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[freehaven-cvs] figures fixed
Update of /home/freehaven/cvsroot/doc/routing-zones
In directory moria.mit.edu:/tmp/cvs-serv30768
Modified Files:
as_observe_75.eps routing-zones.tex
Added Files:
as_observe_all.eps
Log Message:
figures fixed
--- NEW FILE: as_observe_all.eps ---
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Index: as_observe_75.eps
===================================================================
RCS file: /home/freehaven/cvsroot/doc/routing-zones/as_observe_75.eps,v
retrieving revision 1.5
retrieving revision 1.6
diff -u -d -r1.5 -r1.6
--- as_observe_75.eps 29 Jan 2004 02:14:05 -0000 1.5
+++ as_observe_75.eps 29 Jan 2004 04:01:51 -0000 1.6
@@ -1,7 +1,7 @@
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@@ -367,98 +367,90 @@
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Index: routing-zones.tex
===================================================================
RCS file: /home/freehaven/cvsroot/doc/routing-zones/routing-zones.tex,v
retrieving revision 1.49
retrieving revision 1.50
diff -u -d -r1.49 -r1.50
--- routing-zones.tex 29 Jan 2004 03:11:55 -0000 1.49
+++ routing-zones.tex 29 Jan 2004 04:01:51 -0000 1.50
@@ -121,13 +121,13 @@
Tarzan~\cite{freedman:ccs02} and MorphMix~\cite{morphmix:fc04}, are
likely to be ineffective at achieving jurisdictional independence.
-Next, we measure the jurisdictional independence of paths inside the
-mix network. We find that given existing mix network topologies, the
+Next, we measure the jurisdictional independence of paths inside the mix
+network. We find that given existing mix network topologies, the
Mixmaster and Tor path selection algorithms will nearly always create
-paths that can be observed by a single AS in multiple locations. We
-also discover that because paths between mix nodes often cross the same AS,
-a user's vulnerability to eavesdropping does not decrease proportionally
-with the number of mix nodes in the path.
+paths that can be observed by a single AS in multiple locations for
+paths shorter than four hops. Fortunately, we observe that longer mix
+paths significantly reduce the likelihood that a single AS can observe a
+significant fraction of links in the path.
Finally, using a model of typical senders and receivers in anonymity
networks, we measure the likelihood that a single AS can observe both
@@ -717,21 +717,23 @@
\begin{figure}
\begin{minipage}[ht]{5.75cm}
\mbox{\epsfig{figure=as_observe_50.eps,width=6cm}}
-\caption{Fraction of paths where a single AS can observe at least half
- of the links in the mix network path.}
+\caption{Fraction of paths where a single AS can observe all
+ of the links on the mix network path.}
\label{fig:as_observe}
\end{minipage}
\hfill
\begin{minipage}[ht]{5.75cm}
\mbox{\epsfig{figure=as_observe_75,width=6cm}}
\caption{Fraction of paths where a single AS can observe at least 3/4
- of the links in the mix network path.}
+ of the links on the mix network path.\protect\footnotemark
+}
\label{fig:as_observe_75}
\end{minipage}
\hfill
\end{figure}
+
%% \begin{table}[t]
%% \begin{tabular}{r|p{1.25in}|p{0.5in}p{0.5in}p{0.5in}p{0.5in}}
%% {\bf Mix Network} & \parbox{1.25in}{{\centering\bf \# of \\ AS-disjoint Edges}} &
@@ -780,31 +782,15 @@
algorithm and the \emph{onion routing} algorithm, and varying lengths from
two hops to eight hops, we measured the probability that
a path crosses the same AS on multiple links. For each length and
-type of path, we ran 100,000 trials and counted the number of times the
+type of path, we ran 10,000 trials and counted the number of times the
mix network path traversed the same AS more than once.
