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author committer Florian Dold 2018-09-20 00:31:26 +0200 Florian Dold 2018-09-20 00:31:26 +0200 08e10f3ea690c43d2249354e12dc5659679433bc (patch) 6cbabfe4c6902af96162f9eec9670435d3162f56 4d6bc3a5693e832935557b8b0f36481d5dad3b9c (diff) papers-08e10f3ea690c43d2249354e12dc5659679433bc.tar.gzpapers-08e10f3ea690c43d2249354e12dc5659679433bc.tar.bz2papers-08e10f3ea690c43d2249354e12dc5659679433bc.zip
income transparency proof
-rw-r--r--taler-fc19/paper.tex13
1 files changed, 7 insertions, 6 deletions
 diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.texindex 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