[tor-commits] [torspec/master] Further improvements to 238-hs-relay-stats.txt.
nickm at torproject.org
nickm at torproject.org
Tue Jan 6 17:54:02 UTC 2015
commit ae59ee1e346ef31208572c3accd3ed9ae513da81
Author: George Kadianakis <desnacked at riseup.net>
Date: Sun Dec 14 16:42:47 2014 +0200
Further improvements to 238-hs-relay-stats.txt.
- Inverse 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.
- Add links to pfm's graphs.
---
proposals/238-hs-relay-stats.txt | 94 ++++++++++++++++++++++++--------------
1 file changed, 60 insertions(+), 34 deletions(-)
diff --git a/proposals/238-hs-relay-stats.txt b/proposals/238-hs-relay-stats.txt
index e7bf184..d46e35d 100644
--- a/proposals/238-hs-relay-stats.txt
+++ b/proposals/238-hs-relay-stats.txt
@@ -84,14 +84,15 @@ Status: Draft
direction on a circuit after receiving and successfully
processing a RENDEZVOUS1 cell.
- The actual number is obfuscated as detailed in section
- "2.4. Statistics obfuscation". The parameters of the
- obfuscation are included in the key=val part of the line.
+ 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
@@ -111,55 +112,45 @@ Status: Draft
descriptors published to and accepted by this hidden-service
directory.
- The actual number number is obfuscated as detailed in section
- "2.4. Statistics obfuscation". The parameters of the
- obfuscation are included in the key=val part of the line.
+ 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 these statistics are:
- * delta_f = 1
+ 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
+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 -> |additive noise| -> |round-up obfuscation| -> public statistic
- +--------------+ +--------------------+
+ +-----------+ +--------------+
+ 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 deploy
- additive noise in a fashion similar to basic differential
- privacy. Then, we round up this obfuscated result to the nearest
- multiple of an integer (which is a security parameter), to derive a
- final result which can be published safely.
+ 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. Additive noise
-
- We apply additive noise to the actual measurement 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.
+2.4.1. Data binning
-2.4.2. Round-up obfuscation
-
- To further hide any patterns, before publishing statistics, we round
- up the result to the nearest multiple of 'bin_size'. 'bin_size' is
- an integer security parameter and can be found on the respective
+ 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
@@ -168,6 +159,17 @@ Status: Draft
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
@@ -196,7 +198,7 @@ Status: Draft
4. Discussion
-4.1. Why count only RP cells? Why not also count IP cells?
+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
@@ -211,7 +213,7 @@ Status: Draft
4.2. How to use these stats?
- 4.2.1. How to use RP Cell statistics
+ 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
@@ -259,9 +261,33 @@ Status: Draft
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
-5. References
+ 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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