diff options
authorJeff Burdges <>2018-09-19 18:23:17 -0400
committerJeff Burdges <>2018-09-19 18:23:17 -0400
commitdaf111ce8d9703bfe9599a93515b0b7a473d6757 (patch)
parent6ad06690a484dada2d60b5855058c3db88580b5d (diff)
Try to fix expectations
1 files changed, 6 insertions, 8 deletions
diff --git a/taler-fc19/paper.tex b/taler-fc19/paper.tex
index c76b15d..2b9f1bd 100644
--- a/taler-fc19/paper.tex
+++ b/taler-fc19/paper.tex
@@ -1293,8 +1293,8 @@ Our instantiation satisfies {weak income transparency}.
where the expectation runs over
any probability space used by the adversary and challenger.
- We shall optimiz our adversary in ways that maximize $p \over b + p$.
- %TODO: Explain
+ We shall optimize our adversary in ways that maximize $p \over b + p$.
+ %TODO: Explain. % We cannot actually produce this optimize adversary ourselves, but its existence suffices to prove the inequality, and restrict our analysis to them. This is not a reduction
As a reminder, if a refresh operation is initiated using a false commitment
that is detected by the exchange, then the new coin cannot be obtained, and
@@ -1335,13 +1335,11 @@ Our instantiation satisfies {weak income transparency}.
b_i &= (\kappa - 1)v
and thus $\kappa p_i = b_i + p_i$. Now
- \begin{align*}
- \Exp{p} &= {1\over|F|} \sum_{R_i \in F} p_i\\
- \Exp{b} &= {1\over|F|} \sum_{R_i \in F} b_i,
- \end{align*}
- so
- \Exp{{p \over b + p} \middle| F \neq \emptyset} = {1\over\kappa},
+ \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}
+ = {1\over\kappa},
which yields the equality (\ref{eq:income-transparency-proof}).