[tor-commits] [metrics-tasks/master] Add George's censorship detector LaTeX sources (#2718).

[karsten@xxxxxxxxxxxxxx]

commit 83ba791573db7d407aa098d43a43e86692bd7d5c
Author: Karsten Loesing <karsten.loesing@xxxxxxx>
Date:   Mon Aug 22 16:52:40 2011 +0200

    Add George's censorship detector LaTeX sources (#2718).
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 task-2718/detector.tex |  169 ++++++++++++++++++++++++++++++++++++++++++++++++
 1 files changed, 169 insertions(+), 0 deletions(-)

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+\documentclass{article}
+\begin{document}
+\author{George Danezis\\{\tt gdane@xxxxxxxxxxxxx}}
+\title{An anomaly-based censorship-detection\\system for Tor}
+\date{August 11, 2011}
+\maketitle
+
+\section{Introduction}
+
+The Tor project is currently the most widely used anonymity and censorship
+resistance system worldwide.
+As a result, national governments occasionally or regularly block access
+to its facilities for replaying traffic.
+Major blocking might be easy to detect, but blocking from smaller
+jurisdictions, with fewer users, could take some time to detect.
+Yet, early detection may be key to deploy countermeasures.
+We have designed an ``early warning'' systems that looks for anomalies in
+the volumes of connections from users in different jurisdictions and flags
+potential censorship events.
+Special care has been taken to ensure the detector is robust to
+manipulations and noise that could be used to block without raising an
+alert.
+
+The detector works on aggregate number of users connecting to a fraction
+of directory servers per day.
+That set of statistics are gathered and provided by the Tor project in a
+sanitised form to minimise the potential for harm to active users.
+The data collection has been historically patchy, introducing wild
+variations over time that is not due to censorship.
+The detector is based on a simple model of the number of users per day per
+jurisdictions.
+That model is used to assess whether the number of users we observe is
+typical, too high or too low.
+In a nutshell the prediction on any day is based on activity of previous
+days locally as well as worldwide.
+
+\section{The model intuition}
+
+The detector is based on a model of the number of connection from every
+jurisdiction based on the number of connections in the past as well as a
+model of ``natural'' variation or evolution of the number of connections.
+More concretely, consider that at time $t_i$ we have observed $C_{ij}$
+connections from country $j$.
+Since we are concerned with abnormal increases or falls in the volume of
+connections we compare this with the number of connections we observed at
+a past time $t_{i-1}$ denoted as $C_{(t-1)j}$ from the same country $j$.
+The ratio $R_{ij} = C_{ij} / C_{(i-1)j}$ summarises the change in the
+number of users.
+Inferring whether the ratio $R_{ij}$ is within an expected or unexpected
+range allows us to detect potential censorship events. 
+
+We consider that a ratio $R_{ij}$ within a jurisdiction $j$ is ``normal''
+if it follows the trends we are observing in other jurisdictions.
+Therefore for every time $t_i$ we use the ratios $R_{ij}$ of many
+countries to understand the global trends of usage of Tor, and we compare
+specific countries' ratios to this model.
+If they are broadly within the global trends we assume no censorship is
+taking place, otherwise we raise an alarm.
+
+\section{The model details}
+
+We model each data point $C_{ij}$ of the number of users connected at time
+$t_i$ from country $j$ as a single sample of a Poisson process with a rate
+$\lambda_{ij}$ modelling the underlying number of users.
+The Poisson process allows us to take into account that in jurisdictions
+with very few users we will naturally have some days of relatively low or
+high usage---just because a handful of users may or may not use Tor in a
+day.
+Even observing zero users from such jurisdictions on some days may not be
+a significant event. 
+
+We are trying to detect normal or abnormal changes in the rate of change
+of the rate $\lambda_{ij}$ between time $t_i$ and a previous time
+$t_{i-1}$ for jurisdiction $j$ compared with other jurisdictions.
+This is $\lambda_{ij} / \lambda_{(i-1)j}$ which for jurisdictions with a
+high number of users is very close to $C_{ij} / C_{(i-1)j} = R_{ij}$.
+We model $R_{ij}$'s from all jurisdictions as following a Normal
