[tor-commits] [metrics-tasks/master] Move #2647 report sources to tech-reports.git.

[karsten at torproject.org]

commit a11537717ce46139c9bfc57e0e1b5ffe41489be2
Author: Karsten Loesing <karsten.loesing at gmx.net>
Date:   Tue Aug 7 15:27:04 2012 +0200

    Move #2647 report sources to tech-reports.git.
---
 task-2647/.gitignore           |    4 -
 task-2647/README               |    2 +
 task-2647/bridge-users.pdf     |  981 ----------------
 task-2647/countingusers.tex    | 1044 -----------------
 task-2647/dirbytes-mirrors.pdf | 1114 ------------------
 task-2647/entrystats.pdf       | 1304 ----------------------
 task-2647/estimated-users.pdf  | 1467 ------------------------
 task-2647/newusers.pdf         | 1444 ------------------------
 task-2647/trusted-details.pdf  | 2413 ----------------------------------------
 task-2647/trusted.pdf          |  912 ---------------
 10 files changed, 2 insertions(+), 10683 deletions(-)

diff --git a/task-2647/.gitignore b/task-2647/.gitignore
deleted file mode 100644
index bc423ca..0000000
--- a/task-2647/.gitignore
+++ /dev/null
@@ -1,4 +0,0 @@
-*.aux
-*.log
-countingusers.pdf
-
diff --git a/task-2647/README b/task-2647/README
new file mode 100644
index 0000000..a0dabd5
--- /dev/null
+++ b/task-2647/README
@@ -0,0 +1,2 @@
+The report sources are in tech-reports.git/2010/countingusers/
+
diff --git a/task-2647/bridge-users.pdf b/task-2647/bridge-users.pdf
deleted file mode 100644
index bd6ccc6..0000000
--- a/task-2647/bridge-users.pdf
+++ /dev/null
@@ -1,981 +0,0 @@
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diff --git a/task-2647/countingusers.tex b/task-2647/countingusers.tex
deleted file mode 100644
index c05f2b5..0000000
--- a/task-2647/countingusers.tex
+++ /dev/null
@@ -1,1044 +0,0 @@
-\documentclass{article}
-\usepackage[pdftex]{graphicx}
-\usepackage{graphics}
-\usepackage{color}
-
-\begin{document}
-
-\author{Sebastian Hahn and Karsten Loesing\\{\tt\{sebastian,karsten\}@torproject.org}}
-\title{Privacy-preserving Ways to\\Estimate the Number of Tor Users}
-%Counting Users in the Tor Network in a Privacy-Preserving Way
-\maketitle
-
-\section{Introduction}
-
-The Tor network allows hundreds of thousands of users every day to stay
-anonymous online and enables additional tens of thousands of people in
-oppressed countries to circumvent local censorship.
-At least, these are the orders of magnitude of Tor usage that we assume
-at the time of writing this report.
-Estimating the number of users in an anonymity network is a hard
-problem.
-On the one hand, it's important to learn something about the users of a
-network to improve its service.
-On the other hand, the users of an anonymity network have a high
-demand for privacy, which prohibits collecting sensitive information that
-is necessary to obtain exact usage statistics.
-In this report we describe our approaches to collect aggregated usage
-data and derive user number estimates from them.
-% cite WESCR 2010 paper?
-
-We start with our two current approaches to estimate the number of
-non-censored daily users.
-These approaches are based on counting the number of directory
-requests that clients make to update their network information.
-Clients need to download initial network information from a small fixed
-set of relays, the directory authorities, and refresh their network
-information in regular intervals from a larger changing set of relays, the
-directory mirrors.
-We describe our current approach to estimate the number of new and
-returning users from requests seen at directory authorities in
-Section~\ref{sec:auths} and our estimate of recurring users based on
-requests to directory mirrors in Section~\ref{sec:current}.
-%from one of a few hundred relays that are configured as directory mirrors.
-%We count these requests on a fast directory mirror, which also reports
-%what share of the total requests in the network it thinks it has answered.
-%We project the total number of requests in the network using the
-%self-reported share and divide by the number of requests that each client
-%makes to estimate the total number of users.
-
-In Section~\ref{sec:combine}, we extend our current approach to count
-recurring users by combining reported directory requests from multiple
-directory mirrors.
-%We estimate the fraction of observed requests from the number of bytes
-%that directory mirrors spend on answering directory requests instead of
-%relying on self-reported expected shares.
-The result is a less volatile user number estimate with fewer outliers and
-missing data points.
-
-The previous approaches have in common that they estimate user numbers
-based on the number of directory requests.
-In Section~\ref{sec:entry} we discuss an estimation based on the number of
-unique IP addresses seen on a fast directory mirror.
-Clients open numerous connections to directory mirrors to download
-updated network status information such as new consensuses and
-the relay descriptors therein.
-%There are roughly 2000 relays in the Tor network at the time of writing.
-%Clients need to download the descriptors of all relays, so that they can,
-%in theory, use any relay for building a circuit.
-A quick analysis of the logs of a bootstrapping Tor client reveals that a
-relay that is chosen for 5~\% of all directory requests sees at least
-two-thirds of all client IP addresses.
-% Explain what kind of analysis?
-%
-%As a result, Tor is going to introduce the concept of \emph{directory
-%guards} which makes client select a fixed set of directory mirrors for all
-%requests.
-%But until directory guards are implemented, 
-We can use the number of
-unique IP addresses on a fast directory mirror to estimate the number of
-daily users.
-The presented approach is based on data coming from a single directory
-mirror.
-Combining unique IP addresses from multiple directory mirrors needs to be
-done very carefully and is left for future work.