-Figure~\ref{fig:as_observe} shows the probability that a single AS will
-be able to observe at least half of the links along the mix network
-path, for mix network paths of different lengths (paths of length one
-and two have less than two links and, thus, are never observed by the
-same AS twice). Figure~\ref{fig:as_observe_75} shows the probability
-that a single AS will be able to observe at least three-fourths of the
-links along a path of a certain length. The figures show results for
-both the Tor and Mixmaster network topologies, with two different node
-selection schemes: (1)~allowing the same mix node to be used twice along
-the mix path, as long as the same mix node is not used for two
-consecutive hops (as in {\em remailer networks}) and (2)~allowing each
-mix node to be used only once (as in {\em onion routing}).
-Figure~\ref{fig:as_observe} shows two interesting results. First, for
-all mix paths longer than four hops, a single AS can observe at least half
-of the links on the mix network path. Second, Tor's node selection
-algorithm seems to defend it slightly against observation at multiple
-links, but this node selection scheme helps Mixmaster less. This result
-makes sense: because Tor has only 14 nodes, random node selection is much
-more likely to result in the same hop being used twice along a single
-mix path, if this is not explicitly prevented.
+\footnotetext{The fraction is lower for 4-hop (i.e., 3-link) paths than
+ for 5-hop paths as an artifact of discretization: ``at least $3/4$ of
+ the links on a 3-hop path'' is all 3 links, ``at least $3/4$ of the
+ links on a 4-hop path'' is 3 out of 4 links.}
+
-\subsection{Jurisdictional Independence of Entry and Exit Paths}
\begin{table}[t]
\begin{scriptsize}
@@ -865,6 +851,33 @@
\end{table}
+Figure~\ref{fig:as_observe} shows the probability that a single AS will
+be able to observe all of the links along the mix network
+path, for mix network paths of different lengths (paths of length one
+and two have less than two links and, thus, are never observed by the
+same AS twice). Figure~\ref{fig:as_observe_75} shows the probability
+that a single AS will be able to observe at least three-fourths of the
+links along a path of a certain length. The figures show results for
+both the Tor and Mixmaster network topologies, with two different node
+selection schemes: (1)~allowing the same mix node to be used twice along
+the mix path, as long as the same mix node is not used for two
+consecutive hops (``with replacement'', as in {\em remailer networks})
+and (2)~allowing each mix node to be used only once (``without
+replacement'', as in {\em onion routing}). Figure~\ref{fig:as_observe}
+shows two interesting results. First, for all mix paths shorter than
+four hops, a single AS can observe all of of the links on the mix
+network path. Second, Tor's node selection algorithm (i.e., the onion
+routing scheme) provides significant protection against observation at
+multiple links, but this node selection scheme helps Mixmaster less.
+For example, a four-hop onion routing path in Tor will be observed by a
+single AS on every edge with probability 0.06, whereas a four-hop
+remailer path will be observed with probability 0.23. This result makes
+sense: because Tor has only 14 nodes, random node selection is much more
+likely to result in the same hop being used twice along a single mix
+path, if this is not explicitly prevented.
+
+\subsection{Jurisdictional Independence of Entry and Exit Paths}
+
To discover the jurisdictional independence of the entry and exit paths
for typical mix networks, we used the lists of common sender and receiver
locations from Appendix~\ref{sec:send_recv} and modeled typical paths
@@ -997,12 +1010,11 @@
different jurisdictions, we have shown that this technique is not
sufficient to achieve jurisdictional independence.
-\item We analyzed the AS-level path properties of existing mix
- networks and found the likelihood of crossing the same AS more
- than once along a mix network path to be a near certainty. Similarly,
- it is almost always the case
- that a single AS will be able to observe at least
- 75\% of the links along a mix path with more than four hops.
+\item We analyzed the AS-level path properties of existing mix networks
+ and found the likelihood of crossing the same AS more than once along
+ a mix network path to be a near certainty. Mix paths that are shorter
+ than four nodes will almost certainly be observed by a single AS on
+ all links on that path.
\item We have analyzed common entry and exit paths to existing mix
network topologies and shown that, in general, given random entry and
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