[tor-commits] [tech-reports/master] Add raw countingusers report from 2010.

commit 0fb2583669f06d74540e183baaf1cf0333aff0ec Author: Karsten Loesing karsten.loesing@gmx.net Date: Tue Aug 7 15:27:41 2012 +0200

Add raw countingusers report from 2010. --- 2010/countingusers/.gitignore | 3 + 2010/countingusers/bridge-users.pdf | 981 +++++++++++++ 2010/countingusers/countingusers.tex | 1044 +++++++++++++ 2010/countingusers/dirbytes-mirrors.pdf | 1114 ++++++++++++++ 2010/countingusers/entrystats.pdf | 1304 +++++++++++++++++ 2010/countingusers/estimated-users.pdf | 1467 +++++++++++++++++++ 2010/countingusers/newusers.pdf | 1444 ++++++++++++++++++ 2010/countingusers/trusted-details.pdf | 2413 +++++++++++++++++++++++++++++++ 2010/countingusers/trusted.pdf | 912 ++++++++++++ 9 files changed, 10682 insertions(+), 0 deletions(-)

diff --git a/2010/countingusers/.gitignore b/2010/countingusers/.gitignore new file mode 100644 index 0000000..6a1f279 --- /dev/null +++ b/2010/countingusers/.gitignore @@ -0,0 +1,3 @@ +countingusers.pdf +countingusers-2010-11-30.pdf + diff --git a/2010/countingusers/bridge-users.pdf b/2010/countingusers/bridge-users.pdf new file mode 100644 index 0000000..bd6ccc6 --- /dev/null +++ b/2010/countingusers/bridge-users.pdf @@ -0,0 +1,981 @@ +%PDF-1.4 +%âãÏÓ\r +1 0 obj +<< +/CreationDate (D:20101104141647) +/ModDate (D:20101104141647) +/Title (R Graphics Output) +/Producer (R 2.10.0) +/Creator (R) +>> +endobj +2 0 obj +<< +/Type /Catalog +/Pages 3 0 R +>> +endobj +5 0 obj +<< +/Type /Page +/Parent 3 0 R +/Contents 6 0 R +/Resources 4 0 R +>> +endobj +6 0 obj +<< +/Length 7 0 R +>> +stream +q +Q q +Q q +Q q +Q q +Q q +Q q +Q q +1.000 1.000 1.000 rg +0.00 0.00 576.00 324.00 re f +Q q +Q q +Q q +BT +0.000 0.000 0.000 rg +/F2 1 Tf 0.00 12.00 -12.00 0.00 19.42 110.96 Tm (Users (in 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+\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/2010/countingusers/dirbytes-mirrors.pdf b/2010/countingusers/dirbytes-mirrors.pdf new file mode 100644 index 0000000..981c74b --- /dev/null +++ b/2010/countingusers/dirbytes-mirrors.pdf @@ -0,0 +1,1114 @@ +%PDF-1.4 +%âãÏÓ\r +1 0 obj +<< +/CreationDate (D:20101116150408) +/ModDate (D:20101116150408) +/Title (R 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-0.00 10.00 38.86 136.08 Tm (100) Tj +ET +BT +/F2 1 Tf 10.00 0.00 -0.00 10.00 38.86 181.87 Tm (150) Tj +ET +BT +/F2 1 Tf 10.00 0.00 -0.00 10.00 38.86 227.65 Tm (200) Tj +ET +BT +/F2 1 Tf 10.00 0.00 -0.00 10.00 38.86 273.44 Tm (250) Tj +ET +Q q +Q q 38.86 37.28 23.77 0.00 re W n +Q q +Q q 38.86 23.02 23.77 14.27 re W n +Q q +Q q 38.86 23.02 23.77 0.00 re W n +Q q +Q q 62.62 309.60 0.00 0.00 re W n +Q q +Q q 62.62 309.60 0.00 0.00 re W n +Q q +Q q 62.62 37.28 0.00 272.32 re W n +Q q +Q q 62.62 37.28 0.00 0.00 re W n +Q q +Q q 62.62 23.02 0.00 14.27 re W n +Q q +Q q 62.62 23.02 0.00 0.00 re W n +Q q +Q q 62.62 309.60 498.98 0.00 re W n +Q q +Q q 62.62 309.60 498.98 0.00 re W n +Q q +Q q 62.62 37.28 498.98 272.32 re W n +0.898 0.898 0.898 rg +62.62 37.28 498.98 272.32 re f +0.949 0.949 0.949 RG +0.53 w +[] 0 d +1 J +1 j +10.00 M +62.62 48.10 m +561.60 48.10 l +S +62.62 70.99 m +561.60 70.99 l +S +62.62 93.89 m +561.60 93.89 l +S +62.62 116.78 m +561.60 116.78 l +S +62.62 139.67 m +561.60 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