-
-We sketch a design to introduce a new counting cell type in
-Section~\ref{sec:countingcell}.
-Clients would send counting cells once a day to counting authorities or
-entry guards.
-We discuss the attack potential and possible defenses against adversarial actions.
-% TODO is there a better word than 'trick'?  yes.
-
-In Section~\ref{sec:bridges} we describe our current approach to count
-censored users.
-These users cannot connect to the publicly known relays to download
-directory information or establish circuits.
-Therefore, censored users have to learn about one or more bridge relays
-which behave in a similar manner to normal relays except that they are not listed in
-the public directory.
-%Clients fetch all their directory information and establish all their
-%circuits with a bridge as their first entry point into the Tor network.
-Bridges report the number of unique IP addresses they see every day.
-Our current approach to count censored users is to simply sum up these
-unique IP addresses per day.
-We discuss shortcomings and propose improvements to derive a better
-estimate for censored Tor users.
-
-We conclude with a comparison of the described approaches, identify the
-most promising approaches, recommend possible improvements, and outline
-future work in Section~\ref{sec:conclusion}.
-
-\section{Counting requests on directory authorities}
-\label{sec:auths}
-
-As of mid 2010, we use two approaches to estimate the number of
-non-censored Tor users:
-The first approach captures the number of new or returning users, the
-second approach counts the recurring users.
-This distinction comes from the design of our estimates that are both
-based on Tor's directory protocol.
-
-Whenever a client bootstraps or when its network information becomes
-stale, the client requests a fresh network status, which is a list of all
-currently running relays, from the directories.
-New clients which do not have any directory information pick one of
-a fixed set of hard-coded directory authorities for their request.
-There are currently eight such directory authorities, but the set can be
-changed whenever a new version of the Tor software is released.
-Returning clients with outdated network information take the same
-approach.
-Recurring clients with still recent network information choose a directory
-mirror for their update request.
-The approach for counting new and returning users is described in this
-section, the approach for counting recurring users in the next section.
-
-Seven out of eight directory authorities report the number of directory
-requests they're answering every day.
-When we started estimating new and returning users, only one or two
-directory authorities were reporting these data.
-That is why we weight the requests seen by a single directory authority
-with the expected fraction of requests that the directory authority should
-see.
-In 2009, clients knew about 7 directory authorities of which on average 6
-were running at the same time.
-Hence, we made the assumption that the directory authorities reporting
-request numbers were picked for every sixth request by new and returning
-clients.
-Even though an eighth directory authority has been added in 2010, only
-clients running a recent development version of Tor use this new directory
-authority.
-We therefore stick with our original assumption that a directory authority
-sees 1 out of 6 requests.
-We multiply the reported request number by 6 to obtain an estimate of
-daily new or returning users.
-
-\begin{figure}[t]
-\includegraphics[width=\textwidth]{newusers.pdf}
-\caption{Estimated number of new and returning users}
-\label{fig:newusers}
-\end{figure}
-
-Figure~\ref{fig:newusers} shows the estimated number of new or returning
-users based on the request numbers reported by directory authority
-\texttt{gabelmoo} (black) and the average reported request numbers by all
-directory authorities (gray).
-The estimated user number based on the average of all directory
-authorities is 20 to 25 thousand users higher than the numbers reported
-by \texttt{gabelmoo}, but in general, both estimates are of the same order
-of magnitude.
-The peak in March 2010 results from a single directory authority reporting
-ten times as many requests as the other directory authorities.
-This is probably due to a bug in the Tor code and not an actual increase in
-users.
-The increase in April 2010 can also be explained by bugs in the Tor code
-which led to overloading the network.
-We therefore expect the average number of new or returning users to be
-around 100 thousand.
-
-However, it's difficult to interpret this estimated user number in a
-meaningful way.
-We don't know how many hours per day a typical user is connected to the
-network and after how many hours or days they typically return.
-We are more interested in the total number of users connecting to the
-network at least once a day.
-This question can better be answered by the estimates described below
-which attempt to count the number of recurring users.
-
-\section{Counting requests on directory mirrors}
-\label{sec:current}
-
-Our current approach for estimating (recurring) daily users is based on
-the fact that every client needs to refresh its network information every
-few hours in order to make indistinguishable path selection decisions.
-Clients weight their choice of a directory mirror by the relays' bandwidth
-capacities in order to load-balance requests.
-The idea of this approach is to infer the number of users from the number
-of directory requests on a fast directory mirror and weight them with the
-request share the reporting directory mirrors expects to see.
-
-For our user number estimation, we count the number of network status
-requests on a fast directory mirror.
-We first estimate how many network status requests there are in the
-network by dividing the local request number by the share of requests that
-this particular directory mirror thinks it should see.
-As an approximation of the request share, the directory mirror reports
-the probability of picking itself if it were a client.
-In the second step we estimate the number of users by dividing the global
-network status request numbers by 10 on the assumption that every client
-makes on average 10 requests per day.
-10 is probably a too high number, but one that prevents us from
-over-counting our users.
-% We could derive some statistics from the Torperfs running on moria to
-% support our assumption that 10 is too high.