+distribution $N(m,v)$ with a certain mean ($m$) and variance ($v$) to be
+inferred.
+This is of course a modelling assumption.
+We use a normal distribution because given its parameters it represents
+the distribution with most uncertainty: as a result the model has higher
+variance than the real world, ensuring that it gives fewer false alarms of
+censorship.
+
+The parameters of $N(m,v)$ are inferred directly as point estimates from
+the readings in a set of jurisdictions.
+Then the probability of a given country ratio $R_{ij}$ is compared with
+that distribution: an alarm is raised if the probability of the ratio is
+above or below a certain threshold.
+
+\section{The model robustness}
+
+At every stage of detections we follow special steps to ensure the
+detection is robust to manipulation by jurisdictions interested in
+censoring fast without being detected.
+First the parameter estimation for $N(m,v)$ is hardened: we only use the
+largest jurisdictions to model ratios and within those we remove any
+outliers that fall outside four inter-quartile ranges off the median.
+This ensures that a jurisdiction with a very high or very low ratio does
+not influence the model of ratios (and can be subsequently detected as
+abnormal).
+
+Since we chose jurisdictions with many users to build the model of ratios,
+we can approximate the rates $\lambda_{ij}$ by the actual observed number
+of users $C_{ij}$.
+On the other hand when we try to detect whether a jurisdiction has a
+typical rate we cannot make this assumption.
+The rate of a Poisson variable $\lambda_{ij}$ can be inferred by a single
+sample $C_{ij}$ using a Gamma prior, in which case it follows a Gamma
+distribution.
+In practice (because we are using a single sample) this in turn can be
+approximated using a Poisson distribution with parameter $C_{ij}$.
+Using this observation we extract a range of possible rates for each
+jurisdiction based on $C_{ij}$, namely $\lambda_{ij_{min}}$ and
+$\lambda_{ij_{max}}$.
+Then we test whether that full range is within the typical range
+distribution---if not we raise an alarm.
+
+\section{The parameters}
+
+The deployed model considers a time interval of seven (7) days to model
+connection rates (i.e. $t_i$ - $t_{i-1} = 7$ days).
+The key reason for a weekly model is our observation that some
+jurisdictions exhibit weekly patterns.
+A previous day model would then raise alarms every time weekly patterns
+emerged.
+We use the 50 largest jurisdictions to build our models of typical ratios
+of traffic over time---as expected most of them are in countries where no
+mass censorship has been reported.
+This strengthens the model as describing ``normal'' Tor connection
+patterns.
+
+We consider that a ratio of connections is typical if it falls within the
+99.99~\% percentile of the Normal distribution $N(m,v)$ modelling ratios.
+This ensures that the expected rate of false alarms is about $1 / 10000$,
+and therefore only a handful a week (given the large number of
+jurisdictions).
+Similarly, we infer the range of the rate of usage from each jurisdiction
+(given $C_{ij}$) to be the 99.99~\% percentile range of a Poisson
+distribution with parameter $C_{ij}$.
+This full range must be within the typical range of ratios to avoid
+raising an alarm.
+
+\section{Further work}
+
+The detector uses time series of user connections to directory servers to
+detect censorship.
+Any censorship method that does not influence these numbers would as a
+result not be detected.
+This includes active attacks: a censor could substitute genuine requests
+with requests from adversary controlled machines to keep numbers within
+the typical ranges.
+
+A better model, making use of multiple previous readings, may improve the
+accuracy of detection.
+In particular, when a censorship event occurs there is a structural
+change, and a model based on modelling the future on user loads before the
+event will fail.
+This is not a critical problem, as these ``false positives'' are
+concentrated after real censorship events, but the effect may be confusing
+to a reader.
+On the other hand, a jurisdiction can still censor by limiting the rate of
+censorship to be within the typical range for the time period concerned.
+Therefore adapting the detector to run on longer periods would be
+necessary to detect such attacks.
+
+\end{document}
+

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