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author | Florian Dold <florian.dold@gmail.com> | 2018-09-20 00:31:26 +0200 |
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committer | Florian Dold <florian.dold@gmail.com> | 2018-09-20 00:31:26 +0200 |
commit | 08e10f3ea690c43d2249354e12dc5659679433bc (patch) | |
tree | 6cbabfe4c6902af96162f9eec9670435d3162f56 /taler-fc19/paper.tex | |
parent | 4d6bc3a5693e832935557b8b0f36481d5dad3b9c (diff) | |
download | papers-08e10f3ea690c43d2249354e12dc5659679433bc.tar.gz papers-08e10f3ea690c43d2249354e12dc5659679433bc.tar.bz2 papers-08e10f3ea690c43d2249354e12dc5659679433bc.zip |
income transparency proof
Diffstat (limited to 'taler-fc19/paper.tex')
-rw-r--r-- | taler-fc19/paper.tex | 13 |
1 files changed, 7 insertions, 6 deletions
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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