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[freehaven-cvs] more patches throughout
Update of /home/freehaven/cvsroot/doc/e2e-traffic
In directory moria.mit.edu:/home2/arma/work/freehaven/doc/e2e-traffic
Modified Files:
e2e-traffic.tex
Log Message:
more patches throughout
Index: e2e-traffic.tex
===================================================================
RCS file: /home/freehaven/cvsroot/doc/e2e-traffic/e2e-traffic.tex,v
retrieving revision 1.30
retrieving revision 1.31
diff -u -d -r1.30 -r1.31
--- e2e-traffic.tex 25 Jan 2004 11:59:32 -0000 1.30
+++ e2e-traffic.tex 25 Jan 2004 12:23:48 -0000 1.31
@@ -219,8 +219,8 @@
mount a \emph{long-term intersection attack} by correlating the times at
which senders and receivers are active \cite{disad-free-routes}.
-A variety of countermeasures make intersection attacks harder:
-Kesdogan's Stop-and-go mixes
+A variety of countermeasures make intersection attacks harder.
+Kesdogan's stop-and-go mixes
\cite{stop-and-go} provide probabilistic anonymity by letting users
specify message latencies, thereby broadening the range of times
messages might emerge from the mix network. Similarly, batching strategies
@@ -325,9 +325,9 @@
Danezis also derives a precondition that the attack will only succeed when
\( m < \frac{N}{b-1} \), and calculates the expected number of rounds to
-succeed (with $95\%$ confidence for security parameter $\l=2$ and $99\%$
+succeed (with $95\%$ confidence for security parameter $l=2$ and $99\%$
confidence for $l=3$):
-\[t > \left[ ml \left(\sqrt{\frac{m-1}{m}} +
+\[t > \left[ m \cdot l \left(\sqrt{\frac{m-1}{m}} +
\sqrt{\frac{N-1}{N^2}(b-1)} \right) \right]^2 \]
%======================================================================
@@ -380,12 +380,12 @@
$\V{o_i}$ gives us
\[\B{O} = \frac{1}{t}\sum_{i=1}^{t}{\V{o_i}}
\approx
- \frac{\B{m}\V{v} + (b-\B{m})\B{U}}{b}
+ \frac{\B{m} \cdot \V{v} + (b-\B{m})\B{U}}{b}
\mbox{\ where\ } \B{m} = \frac{1}{t}\sum{m_i} \]
From this, the attacker estimates Alice's behavior as
\[\V{v} \approx \frac{1}{\B{m}}
- \left[ b\B{O} - (b-\B{m})\B{U} \right] \]
+ \left[ b \cdot \B{O} - (b-\B{m})\B{U} \right] \]
\subsubsection{Attacking pool mixes and mix networks:}
% \label{subsubsec:complex-mix} can't usefully label subsubsections.
@@ -446,8 +446,8 @@
compute $\B{O_w}$, the mean of the observations from all of these rounds,
weighted by the expected number of messages from Alice exiting in each
round:
-\[ \B{O_w} = \sum_i \sum_{r=0}^k P_R^i(r) m_i \V{o_{i+r}}
- \approx \frac{\B{m}\V{v} + (\B{n}-\B{m})\V{u}}{\B{n}} \]
+\[ \B{O_w} = \sum_i \sum_{r=0}^k P_R^i(r) \cdot m_i \cdot \V{o_{i+r}}
+ \approx \frac{\B{m} \cdot \V{v} + (\B{n}-\B{m})\V{u}}{\B{n}} \]
To solve for Alice's behavior $\V{v}$, the attacker now needs a good estimate
for the background $\V{u}$. The attacker gets this by
@@ -461,7 +461,7 @@
and the attacker can thus solve again for $\V{v}$ in the earlier equation for
$\B{O_w}$, now using
\[\V{u} \approx \frac{1}{1-\delta_a}
- \left[ \B{n} \B{U'} - \delta_a \V{v} \right] \]
+ \left[ \B{n} \cdot \B{U'} - \delta_a \cdot \V{v} \right] \]
Senders can also deviate from the original model
by directing their messages through multi-hop paths
@@ -799,7 +799,7 @@
original statistical disclosure attack as reference. As expected, the attack
succeeds easily, and finishes faster against uniform senders than weighted
senders for equivalent values of $\left<N,m,b\right>$.
-Interestingly, the attack against uniform senders was {\it faster} than the
+Interestingly, the attack against uniform senders is {\it faster} than the
original statistical disclosure attack---because the background traffic is
now clustered about popular recipients, Alice's recipients stand out
more. %than they did before.
