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

commit a11537717ce46139c9bfc57e0e1b5ffe41489be2 Author: Karsten Loesing karsten.loesing@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 @@ -%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 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-\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 deleted file mode 100644 index 981c74b..0000000 --- a/task-2647/dirbytes-mirrors.pdf +++ /dev/null @@ -1,1114 +0,0 @@ -%PDF-1.4 -%âãÏÓ\r -1 0 obj -<< -/CreationDate (D:20101116150408) -/ModDate (D:20101116150408) -/Title (R Graphics Output) 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