847df968e7d54b98befbef1a7016685ca0a2d94 (patch) 9bd09053ba0637e64f338f973aed51c6b849a981 696b05a36f2959906562eebd967f81c04c9b9a77 (diff) papers-5847df968e7d54b98befbef1a7016685ca0a2d94.tar.gzpapers-5847df968e7d54b98befbef1a7016685ca0a2d94.tar.bz2papers-5847df968e7d54b98befbef1a7016685ca0a2d94.zip
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 diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.texindex 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}).