-
-\begin{equation}
-U_t = \frac{r_t}{s_t \times 10}
-\end{equation}
-
-\begin{center}
-\begin{tabular}{p{0.75cm}p{9cm}}
-$U_t$ & User number estimate based on directory requests to directory
-mirror \texttt{trusted}\\
-$r_t$ & Directory requests to directory mirror \texttt{trusted}\\
-$s_t$ & Share of directory requests expected at directory mirror
-\texttt{trusted}\\
-\end{tabular}
-\end{center}
-
-\begin{figure}[t]
-\includegraphics[width=\textwidth]{trusted.pdf}
-\caption{User number estimate based on directory requests to directory
-mirror \texttt{trusted}}
-\label{fig:trusted}
-\end{figure}
-
-\begin{figure}[t]
-\includegraphics[width=\textwidth]{trusted-details.pdf}
-\caption{Directory requests, shares, and user number estimate, based on
-directory requests to directory mirror \texttt{trusted}}
-\label{fig:trusted-details}
-\end{figure}
-
-Figure~\ref{fig:trusted} shows the daily user number estimate based on
-directory requests to the fast directory mirror \texttt{trusted}.
-Evidently, this estimate is flawed by having outliers and lots of missing
-values.
-Some of these problems can be explained when looking at the input data.
-Figure~\ref{fig:trusted-details} shows the directory requests $r_t$ and
-expected share of requests $s_t$ as well as the estimated user number
-$U_t$.
-From these two graphs we can make a few observations:
-
-\begin{itemize}
-\item The peaks in May 2010 and later with 1.2 million and 800
-thousand daily users (marked with gray circles) are probably not accurate user
-numbers, but more likely measurement errors.
-These data points result from directory request shares being slightly
-higher than 1~\%.
-(Data points with directory request shares of 1~\% or less are excluded
-anyway; if these data points were included, there would have been even
-more outliers with millions of users which are unlikely real.)
-Raising the bar to 1.5~\% would eliminate these outliers, but would also
-remove a lot of, apparently correct, data points.
-\item In September 2009 (first dashed line), user numbers increased from
-roughly 150 to 250 thousand, and volatility of user numbers increased by
-factor 2 to 3.
-While the request numbers remain more or less stable during this time,
-the expected share of requests seen by \texttt{trusted} drops from 3.5~\%
-to 2~\%.
-The reason for this decrease is that more recent clients started weighting
-relays by active bandwidth scanner results instead of the relays'
-self-reported bandwidth claims.
-However, \texttt{trusted} assumes that all clients use the bandwidth
-scanner results for path selection which is not the case.
-\item Beginning in June 2010 (second dashed line), shares drop to zero for
-about a month, stabilize at around 1.5~\% for two months and then
-oscillate between 0 and 9~\%.
-The reason for this behavior is the introduction of consensus weights that further help
-clients to make good path selection decisions.
-Again, \texttt{trusted} bases its expected request share on the
-assumption that all clients use consensus weights for their path selection
-decisions which is wrong.
-\end{itemize}
-
-In summary, the major problem with the described approach is the
-approximation of the request share that a directory mirror expects to see.
-The various deployed Tor versions all use different weights for picking a
-directory mirror:
-Clients running Tor version 0.2.0.x use the relays' self-advertised
-bandwidths to decide which directory mirror to pick.
-Clients on version 0.2.1.x use actively measured bandwidths from four
-bandwidth scanners running on the authoritative directory servers for
-their choice.
-Clients running version 0.2.2.x base their decision on the measured
-bandwidths, but weighted by network-wide factors depending on the assigned
-relay flags of a directory mirror.
-The shares reported by directory mirror \texttt{trusted} reflect a
-situation in which all clients run the same Tor version as
-\texttt{trusted} at the given time, which is not the case.
-While we could calculate shares independent of \texttt{trusted}, we have
-no reliable data about the fractions of running client versions and could
-therefore not weight the calculated version-specific request shares.
-In the next section we discuss an approach to combine the findings of
-multiple directory mirrors and replace the expected request share by a
-more reliable metric.
-
-% It might also be problematic that relays update their advertised
-% bandwidth only every 18 hours when publishing a new descriptor.
-% Likewise, bandwidth scanners scan a relay only every so often. There
-% may be significant changes from one bandwidth value to the next, but
-% clients take a few hours to notice that change. More research would be
-% necessary, but we already know the approach is broken, so might as well
-% not care.
-
-The second problem with the described approach is that the estimated user
-number is less precise the fewer requests a directory mirror sees.
-When we started estimating user numbers based on directory mirror
-\texttt{trusted}, it reported shares of roughly 3.5~\% of all requests in
-the network.
-With the introduction of the various performance improvements and with the
-recent increase in fast directory mirrors, this share has decreased to
-1.5~\%.
-As we can see, estimations based on a fraction of observations this small
-are not very reliable.
-
-The third problem is that we can only guess that a client makes 10 network
-status requests per day.
-While this assumption may work for clients which are connected to the Tor
-network all day, other clients may well send fewer requests than 10.
-We do not have any data about the average hours of Tor usage per day to
-come up with a better number than 10 requests.
-If, for example, the real number of requests per client was 5, our
-estimate would be off by a factor 2.
-The good news is that, while being off by an unknown factor, we're off by
-that factor all the time, so that comparisons over time are still
-accurate.
-
-% Idea for implementing directory guards: With all relays caching
-% directory information, instead of building circuits to directories
-% *using* directory guards, clients could simply ask their directory
-% guards for whatever directory information they want to know.
-
-\section{Combining requests to directory mirrors}
-\label{sec:combine}
-
-%\paragraph{Summing up requests and shares}
-%
-%The first new approach combines directory requests simply by summing up
-%requests and shares of all directory mirrors reporting these numbers.
-%While \texttt{trusted} was the only fast directory mirror reporting
-%directory requests for about a year, a couple of even faster relays
-%started reporting these numbers in August 2010.
