[freehaven-cvs] More thanks to arma and Ben. Clearer, leaner.

[rabbi@seul.org]

Update of /home2/freehaven/cvsroot/doc/mixmaster-vs-reliable
In directory moria.mit.edu:/tmp/cvs-serv23000

Modified Files:
	mixvreliable.tex 
Log Message:
More thanks to arma and Ben. Clearer, leaner.


Index: mixvreliable.tex
===================================================================
RCS file: /home2/freehaven/cvsroot/doc/mixmaster-vs-reliable/mixvreliable.tex,v
retrieving revision 1.34
retrieving revision 1.35
diff -u -d -r1.34 -r1.35
--- mixvreliable.tex	1 Jul 2004 09:20:47 -0000	1.34
+++ mixvreliable.tex	1 Jul 2004 09:49:50 -0000	1.35
@@ -166,7 +166,15 @@
 should set the delay parameter according to the amount of input traffic it
 is receiving. This feature is not implemented in Reliable, which has a
 static delay parameter. True S-G mixes also implement timestamps in order
-to prevent active attacks ($n-1$ attacks in particular). Reliable cannot
+to prevent active attacks ($n-1$ attacks in particular). Previous work has
+shown that this method may not be effective~\cite{sds}. Regardless, as the
+message protocol was originally designed with only a pool mix network in
+mind, these timestamps are not used, nor is it clear that they could be
+used effectively.
+
+%FIXME
+
+Reliable cannot
 implement this feature given that it interoperates in a network with pool
 mixes, whose delays are unpredictable (these timestamps can only be
 effectively utilized if the whole chain of mixes is S-G and the user is
@@ -175,7 +183,7 @@
 
 In Reliable, the delay may be chosen by the sender from an exponential
 distribution of mean one hour. If the sender does not provide any delay to
-the mix, then the mix itself picks a delay from a uniform distribution of
+the mix, then the mix itself picks a delay from a \em{uniform] distribution of
 one and four hours. Note that these parameters of the delay distributions
 are configurable, and therefore many remailer operators may set them lower
 in order to provide a faster service.
@@ -196,18 +204,18 @@
 the messages flushed by the mix. Dummy traffic has an impact when
 analyzing the mix network as a whole. We have made measurements that
 show that the impact of dummies on the anonymity provided by a single
-mix is very small. In order to make the fair comparison of Mixmaster and
+mix is very small. In order to make the comparison of Mixmaster and
 Reliable easier, we have not taken into account the dummy policies of
 these two mixes in the results presented in this paper. 
 
 \paragraph{Dummy policy of Mixmaster}
-Every time a message is received by Mixmaster, an algorithm runs to
-generate $d_1$ dummies that are inserted in the pool of the mix. The
-number $d_1$ of dummies generated follow a geometrical distribution whose
-parameter has the default value of $1/10$. In addition, every time
-Mixmaster flushes messages, it generates a number $d_2$ of dummies that
-are sent along with the messages. The number $d_2$ of dummies follows a
-geometrical distribution whose parameter has the default value $1/30$.
+Each time a message is received by Mixmaster, $d_1$ dummies are generated
+and inserted in the pool of the mix. The number $d_1$ of dummies generated
+follow a geometrical distribution whose parameter has the default value of
+$1/10$. In addition, each time Mixmaster flushes messages, it generates a
+number $d_2$ of dummies that are sent along with the messages. The number
+$d_2$ of dummies follows a geometrical distribution whose parameter has
+the default value $1/30$.
 
 
 \paragraph{Dummy policy of Reliable}
@@ -242,8 +250,7 @@
 In order to compute the sender anonymity, we want to know the effective
 size of the anonymity set of senders for a message output by the mix.  
 Therefore, we compute the entropy of the probability distribution that
-relates an outgoing message of the mix (the one for which we want to know
-the anonymity set size) with all the possible inputs.
+relates our target outgoing message with all the possible inputs.
 
 \paragraph{Recipient anonymity.}
 If we want to compute the effective recipient anonymity set size of an
@@ -310,8 +317,7 @@
 to the infeasibility of implementing algorithms that compute the
 anonymity for such a delay distribution without making assumptions on
 the traffic pattern, as explained in
-Appendix~\ref{form-reliable}. Moreover, the choice of a uniform delay for
-the messages is completely non-standard.
+Appendix~\ref{form-reliable}. 
 
 The simulators log the delay and the anonymity for every
 message. Mixes are empty at the beginning of the simulation. The
@@ -322,7 +328,7 @@
 the transitory initial and final phases. In our simulations, the
 number of rounds discarded in the initial phase is $3$, and the number
 of rounds discarded in the final phase is $39$. The total number of
-rounds for our input traffic is $11.846$.  
+rounds for our input traffic is $11,846$.  
 
 \section{Results}
 \label{results}
@@ -336,7 +342,7 @@
 It is a common assumption in the literature that the arrivals at a mix
 node follow a Poisson process. We have analyzed the input traffic, and
 found that it does not follow a Poisson distribution nor can it be modeled 
-with one time-independent parameter. 
+with a single time-independent parameter. 
 
 % ADDED (Evelyne)
 A Poisson process is modeled by a single parameter $\lambda$ representing the
@@ -344,7 +350,7 @@
 mix are assumed to follow a Poisson process with an average of $\lambda$ 
 arrivals per time interval $\Delta t$ and we denote the number of arrivals
 in such a time interval by $X$, then $X$ is Poisson distributed with parameter
-$\lambda$: $X \sim \mathrm{Poiss}(\lambda)$. Important to note is that $\lambda$
+$\lambda$: $X \sim \mathrm{Poiss}(\lambda)$. It is important to note that $\lambda$
 is \emph{time-independent}.
 
 In our statistical analysis we first \emph{assumed} that the process of arrivals
@@ -354,7 +360,7 @@
 of arrivals per time interval $\Delta t = 15$ minutes ($N=11800$). We also
 constructed a $95$\% confidence interval for this estimate. In this way we
 found
-$\hat{\lambda} = 19.972$ with confidence region $[19.891 ; 20.052]$.  Then we
+$\hat{\lambda} = 19,972$ with confidence region $[19,891 ; 20,052]$.  Then we
 performed a goodness-of-fit test: can we reject the hypothesis
 \begin{equation*}
 H_0: \mathrm{the\ number\ of\ arrivals\ per\ time\ interval\ } \sim\ \mathrm{Poiss}(\bar\lambda)\ ,
@@ -371,7 +377,7 @@
 arrived to the mix during the first month is much heavier than in the
 following three months. This shows that the input traffic pattern that
 gets to a mix node is highly unpredictable and that the assumption of
-lambda being time-independent cannot be hold.
+lambda being time-independent cannot hold.
 
 Figure~\ref{frec-day} shows the frequency in hours and in days of receiving a
 certain number of arrivals. We can see that in most of the hours 
@@ -710,7 +716,7 @@
 third-party application, Mixmaster 2.0.4.\footnote{Mixmaster 2.0.x is
 derived from an entirely different codebase than that of Mixmaster 3.0.
 While Reliable relies on the Mixmaster 2.0.4 binary for some of its
-functionality, Reliable is a substantive application in its own right, and
+functionality, Reliable is a independent application in its own right, and
 should not be considered a mere extension to the Mixmaster codebase.}
 
 \subsection{Cryptographic functions}

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