From 0ee78397d5cf0cb1e7696324be717222df639e95 Mon Sep 17 00:00:00 2001 From: Florian Dold Date: Wed, 19 Sep 2018 10:40:41 +0200 Subject: typo --- taler-fc19/paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'taler-fc19/paper.tex') diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex index afcacc4..c415ec3 100644 --- a/taler-fc19/paper.tex +++ b/taler-fc19/paper.tex @@ -612,7 +612,7 @@ Hence we ensure that: \item if a coin was refreshed, the customer ``owns'' the resulting coins, even if the operation was aborted, and \item if the customer withdraws, they can always obtain a coin whenever the - exchange accounted for a withdrawl, even when protocol executions are + exchange accounted for a withdrawal, even when protocol executions are intermittently aborted. \end{itemize} -- cgit v1.2.3 From 4d6bc3a5693e832935557b8b0f36481d5dad3b9c Mon Sep 17 00:00:00 2001 From: Florian Dold Date: Thu, 20 Sep 2018 00:22:58 +0200 Subject: typo --- taler-fc19/paper.tex | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) (limited to 'taler-fc19/paper.tex') diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex index 134d03f..ec868db 100644 --- a/taler-fc19/paper.tex +++ b/taler-fc19/paper.tex @@ -1338,7 +1338,7 @@ Our instantiation satisfies {weak income transparency}. \begin{equation*} \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 \ovver \kappa p_i} + = |F| \sum_{R_i\in F} {p_i \over \kappa p_i} = {1\over\kappa}, \end{equation*} which yields the equality (\ref{eq:income-transparency-proof}). -- cgit v1.2.3 From 08e10f3ea690c43d2249354e12dc5659679433bc Mon Sep 17 00:00:00 2001 From: Florian Dold Date: Thu, 20 Sep 2018 00:31:26 +0200 Subject: income transparency proof --- taler-fc19/paper.tex | 13 +++++++------ 1 file changed, 7 insertions(+), 6 deletions(-) (limited to 'taler-fc19/paper.tex') 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 -- cgit v1.2.3