-%
-%\begin{equation}
-%U_s = \frac{r}{s \times 10}
-%\end{equation}
-%
-%\begin{center}
-%\begin{tabular}{p{1cm}p{9cm}}
-%$U_s$ & User estimate based on sums of all directory requests and shares\\
-%$r$ & Directory requests to all reporting directory mirrors\\
-%$s$ & Share of directory requests expected at all reporting directory
-%mirrors\\
-%\end{tabular}
-%\end{center}
-%
-%\begin{figure}[t]
-%\includegraphics[width=\textwidth]{share.png}
-%\caption{Directory requests, shares and user number estimate based on
-%directory requests by all reporting directory mirrors (black), compared
-%to \texttt{trusted} only (gray)}
-%\label{fig:share}
-%\end{figure}
-%
-%Figure~\ref{fig:share} shows the total requests, shares, and estimated
-%users based on all reporting directory mirrors.
-%The total request numbers and reported shares exceed those of
-%\texttt{trusted} in May 2010 and from August 2010 on.
-%The resulting user number estimate is similar to the current approach
-%until May 2010, because \texttt{trusted} was reporting most of the
-%requests during that time anyway.
-%Beginning in May 2010, the combined numbers have by far fewer missing
-%data points, because it's easier to reach shares of 1~\% or higher with
-%multiple data source.
-%At the same time, the estimated user numbers are lower when combining all
-%available data sources.
-%
-%The results of this new approach are still not satisfactory.
-%In particular the estimates of about 1 million users in May 2010 and later
-%are hardly correct.
-%In addition to that, it's unlikely that the reporting directory mirrors
-%saw up to 80~\% of all requests in September and October 2010.
-%In the two approaches below we drop the self-reported expected directory
-%request shares completely and use different metrics to answer what
-%fraction of directory requests have been reported on a given day.
-%
-%\paragraph{Estimating total requests using bandwidth histories}
-%
-%The second new approach to combine directory requests makes use of
-%bandwidth histories to estimate what fraction of directory requests has
-%been reported.
-%Rather than resembling clients' decisions for selecting relays (which can
-%be difficult with the different deployed path selection strategies), we
-%use the bandwidth histories reported by relays to estimate what fraction
-%of directory requests they have seen.
-%If all directory mirrors reporting directory requests together have
-%pushed $b_{pr}$ bytes and all directory mirrors, whether or not they
-%report directory requests, have pushed $b_p$ bytes, we expect that in the
-%whole network, there have been $\frac{b_p}{b_{pr}}$ as many directory
-%requests as we have seen.
-%The underlying assumption is that the directory mirrors reporting
-%directory requests spend the same fraction of bytes on answering directory
-%requests as all directory mirrors.
-%
-%\begin{equation}
-%U_p = r \times \frac{b_p}{b_{pr} \times 10}
-%\end{equation}
-%
-%\begin{center}
-%\begin{tabular}{p{1cm}p{9cm}}
-%$U_p$ & User estimate based on directory requests to all reporting
-%directory mirrors, weighted by bandwidth histories\\
-%$r$ & Directory requests answered by all reporting directory mirrors\\
-%$b_p$ & Written and read bytes by all directory mirrors\\
-%$b_{pr}$ & Written and read bytes by directory mirrors that report
-%directory requests\\
-%\end{tabular}
-%\end{center}
-%
-%\begin{figure}[t]
-%\includegraphics[width=\textwidth]{bwhist.png}
-%\caption{Directory requests, shares and user number estimate based on
-%directory requests weighted by bandwidth histories}
-%\label{fig:bwhist}
-%\end{figure}
-%
-%Figure~\ref{fig:bwhist} shows the estimated users based on directory
-%requests weighted by written and read bytes of reporting directory mirrors
-%compared to all directory mirrors.
-%The user number estimate is less volatile than the previous two estimates
-%and has no outliers in the millions.
-%There are also only very few missing data points, because the share is
-%above 1~\% most of the time.
-%
-%However, the range of 50 to 500 thousand daily users is still higher than
-%expected.
-%It might be that the assumption that directory mirrors reporting directory
-%requests spend the same fraction of bytes on answering directory requests
-%as all directory mirrors is inaccurate.
-%We hope that this assumption becomes less important with an even higher
-%number of directory mirrors reporting directory requests in the future.
-
-The major shortcomings of the approach described in the previous section
-are very low request shares of 1.5~\% or less and the difficulty to
-accurately estimate shares of directory requests seen at directory mirrors.
-In this section we discuss a new approach to overcome these two problems.
-The presented approach combines the reported directory request numbers
-from multiple directory mirrors and uses the relays' bandwidth histories
-to determine what fraction of the total requests in the network have been
-reported.
-
-This new approach utilizes a recently introduced metric: bytes spent on
-answering directory requests.
-Directory mirrors running Tor version 0.2.2.15-alpha or higher report
-how many bytes they spent on answering directory requests in addition to
-the number of bytes they spent on all traffic.
-By looking at the relay descriptor archives, we can estimate the number of
-directory bytes written on a give day by both the relays reporting directory requests and all
-directory mirrors (including those that did not report directory requests).
-
-As a first step we estimate the number of directory bytes written by
-directory mirrors.
-Only a fraction of the directory mirrors are running Tor version
-0.2.2.15-alpha or higher, which is why we have to extrapolate the number
-of directory bytes from the reported number.
-For the first estimation we assume that every directory mirror spends the
-same fraction of its total bytes on answering directory requests.
-Hence, the reported number of directory bytes constitute a fraction of
-total directory bytes in the network that is equal to the number of bytes
-written by directory mirrors reporting directory bytes divided by the
-number of bytes written by all directory mirrors.
