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Re: [tor-dev] Proposal draft: Better hidden service stats from Tor relays
George Kadianakis <desnacked@xxxxxxxxxx> writes:
> George Kadianakis <desnacked@xxxxxxxxxx> writes:
>
>> Hello there,
>>
>> I inline a copy of a proposal we've been working on lately. Discussion
>> can be found in the "Feedback on obfuscating hidden-service statistics"
>> thread.
>>
>> The proposal suggests that Tor relays add some stats about hidden
>> service usage. We believe that these stats are not dangerous and can
>> be useful to Tor developers and to people who want to understand
>> hidden services and the onionspace better.
>>
>> Any feedback is appreciated :)
>>
>
> Hello,
>
> I inline a better version of that proposal.
>
And now I inline an even better version of the proposal.
Changes include:
- Inverted the order of the obfuscation methods as discussed in
the mailing list.
- Change delta_f of the HSDir stats to be 8 instead of 1.
- Switched from 'round-up obfuscation' to 'data binning'.
- Add links to pfm's graphs.
You can also find this proposal (and a diff from its previous state) at:
https://gitweb.torproject.org/user/asn/torspec.git/log/?h=hs_stats
Thanks!
------
Filename: 238-hs-relay-stats.txt
Title: Better hidden service stats from Tor relays
Author: George Kadianakis, David Goulet, Karsten Loesing, Aaron Johnson
Created: 2014-11-17
Status: Draft
0. Motivation
Hidden Services is one of the least understood parts of the Tor
network. We don't really know how many hidden services there are
and how much they are used.
This proposal suggests that Tor relays include some hidden service
related stats to their extra info descriptors. No stats are
collected from Tor hidden services or clients.
While uncertainty might be a good thing in a hidden network,
learning more information about the usage of hidden services can be
helpful.
For example, learning how many cells are sent for hidden service
purposes tells us whether hidden service traffic is 2% of the Tor
network traffic or 90% of the Tor network traffic. This info can
also help us during load balancing, for example if we change the
path building of hidden services to mitigate guard discovery
attacks [GUARD-DISCOVERY].
Also, learning the number of hidden services, can give us an
understanding of how widespread hidden services are. It will also
help us understand approximately how much load is put in the
network by hidden service logistics, like introduction point
circuits etc.
1. Design
Tor relays shall add some fields related to hidden service
statistics in their extra-info descriptors.
Tor relays collect these statistics by keeping track of their
hidden service directory or rendezvous point activities, slightly
obfuscating the numbers and posting them to the directory
authorities. Extra-info descriptors are posted to directory
authorities every 24 hours.
2. Implementation
2.1. Hidden service statistics interval
We want relays to report hidden-service statistics over a long-enough
time period to not put users at risk. Similar to other statistics, we
suggest a 24-hour statistics interval. All related statistics are
collected at the end of that interval and included in the next
extra-info descriptors published by the relay.
Tor relays will add the following line to their extra-info descriptor:
"hidserv-stats-end" YYYY-MM-DD HH:MM:SS (NSEC s) NL
[At most once.]
YYYY-MM-DD HH:MM:SS defines the end of the included measurement
interval of length NSEC seconds (86400 seconds by default).
A "hidserv-stats-end" line, as well as any other "hidserv-*" line,
is first added after the relay has been running for at least 24
hours.
2.2. Hidden service traffic statistics
We want to learn how much of the total Tor network traffic is
caused by hidden service usage. More precisely, we measure hidden
service traffic by counting RELAY cells seen on a rendezvous point
after receiving a RENDEZVOUS1 cell. These RELAY cells include
commands to open or close application streams, and they include
application data.
Tor relays will add the following line to their extra-info descriptor:
"hidserv-rend-relayed-cells" SP num SP key=val SP key=val ... NL
[At most once.]
Where 'num' is the number of RELAY cells seen in either
direction on a circuit after receiving and successfully
processing a RENDEZVOUS1 cell.
The actual number is obfuscated as detailed in
[STAT-OBFUSCATION]. The parameters of the obfuscation are
included in the key=val part of the line.
The obfuscatory parameters for this statistic are:
* delta_f = 2048
* epsilon = 0.3
* bin_size = 1024
(Also see [CELL-LAPLACE-GRAPH] for a graph of the Laplace distribution.)
So, an example line could be:
hidserv-rend-relayed-cells 19456 delta_f=2048 epsilon=0.30 binsize=1024
2.3. HSDir hidden service counting
We also want to learn how many hidden services exist in the
network. The best place to learn this is at hidden service
directories where hidden services publish their descriptors.
Tor relays will add the following line to their extra-info descriptor:
"hidserv-dir-onions-seen" SP num SP key=val SP key=val ... NL
[At most once.]
Approximate number of unique hidden-service identities seen in
descriptors published to and accepted by this hidden-service
directory.
The actual number number is obfuscated as detailed in
[STAT-OBFUSCATION]. The parameters of the obfuscation are
included in the key=val part of the line.
The obfuscatory parameters for this statistic are:
* delta_f = 8
* epsilon = 0.3
* bin_size = 8
(Also see [ONIONS-LAPLACE-GRAPH] for a graph of the Laplace distribution.)
So, an example line could be:
hidserv-dir-onions-seen 112 delta_f=1 epsilon=0.30 binsize=8
2.4. Statistics obfuscation [STAT-OBFUSCATION]
We believe that publishing the actual measurement values in such a
system might have unpredictable effects, so we obfuscate these
statistics before publishing:
+-----------+ +--------------+
actual value -> | binning | -> |additive noise| -> public statistic
+-----------+ +--------------+
We are using two obfuscation methods to better hide the actual
numbers even if they remain the same over multiple measurement
periods.
