[tor-dev] Proposal draft: Better hidden service stats from Tor relays

[George Kadianakis]

"A. Johnson" <aaron.m.johnson at nrl.navy.mil> writes:

> Hi George,
>

Hello!

> I recommend a change to the way that these statistics are
> obfuscated. The problem is that new noise is used every day, and from
> the distribution of the reported bins, the exact location within the
> bin (assuming the stat stats constant) can be reported.
>

Assuming that the underlying value is constant and since our Laplace
distribution is public, the adversary can observe which bin is
reported each time and get a probability distribution for the
underlying value.

This indeed seems plausible under the powerful assumption that the
underlying stat is constant.

> So instead of this
>
>>                   +--------------+    +--------------------+
>>   actual value -> |additive noise| -> |round-up obfuscation| -> public statistic
>>                   +--------------+    +——————————+
>
> I recommend that you flip the order, so that it is like this
>                   +--------------+    +--------------------+
>   actual value -> |round-up obfuscation| -> |additive noise| -> public statistic
>                   +--------------+    +——————————+
>
> “Additive noise” in the context of bins is actually just a distribution over bins. You can think of it in two ways:
>   1. Add Laplace noise to the bin center, and then report the bin of the resulting number.


Hm, you mean something like this, right?

                   +--------------+    +--------------------+    +--------------+
   actual value -> |   binning    | -> |  addditive noise   | -> |   binning    | -> public statistic
                   +--------------+    +——————————----------+    +--------------+

where the additive noise is applied to the center of the first bin?

I can see how this is better, since the underlying value gets
immediately smoothed by binning. However, it does give me a weird
hacky feeling...

Is this construction something that has been used before?

Thanks for the feedback!