-%
-%\begin{equation}
-%d_p = \frac{d \times b_p}{b_d}
-%\end{equation}
-%
-%\begin{center}
-%\begin{tabular}{p{1cm}p{9cm}}
-%$d_p$ & Estimated directory bytes\\
-%$d$ & Reported directory bytes\\
-%$b_p$ & Reported written bytes by all directory mirrors\\
-%$b_d$ & Reported written bytes by directory mirrors reporting directory
-%bytes\\
-%\end{tabular}
-%\end{center}
-
-For the second estimation we assume that the difference between total
-written and total read bytes on directory mirrors is to a large extent the
-result of answering small directory requests with large directory objects.
-We observed that relays that don't mirror the directory write more bytes
-than they read, too, but the difference between written and read bytes is
-much smaller than on directory mirrors.
-We weight the bytes written by directory mirrors with the quotient of
-read and written bytes on relays that don't mirror the directory in order
-to account for non-directory related factors.
-We then subtract the number of bytes read by directory mirrors and obtain
-an estimate of directory bytes written by directory mirrors.
-
-\begin{figure}[t]
-\includegraphics[width=\textwidth]{dirbytes-mirrors.pdf}
-\caption{Estimated directory bytes written by directory mirrors based on
-the extrapolation of reported directory bytes (gray) and the difference
-between written and read bytes (black)}
-\label{fig:dirbytes-mirrors}
-\end{figure}
-
-Figure~\ref{fig:dirbytes-mirrors} shows the two directory bytes
-estimations.
-Until mid-September 2010, the extrapolation of reported directory bytes
-(gray) is slightly higher than the difference between written and read
-bytes (black), but both estimates are of the same order of magnitude.
-The difference of up to 4~MiB/s is not much when comparing it to the total
-number of bytes written by directory mirrors, which is 300~MiB/s at the
-time of writing.
-With only three months of data, it is unclear which of the two estimates
-is more accurate.
-For the following analysis we use the difference between written and read
-bytes as estimate for directory bytes, because these numbers are available
-for the past 1.5 years.
-Once we have a larger fraction of directory mirrors reporting directory
-bytes we are going to revisit and possibly adjust this estimate.
-
-Now that we have an estimate of directory bytes written by all directory
-mirrors and by the directory mirrors reporting directory requests, we can
-extrapolate the number of observed directory requests to learn the total
-number of directory requests in the network.
-We assume that directory mirrors reporting directory requests spend the
-same fraction of directory bytes on answering directory requests as all
-directory mirrors.
-
-\begin{equation}
-U_d = \frac{r \times (b^w_p \times \frac{b^r_n}{b^w_n} - b^r_p)}{(b^w_{pr} \times \frac{b^r_n}{b^w_n} - b^r_{pr}) \times 10}
-\end{equation}
-
-\begin{center}
-\begin{tabular}{p{0.75cm}p{9cm}}
-$U_d$ & User number estimate based on multiple directory mirrors reporting
-directory requests\\
-$r$ & Reported directory requests\\
-$b^w_p$ & Total bytes written by all directory mirrors\\
-$b^r_p$ & Total bytes read by all directory mirrors\\
-$b^w_n$ & Total bytes written by all relays that don't mirror the
-directory\\
-$b^r_n$ & Total bytes read by all relays that don't mirror the directory\\
-$b^w_{pr}$ & Total bytes written by all directory mirrors reporting
-directory requests\\
-$b^r_{pr}$ & Total bytes read by all directory mirrors reporting directory
-requests\\
-\end{tabular}
-\end{center}
-
-\begin{figure}[t]
-\includegraphics[width=\textwidth]{estimated-users.pdf}
-\caption{User number estimate based on all reported directory requests
-weighted by estimated written directory bytes (black) compared to the
-current approach based on directory requests to directory mirror
-\texttt{trusted} (gray)}
-\label{fig:estimated-users}
-\end{figure}
-
-Figure~\ref{fig:estimated-users} shows the new user number estimate
-(black) and compares it to the current approach (gray).
-The new user number estimate is less volatile and has no outliers in the
-millions.
-There are also no missing data points anymore, because the combined
-directory requests originate from a fraction of directory mirrors that is
-greater than 1~\% in the observed time interval.
-
-%We recommend to increase the fraction of directory mirrors reporting
-%directory requests to have a more solid data basis.
-%Possible next steps are to ask relay operators running fast and stable
-%relays to collect and report these aggregate statistics.
-%Further, the configuration option for reporting directory requests could
-%be set by default for all relays.
-%Once we have more data, we are going to revisit this approach and maybe
-%fine-tune it.
-
-%\paragraph{Projecting requests using read/written directory bytes}
-%
-%We need to learn two data points to calculate what fraction of directory
-%bytes the directory mirrors reporting directory requests have pushed.
-%First, we need to calculate the number of directory bytes that all
-%directory mirrors in the network pushed.
-%
-%\begin{verbatim}
-%We need to find out what fraction of dirreqs are reported to us.
-%We assume that the number of dirreqs that a relay answers scales
-%proportionally to the number of dirbytes that the relay pushes, i.e., a
-%relay that pushes 10 % of all dirbytes also answers 10 % of all dirreqs.
-%We need to learn two things in order to answer this question:
-%First, how many dirbytes did all relays in the network push?
-%Second, how many dirbytes did the relays that report dirreqs push?
-%
-%We'll start by answering the first subproblem.
-%We'd like to learn how many dirbytes were read/written in the network,
-%but not all relays report dirbytes.
-%Therefore, we weight the reported dirbytes with the fraction of total
-%(non-dir) bytes that the relays reporting dirbytes pushed as compared to
-%all pushed bytes.
-%In order to answer the first question, we count:
-%
-%b: total reported bytes
-%d: total reported dirbytes
-%b_d: bytes reported by relays reporting dirbytes
-%
-%We then can estimate the total number of dirbytes.