Specifically, given the actual measurement value, we first apply
data binning to it (basically we round it up to the nearest multiple
of an integer, see [DATA-BINNING]). And then we apply additive noise
to the binned value in a fashion similar to differential privacy.
More information about the obfuscation methods follows:
2.4.1. Data binning
The first thing we do to the original measurement value, is to round
it up to the nearest multiple of 'bin_size'. 'bin_size' is an
integer security parameter and can be found on the respective
statistics sections.
This is similar to how Tor keeps bridge user statistics. As an
example, if the measurement value is 9 and bin_size is 8, then the
final value will be rounded up to 16. This also works for negative
values, so for example, if the measurement value is -9 and bin_size
is 8, the value will be rounded up to -8.
2.4.2. Additive noise
Then, before publishing the statistics, we apply additive noise to
the binned value by adding to it a random value sampled from a
Laplace distribution . Following the differential privacy
methodology [DIFF-PRIVACY], our obfuscatory Laplace distribution has
mu = 0 and b = (delta_f / epsilon).
The precise values of delta_f and epsilon are different for each
statistic and are defined on the respective statistics sections.
3. Security
The main security considerations that need discussion are what an
adversary could do with reported statistics that they couldn't do
without them. In the following, we're going through things the
adversary could learn, how plausible that is, and how much we care.
(All these things refer to hidden-service traffic, not to
hidden-service counting. We should think about the latter, too.)
3.1. Identify rendezvous point of high-volume and long-lived connection
The adversary could identify the rendezvous point of a very large and
very long-lived HS connection by observing a relay with unexpectedly
large relay cell count.
3.2. Identify number of users of a hidden service
The adversary may be able to identify the number of users
of an HS if he knows the amount of traffic on a connection to that HS
(which he potentially can determine himself) and knows when that
service goes up or down. He can look at the change in the total
reported RP traffic to determine about how many fewer HS users there
are when that HS is down.
4. Discussion
4.1. Why count only RP cells? Why not count IP cells too?
There are three phases in the rendezvous protocol where traffic is
generated: (1) when hidden services make themselves available in
the network, (2) when clients open connections to hidden services,
and (3) when clients exchange application data with hidden
services. We expect (3), that is the RP cells, to consume most
bytes here, so we're focusing on this only.
Furthermore, introduction points correspond to specific HSes, so
publishing IP cell stats could reveal the popularity of specific
HSes.
4.2. How to use these stats?
4.2.1. How to use rendezvous cell statistics
We plan to extrapolate reported values to network totals by dividing
values by the probability of clients picking relays as rendezvous
point. This approach should become more precise on faster relays and
the more relays report these statistics.
We also plan to compare reported values with "cell-*" statistics to
learn what fraction of traffic can be attributed to hidden services.
Ideally, we'd be able to compare values to "write-history" and
"read-history" lines to compute similar fractions of traffic used for
hidden services. The goal would be to avoid enabling "cell-*"
statistics by default. In order for this to work we'll have to
multiply reported cell numbers with the default cell size of 512 bytes
(we cannot infer the actual number of bytes, because cells are
end-to-end encrypted between client and service).
4.2.2. How to use HSDir HS statistics
We plan to extrapolate this value to network totals by calculating what
fraction of hidden-service identities this relay was supposed to see.
This extrapolation will be very rough, because each hidden-service
directory is only responsible for a tiny share of hidden-service
descriptors, and there is no way to increase that share significantly.
Here are some numbers: there are about 3000 directories, and each
descriptor is stored on three directories. So, each directory is
responsible for roughly 1/1000 of descriptor identifiers. There are
two replicas for each descriptor (that is, each descriptor is stored
under two descriptor identifiers), and descriptor identifiers change
once per day (which means that, during a 24-hour period, there are two
opportunities for each directory to see a descriptor). Hence, each
descriptor is stored to four places in
identifier space throughout a 24-hour period. The probability of any
given directory to see a given hidden-service identity is
1-(1-1/1000)^4 = 0.00399 = 1/250. This approximation constitutes an
upper threshold, because it assumes that services are running all day.
An extrapolation based on this formula will lead to undercounting the
total number of hidden services.
A possible inaccuracy in the estimation algorithm comes from the fact
that a relay may not be acting as hidden-service directory during the
full statistics interval. We'll have to look at consensuses to
determine when the relay first received the "HSDir" flag, and only
consider the part of the statistics interval following the valid-after
time of that consensus.
4.3. Why does the obfuscation work?
By applying data binning, we smudge the original value making it
harder for attackers to guess it. Specifically, an attacker who
knows the bin, can only guess the underlying value with probability
1/bin_size.
By applying additive noise, we make it harder for the adversary to
find out the current bin, which makes it even harder to get the
original value. If additive noise was not applied, an adversary
could try to detect changes in the original value by checking when
we switch bins.
5. Acknowledgements
Thanks go to 'pfm' for the helpful Laplace graphs.
6. References
[GUARD-DISCOVERY]: https://lists.torproject.org/pipermail/tor-dev/2014-September/007474.html
[DIFF-PRIVACY]: http://research.microsoft.com/en-us/projects/databaseprivacy/dwork.pdf
[DATA-BINNING]: https://en.wikipedia.org/wiki/Data_binning
[CELL-LAPLACE-GRAPH]: https://raw.githubusercontent.com/corcra/pioton/master/vis/laplacePDF_mu0_b6800.png
https://raw.githubusercontent.com/corcra/pioton/master/vis/laplaceCDF_mu0_b6800.png
[ONIONS-LAPLACE-GRAPH]: https://raw.githubusercontent.com/corcra/pioton/master/vis/laplacePDF_mu0_b3.png
https://raw.githubusercontent.com/corcra/pioton/master/vis/laplaceCDF_mu0_b3.png
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