@@ -817,20 +817,18 @@
round. We also assume that all senders choose paths of exactly the same
length.
-Unlike in the simulations above, `rounds' are now determined not by a batch
+Unlike earlier, `rounds' are now determined not by a batch
mix receiving a fixed number $b$ of messages, but by the passage of a fixed
interval of time. Thus, the number of messages sent by the background is no
longer a fixed $b-n_a$ (where $n_a$ is the number of messages Alice sends),
but now follows a normal distribution with mean $BG$ (and standard deviation
set arbitrarily to $BG/10$).\footnote{It's hard to determine
- standard deviations for actual message volumes on the currently deployed
- remailer
+ standard deviations for actual message volumes on the deployed remailer
network: automatic reliability checkers that send messages to themselves
- (``pingers'') contribute to a false sense of uniformity, while other users
+ (``pingers'') contribute to a false sense of uniformity, while some users
generate volume spikes by sending enormous fragmented files, or maliciously
- flooding discussion groups and remailer nodes. Neither group blends with
- the bulk
- of the senders on the network.}
+ flooding discussion groups and remailer nodes. Neither group blends
+ well with the other senders.}
\begin{figure}[ht]
\centering
@@ -840,7 +838,7 @@
\end{figure}
To examine the effect of pool parameters, we fixed $m$ at $32$ and $N$ at
-$2^16$, and had Alice use the `uniform' model discussed above. The results
+$2^{16}$, and had Alice use the `uniform' model discussed above. The results
of these simulations are presented in Figure~\ref{fig34}. Lines running off
the top of the graph represent cases in which fewer than half of the attacks
converged upon Alice's recipients within 1,000,000 rounds, and so no median
@@ -851,11 +849,9 @@
input message from Alice, effectively `spreading' each message across several
output rounds. More interestingly, pooling is most effective at especially
high or especially low volumes of traffic from Alice: the `spreading' effect
-here makes it especially hard for the attacker to recognize rounds that
-contain messages from Alice (when she sends less) or to recognize
-rounds that contain more messages (when she sends more).
-% XXX can you explain this better? -NM
-
+here makes it especially hard for the attacker to discern rounds that
+contain messages from Alice when she sends few messages, or to discern
+rounds that don't contain Alice's messages when she sends many messages.
\subsubsection{The impact of dummy traffic:}
%\label{subsec:sim-dummies}
@@ -865,16 +861,15 @@
low-latency systems \cite{defensive-dropping}, little work has been done to
examine their effectiveness against long-term intersection attacks.
-%hm. tense switches between present and past. -rd
-First, we chose to restrict our examination (due to time constraints) to the
+First, we choose to restrict our examination (due to time constraints) to the
effects of dummy messages in several cases of the pool-mix/mix network
simulation
above. Because we are interested in learning how well dummies thwart
-analysis, we chose cases where, in the absence of dummies, the attacker had
+analysis, we choose cases where, in the absence of dummies, the attacker had
little trouble in learning Alice's recipients.
% Are there better citations for these strategies? Are there better names?
-The first passing strategy we evaluated (``independent geometric padding'')
+Our first padding strategy (``independent geometric padding'')
is based on the link padding strategy from the Mixminion design
\cite{minion-design}: Alice generates a random number of dummy messages in
each round according to a geometric distribution with parameter $\Pjunk$,
@@ -902,7 +897,7 @@
Padding slows the attack, but does not necessarily stop it. As shown in
Figure~\ref{fig5a}, geometric padding is most helpful when the underlying
mix network has a higher variability in message delay to `spread' the padding
-between rounds. With lower variability, Alice needs to send far more padding
+between rounds. Otherwise, Alice must send far more padding
messages to confuse the attacker.
We are currently running our simulations on other padding models, including
@@ -915,11 +910,11 @@
Finally, we examine the degree to which a non-global passive adversary can
mount the statistical disclosure attack. Again, we base our simulation on
the mix network simulation where the attacker can only observe a few mixes, and
-try to see whether a non-global observer can do so also.
+see whether a non-global observer can do so also.
% (have we defined 'entry'?) -NM
Clearly, if Alice chooses only from a fixed set of entry and exit mixes as
-suggested by \cite{XXXX}, and the attacker is watching none of
+suggested by \cite{wright03}, and the attacker is watching none of
her chosen mixes, the attack will fail---and conversely, if the attacker is
watching all of her chosen mixes, the attack proceeds as before. For our
simulation, therefore, we assume that all senders (including Alice) choose
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