-%
-%D = d * b / b_d
-%D: total estimated dirbytes
-%
-%<dirbytes-total.png>
-%
-%We need to make sure that enough relays report dirbytes, or our
-%extrapolation is based on too few data points.
-%The fraction of bytes reported by relays that report dirbytes shouldn't
-%
-%drop below, say, 15 %.
-%The graph only shows data for the fraction being 15 % or higher.
-%
-%f_bd = b_d / b
-%f_bd: fraction of bytes reported by relays that report dirbytes
-%
-%The second sub problem to solve is to find out how many dirbytes have been
-%pushed by the relays that report dirreqs.
-%We again use the non-dir bytes that are reported by all relays for the
-%extrapolation.
-%We count:
-%
-%d_r:  dirbytes reported by relays reporting dirreqs
-%b_r:  bytes reported by relays reporting dirreqs
-%b_dr: bytes reported by relays reporting dirbytes and dirreqs
-%
-%We can then estimate the number of dirbytes being pushed by all relays
-%reporting dirreqs.
-%
-%D_r = d_r * b_r / b_dr
-%D_r: total estimated dirbytes reported by relays reporting dirreqs
-%
-%<dirbytes-part.png>
-%
-%Finally, we can estimate the total number of dirreqs by using the two
-%estimates calculated above.
-%
-%R = r * D / D_r = r * (d * b / b_d) / (d_r * b_r / b_dr)
-%R: total estimated dirreqs, different approaches
-%
-%Finally assume that each user makes 10 requests per day:
-%U = R / 10
-%U: total estimate daily users
-%
-%\end{verbatim}
-
-\section{Counting IP addresses at directory mirrors}
-\label{sec:entry}
-
-An alternative approach to count daily users is to count unique IP
-addresses on a relay that sees most of the clients at least once a day.
-A fast directory mirror is such a relay.
-Clients open numerous connections to directory mirrors, in addition to
-downloading network statuses, to download relay descriptors.
-The Tor network consists of roughly 2000 relays at the time of writing,
-and clients attempt to download all relay descriptors, so that they can
-build circuits with any of these relays.
-Clients split downloads among directory mirrors, because requests cannot
-contain more than 96 relay descriptor identifiers.
-
-A quick analysis shows that an always running Tor client sends out on
-average 80 requests for relay descriptors per day.
-The probability of a fast directory mirror, say, one that is chosen for
-5~\% of all directory requests, to be contacted at least once a day is
-$1-0.95^{80} = 98.3\%$.
-Even a client that only connects to the network for a few minutes per day
-downloads all current descriptors which takes at least
-$\lceil2000 / 96\rceil = 21$ requests.
-The probability of such a client contacting a directory mirror that sees
-5~\% of all requests is $1-0.95^{21} = 65.9\%$.
-
-In the near future, Tor is going to introduce \emph{directory guards}.
-The idea is that clients pick a small number of relays as their directory
-guards and send all directory requests to them.
-This is meant to prevent a single malicious directory mirror from learning
-about many client IP addresses.
-But until directory guards are implemented, we can use the number of
-unique IP addresses observed on a fast directory mirror to estimate the
-number of daily users.
-
-\begin{figure}[t]
-\includegraphics[width=\textwidth]{entrystats.pdf}
-\caption{User number estimates based on unique IP addresses reported by
-the fast directory mirror \texttt{trusted} (black) and two other fast
-directory mirrors}
-\label{fig:entrystats}
-\end{figure}
-
-Figure~\ref{fig:entrystats} shows the user number estimates
-based on unique IP addresses seen on three fast directory mirrors.
-The fast directory mirror {\tt trusted} reports the highest number of
-unique IP addresses of all three directory mirrors.
-There are two time intervals when two or all three directory mirrors
-report similar numbers: from December 2009 to January 2010 and from late
-April to early May 2010.
-The fact that the directory mirrors report similar numbers during those
-times is an indication that they all saw the majority of clients in the
-network.
-We therefore believe that the user number estimates of 150 to 250 thousand
-daily users are accurate and pose a realistic upper bound of the real
-number of daily Tor users.
-These estimates are also of the same order of magnitude as the estimates
-described in the previous section.
-
-The major shortcoming of the described approach is that there is no simple
-way to combine reported unique IP addresses of two or more directory
-mirrors.
-Directory mirrors keep the observed client IP addresses in memory for at
-most 24 hours, report the absolute number of distinct addresses, and
-discard the IP addresses.
-It may be possible to exchange data structures containing IP addresses
-between directory mirrors in a privacy-preserving way and combine them to
-learn about the union size of unique IP address sets.
-Possible approaches might be based on private set intersection techniques
-or probabilistic data structures like Bloom filters.
-We leave these approaches as future work.
-
-\section{Introducing a counting cell}
-\label{sec:countingcell}
-
-Another approach is to introduce a new cell type to the Tor protocol; the counting cell.
-This approach doesn't estimate user numbers by counting directory
-requests or unique IP addresses.
-Under this approach, clients would send counting cells once per day to special relays, called
-counting authorities.
-
-\subsection{Counting cell overview}
-The most important statistic for Tor's user count is the number of daily
-users.
-Our other metrics are passive observations by certain routers,
-whereas the counting cell would be an active approach.
-Tor clients would send a notification of their presence once daily, so that
-the presence notifications can be added together to get the user count.
-Tor has a notion of different cell types to encapsulate different information
-when sending it along a circuit.
-A new type of cell can easily be created to transport presence information.
-This presence information is then reported to the metrics engine and
-aggregated to find the actual user count for one day.
