[freehaven-cvs] add a bit more about results in cases1..4

[nickm@seul.org (Nick Mathewson)]

Update of /home/freehaven/cvsroot/doc/e2e-traffic
In directory moria.mit.edu:/tmp/cvs-serv24383

Modified Files:
	e2e-traffic.tex 
Log Message:
add a bit more about results in cases1..4

Index: e2e-traffic.tex
===================================================================
RCS file: /home/freehaven/cvsroot/doc/e2e-traffic/e2e-traffic.tex,v
retrieving revision 1.19
retrieving revision 1.20
diff -u -d -r1.19 -r1.20
--- e2e-traffic.tex	23 Jan 2004 18:08:29 -0000	1.19
+++ e2e-traffic.tex	24 Jan 2004 02:39:34 -0000	1.20
@@ -15,6 +15,7 @@
 \newcommand\PMIX{P_{\mbox{\scriptsize MIX}}}
 \newcommand\Pobserve{P_{\mbox{\scriptsize observe}}}
 \newcommand\Ponline{P_{\mbox{\scriptsize online}}}
+\newcommand\Pjunk{P_{\mbox{\scriptsize junk}}}
 \newcommand\V[1]{\overrightarrow{#1}}
 \newcommand\B[1]{\overline{#1}}
 
@@ -748,7 +749,14 @@
 \label{fig1}
 \end{figure}
 
-(Describe results)
+We present the results of our simulations in figure \ref{fig1}.  (We found
+that the time required for the attacker to learn Alice's last few recipients
+was highly variable, especially in later simulations, so we present instead
+the $90^{th}$ percentile of number of rounds required to $m-1$ of Alice's
+recipients, across 100 trials per data point.)  As expected, the attack
+becomes more effective when Alice's sends messages to a brader group of
+recipients (large $m$); when there are fewer recipients for Alice to hide
+hers among (small $N$); or when batch sizes are large (large $b$).
 
 \subsubsection{Complex sender behavior and unknown background traffic}
 % trial2
@@ -803,19 +811,27 @@
 \begin{figure}[ht]
 \centering
 \mbox{\epsfig{angle=0,figure=graphs/fig2a,width=4in}}
-\caption{caption for fig2a}
+\caption{Unknown background ($P_M=.60$): rounds to guess $m-1$ recipients 
+     ($90^{th}$ percentile of trial attacks)}
 \label{fig2a}
 \end{figure}
 
 \begin{figure}[ht]
 \centering
 \mbox{\epsfig{angle=0,figure=graphs/fig2b,width=4in}}
-\caption{caption for fig2b}
+\caption{Unknown background ($P_M=.90$): rounds to guess $m-1$ recipients 
+     ($90^{th}$ percentile of trial attacks)}
 \label{fig2b}
 \end{figure}
 
-
-(Describe results)
+The results are in figures \ref{fig2a} and \ref{fig2b}.  Lines that run off
+the top of the graph represent cases in which the attacks did not converge on
+$m-1$ of Alice's recipients within 1,000,000 rounds.  As expected, the attack
+succeeded fastest against the UU cases for equivalent values of
+$\left<N,m,b>\right>$, followed by BU and BB.  Also, Alice's message volume
+parameter $P_M$ had little effect on the attack for the range examined, other
+than to force the attacker to wait for a greater number of rounds to elapse
+before Alice has sent enought traffic.
 
 \subsubsection{Attacking pool mixes and mix-nets}
 \label{subsec:sim-complex-mixes}
@@ -844,11 +860,21 @@
 \begin{figure}[ht]
 \centering
 \mbox{\epsfig{angle=0,figure=graphs/fig34,width=4in}}
-\caption{caption for fig34}
+\caption{Pool mixes and mix-nets: Rounds to guess $m-1$ recipients 
+         ($90^{th$} percentile of trial attacks)}
 \label{fig34}
 \end{figure}
 
-(Results go here.)
+To examine the effect of pool paramters, we fixed $m$ at $32$ and $N$ at
+$2^16$.  The results of these simulations are presented in figure
+\ref{fig34}.  From this, we note two interesting effects:  first,
+pooling has the most effect when Alice has a very high traffic volume, and is
+only incrementally helpful when Alice has 
+
+
+less effective with intermediary values.  Second, 
+
+
 
 \subsubsection{The impact of dummy traffic}
 \label{subsec:sim-dummies}
@@ -869,7 +895,8 @@
 We evaluated the effectiveness of two padding strategies.  The first
 strategy (`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,
+of dummy messages in each round according to a geometric distribution with
+parameter $\Pjunk$,
 independent of her number of real messages.  With second strategy
 (`imperfect threshold-padding'), we assume that Alice attempts to implement
 the unbreakable threshold-padding strategy (always send $M$ messages total

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