Re: [tor-dev] Feedback on obfuscating hidden-service statistics

["A. Johnson" <aaron.m.johnson@xxxxxxxxxxxx>]

Hi George,

> I posted an initial draft of the proposal here:
> https://lists.torproject.org/pipermail/tor-dev/2014-November/007863.html
> Any feedback would be awesome.

OK, I’ll have a chance to look at this in the next few days.

> Specifically, I would be interested in undertanding the concept of
> additive noise a bit better. As you can see the proposal draft is
> still using multiplicative noise, and if you think that additive is
> better we should change it. Unfortunately, I couldn't find any good
> resources on the Internet explaining the difference between additive
> and multiplicative noise. Could you expand a bit on what you said
> above? Or link to a paper that explains more? Or link to some other
> system that is doing additive noise (or even better its implementation)?

The technical argument for differential privacy is explained in <http://research.microsoft.com/en-us/projects/databaseprivacy/dwork.pdf>.  The definition appears in Def. 2, the Laplace mechanism is given in Eq. 3 of Sec. 5, and Thm. 4 shows why that mechanism achieves differential privacy.

But that stuff is pretty dry. The basic idea is that you’re trying to the contribution of any one sensitive input (e.g. a single user’s data or a single component of a single user’s data). The noise that you need to cover that doesn’t scale with the number of other users, and so you use additive noise.

Hope that helps,
Aaron
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