-
-Two different approaches are examined here:
-The first approach uses Tor's directory authorities as counting authorities.
-Clients report their presence via an anonymized tunnel.
-Picking guard nodes as counting authorities is the other possibility.
-Clients would not need to create a special circuit and can instead just use
-one of their regular circuits to send the counting cell to the first hop directly.
-
-Some general considerations are valid for both types:
-Counting authorities have to be very stable and well-connected so that
-clients can report their presence reliably.
-The counting authorities also need to export the data they received in
-some document that can be collected by the metrics engine to analyze and
-present the statistics.
-Tor already has an extra-info descriptor mechanism in place that can be
-used.
-
-\subsection{Using directory authorities as counting authorities}
-Directory authorities have the same requirements as outlined above:
-They need to be very stable, because everyone relies on them to
-generate and sign the consensus.
-They also already export their votes which get collected by the metrics
-engine.
-
-Two options are available for how clients report their presence to these
-counting authorities; they can either send a counting cell to each of
-them or pick one at random.
-Both approaches have advantages and drawbacks, outlined below:
-
-Sending the cell to all authorities might raise a scalability
-problem as a single counting authority might not be able to keep
-up with the load if all clients make one connection per day to report
-their presence.
-In a network with 250,000 users, an average of almost 3 reports per
-second is to be expected.
-In reality, since Tor's user base isn't distributed among timezones
-equally, much higher report rates per second are to be anticipated.
-The load this induces on each directory authorities should be carefully
-examined, because it will increase proportional to an increase in the
-user base.
-
-The advantage of reporting presence to all counting authorities is that
-if a single report fails, the others can still count the user.
-If any of the counting authorities reports a much lower value than
-the others for a specific day, it can be taken out of the statistics
-aggregating process for that day or until the connectivity problems
-are resolved.
-
-Sending a counting cell to just one counting authority increases the
-scalability of the system, as new counting authorities
-could easily be added once the others are becoming overloaded.
-Another advantage is that the user doesn't have to create one circuit
-per counting authority, but rather just one per day.
-This means that a user who doesn't use Tor for very long on a certain
-day can still be counted correctly, even if she wouldn't have had the
-time to report her presence to all authorities.
-
-
-Data loss or other malfunctions on one of the counting authorities
-poses a major problem in this scheme.
-Such data loss cannot be corrected, and statistics for the time period
-will be inaccurate.
-
-\paragraph{Abuse potential and inaccuracies}
-
-In a system where cells are reported to all counting authorities,
-there is no strong protection against a counting authority that
-increases the count of users by reporting a higher number of users by
-just sending counting cells to the other authorities.
-It would, however, prevent an authority from under-reporting the number
-of users, because the others will report a higher user count so that
-the data from the dishonest authority can be discarded by the statistics
-aggregator.
-
-When users report their presence to only one counting authority, this
-counting authority can under-report the number of users,
-because under-reporting cannot be distinguished from being unavailable
-for a part of the day.
-It is also possible to increase the count of users even without sending
-counting cells to the other counting authorities.
-Detection of such behavior is very difficult, as lower numbers can
-always be explained to be due to network problems at the counting
-authority; and only very unusually high numbers would indicate increasing
-the number of users maliciously.
-
-It is trivial to arbitrarily increase the count of users by sending on
-average more than one counting cell per 24 hour window.
-Because counting cells are anonymized, there are no special resources
-necessary to execute the attack, other than the ability to make circuits
-to the counting authorities.
-This attack needs to be continued for as long as the user count is to be
-influenced.
-When the attack is stopped, the result will be an apparent loss of Tor
-users.
-
-When the scheme is newly deployed or when alternative
-implementations of Tor clients that don't include counting cells are
-introduced, the number of Tor users will be undercounted.
-Both cases have to be taken into consideration when evaluating the
-collected data.
-
-\paragraph{Possibility for additional statistics}
-Because clients report their presence anonymously under the counting cell scheme, additional statistics
-can be gathered using this approach.
-
-Example statistics are client version and the uptime since the last
-cell was sent.
-%
-While adding additional statistics, care must be taken that the anonymity
-set is still sufficiently large.
-For the client version, we could report the accurate version while it is
-still recommended or ``outdated'' as a catch-all for older versions.
-%
-For the uptime since the last cell was sent, reporting uptime in half-hour
-time intervals could provide proficient accuracy.
-
-More work is necessary to evaluate the additional risks of adding more
-statistics.
-If these statistics are deemed important, they can
-use the same infrastructure set up for user number estimation.
-Directory authorities are expected to be upgraded quickly, so the
-new statistics would become available as soon as enough clients
-upgrade.
-
-
-\subsection{Using entry guards as counting authorities}
-To address the scalability concerns outlined above, an alternative approach
-is to use the entry guards that a client connects to anyway.
-Not reporting presence information via an anonymized channel to one
-of the chosen guard nodes has the advantage of being more scalable
-than either proposed system.
-The entry guards can keep track of which IP addresses have already
-reported presence information on a given day and refuse
-to accept another counting cell.
-Also, availability concerns are reduced because a given entry guard
-will see fewer counting cells compared to a counting authority.
-
-Guards that support acting as counting authorities and choose to do so
-should be marked as such in the consensus by a special flag
-so that clients can see which relays are acting as counting authorities.
-
-\paragraph{Abuse potential and inaccuracies}
-Using entry guards as counting authorities gives them the same
-abuse abilities as directory authorities have in the system where
-presence information is reported to one of them; but it could be easier
-to filter out extreme values as the reported values are expected to
-be generally lower.
-
-The directory authorities should make sure that enough guards exist
-so that over and undercounting guards can be detected and excluded
-by the metrics engine.
