commit fdd7a1d37813657166a66dc110952fe3e1e8ae2d Author: Karsten Loesing karsten.loesing@gmx.net Date: Thu Jul 12 13:33:27 2012 +0200
Move #2718 report sources to tech-reports.git. --- task-2718/detector.tex | 169 ------------------------------------------------ 1 files changed, 0 insertions(+), 169 deletions(-)
diff --git a/task-2718/detector.tex b/task-2718/detector.tex deleted file mode 100644 index 10822d5..0000000 --- a/task-2718/detector.tex +++ /dev/null @@ -1,169 +0,0 @@ -\documentclass{article} -\begin{document} -\author{George Danezis\{\tt gdane@microsoft.com}} -\title{An anomaly-based censorship-detection\system for Tor} -\date{September 9, 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 relaying 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 deploying countermeasures. -We have designed an ``early warning'' system 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 -jurisdiction. -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 connections 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 $C_{(i-1)j}$ 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 of 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 -emerge. -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 of 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} -