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authorJeff Burdges <burdges@gnunet.org>2018-04-25 07:33:56 +0200
committerJeff Burdges <burdges@gnunet.org>2018-04-25 07:33:56 +0200
commitcf4086163362d68011d093bc683732bacac5aba1 (patch)
tree0a730a4a1f44481206e53e600f2b97fd2f33d9de /games
parent0edaad75bb56814a2186fa488b540ede18581f6f (diff)
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Rearange income game
Diffstat (limited to 'games')
-rw-r--r--games/games.tex17
1 files changed, 10 insertions, 7 deletions
diff --git a/games/games.tex b/games/games.tex
index e5bb2fc..ebe551a 100644
--- a/games/games.tex
+++ b/games/games.tex
@@ -493,13 +493,16 @@ Let \oraSet{Income} stand for access to the oracles
\item $(C_1, \dots, C_\ell) \leftarrow \mathcal{A}^{\oraSet{Income}}(pkExchange)$
\item Augment the wallets of all non-corrupted users with their
transitive closure using the \algo{Link} protocol.
- Spend all remaining value on coins in wallets of non-corrupted users with \algo{Deposit}.\footnote{If \algo{Deposit} can only be run once per coin, then run a similar algorithm that ignores this check.}
- \item Let $L$ be the sum of unspent value for valid coins in $C_1, \dots\, C_\ell$, after
- accounting for the previous spending step.
- \item Let $w$ be the sum of coins withdrawn by non-corrupted users,
- $w'$ be the sum of coins withdrawn by corrupted users, and $s$ be the value marked as spent
- by non-corrupted users.
- \item If defined, we return $p \over b + p$ where $b := w - s$ gives the lost coins and $p := L - w'$ gives the adversary's winnings.
+ Spend all remaining value on coins in wallets of non-corrupted users
+ with \algo{Deposit}.\footnote{If \algo{Deposit} can only be run once per coin, then run a similar algorithm that ignores this check.}
+ \item Let $L$ denote the sum of unspent value on valid coins in $C_1, \dots\, C_\ell$,
+ after accounting for the previous spending step.
+ Also let $w'$ be the sum of coins withdrawn by corrupted users.
+ So $p := L - w'$ gives the adversary's winnings.
+ \item Let $w$ be the sum of coins withdrawn by non-corrupted users, and
+ $s$ be the value marked as spent by non-corrupted users, so that
+ $b := w - s$ gives the coins lost during refresh.
+ \item If defined, return $p \over b + p$.
Also, we note our adversary wins the strong income transparency game if $L - w' > 0$.
\comment{$(L, w, w', s)$ Big stile break so split into two games. Return ratio. Two expectations is wrong. }
\end{enumerate}