-
-\paragraph{Possibility for additional statistics}
-Because guards know who is connecting to them, there is more concern
-when adding additional statistics compared to the directory authority
-approach.
-By including additional information about their presence, Tor clients add
-bits of information that can help identify them across IP address changes.
-This must be prevented, so additional statistics can not be implemented
-when using guard nodes without further analysis showing their safety.
-
-\subsection{Usefulness of counting cells}
-Because of the presented attacks, counting cells are likely to be useful
-in addition to other user number estimation schemes only.
-They can, however, provide an easy way to evaluate trends and
-might allow new statistics to be gathered.
-
-\section{Counting IP addresses at bridges}
-\label{sec:bridges}
-
-As a special case of counting Tor users, we are interested in the number
-of censored Tor users connecting via bridges.
-Censored users cannot connect to the publicly known relays to download
-directory information or establish circuits.
-Censored users have to learn about one or more bridge relays which are
-similar to normal relays except that they are not listed in the public
-directory and are therefore harder to block.
-Bridge clients fetch all their directory information and establish all
-their circuits with a bridge as first entry point into the Tor network.
-Bridges report the number of unique IP addresses they see every day.
-Our current approach to count censored users is to simply sum up these
-unique IP addresses per day and interpret the result as estimated user
-number.
-
-\begin{figure}
-\includegraphics[width=\textwidth]{bridge-users.pdf}
-\caption{Estimated number of users connecting via bridges}
-\label{fig:bridge-users}
-\end{figure}
-
-Figure~\ref{fig:bridge-users} shows the estimated number of users
-connecting via bridges.
-These numbers are not expected to be as stable as the number of directly
-connecting users, because some countries have successfully blocked relays or
-even bridges in the past, which has led to sudden increases or decreases in
-bridge user numbers.
-
-There are some shortcomings with this approach to count bridge users.
-First, the approach makes the assumption that bridge users only connect to
-a single bridge every day which is not necessarily the case.
-As a result we may over-count bridge clients connecting to two or more
-bridges.
-
-The second shortcoming is that we're excluding between 15 and 50~\% of
-bridges from the statistics for various reasons:
-bridges with fewer than 24 hours uptime are excluded, because bridges only
-report statistics every 24 hours to hide the exact connection times and
-protect the bridge users' privacy;
-bridges that have been running as a non-bridge relay are excluded, because
-they might report non-bridge users;
-bridges without a GeoIP database are excluded, because they don't report
-any statistics about connecting clients;
-bridges running a few early versions of the 0.2.2 series are excluded,
-because they had a bug in reporting bridge user statistics;
-finally, an unknown number of bridges is excluded, because bridge
-operators decide not to publish their bridge to the bridge authority and
-circulate the bridge address to bridge users themselves.
-
-In the future, we might count the number of directory requests to bridges
-in the same way as we do on directory mirrors.
-Bridge clients need to refresh their view of the network at regular
-intervals, too.
-So, it should be possible to count bridge users in the same way as we
-estimate directly connecting users.
-
-\section{Conclusion}
-\label{sec:conclusion}
-
-In this report we described our current approaches to estimate daily Tor
-users based on counting directory requests and unique IP addresses, and we
-sketched a design to introduce special counting cells for this purpose.
-We conclude with a brief summary.
-
-In Section~\ref{sec:auths} we discussed our current approaches for
-counting new and returning as well as recurring users based on counting
-directory requests.
-We found that it is hard to interpret the estimate of new and returning
-users without knowing how many hours per day our users are connected and
-after how many hours or days they return.
-We suggest discontinuance of this statistic because the rather
-technical distinction between new/returning and recurring users is not
-obvious.
-
-We described our approach to estimate recurring users based on directory
-requests reported by directory mirror \texttt{trusted} in
-Section~\ref{sec:current}.
-We are facing two major problems with this approach, namely approximating
-the request share that \texttt{trusted} can expect to see and the decrease
-of said share over the past 12 months.
-We recommend discontinuance of this statistic as well and recommend replacing it with a
-statistic based on directory requests reported by multiple directory
-mirrors.
-
-In Section~\ref{sec:combine} we described such an approach to combine the
-directory requests from multiple directory mirrors.
-This approach is based on the estimated number of directory bytes written
-by directory mirrors.
-We hope to gather more data from directory mirrors to improve this
-promising approach.
-Once we have confirmed its correctness, we propose to replace the current
-two approaches to estimate direct users with this approach.
-
-We presented results from counting unique IP addresses on fast directory
-mirrors in Section~\ref{sec:entry}.
-These results are interesting, because they allow us to determine an upper
-bound of daily users.
-However, we did not find a simple way to combine reported unique IP
-addresses of two or more directory mirrors in a privacy-preserving way.
-Once the directory guard design is implemented, this approach won't
-deliver useful estimates anymore.
-We leave this problem as future work.
-
-In Section~\ref{sec:countingcell} we sketched a new design to introduce
-counting cells that clients would send once a day to counting authorities
-or entry guards.
-Such an approach would allow us to gather better statistics about clients.
-However, more work is needed to reduce the potential for abuse.
-
-Finally, in Section~\ref{sec:bridges} we described our current approach to
-count censored users.
-This statistic is based on the sum of unique IP addresses observed on
-bridges with at least 24 hours uptime.
-We suggest extending the statistics on bridges to count directory
-requests.
-We could then try to estimate the number of censored users by weighting
-the observations with the bridges' reported bandwidth.
-Again, we leave this extension as future work.
-
-\end{document}
-
diff --git a/task-2647/dirbytes-mirrors.pdf b/task-2647/dirbytes-mirrors.pdf
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