>> in Prio, servers use a generic secure multi-party computation (MPC) protocol 
>> to compute the circuits. If Tor is going to do that, why not just run a 
>> generic MPC protocol over all of the inputs? Doing so would allow Tor 
>> statistics aggregations to be robust to inputs that are likely “incorrect” 
>> given the values of the other inputs (see “robust statistics” for a wide 
>> variety of useful such computations, including for example median, trimmed 
>> mean, least trimmed squares, maximum likelihood estimation). Applying MPC 
>> over all inputs would only require implementing the “offline” phase of the 
>> computation (e.g. producing the “multiplication triples”, which are supplied 
>> by the client in Prio). There are reasonably efficient protocols for doing 
>> so, including SDPZ and TinyOT [1].
> 
> If I understand you correctly, you are saying that we can add
> a secure multiparty computation to the Tally Reporters without
> changes on the Data Collectors?

Yes, that is correct. The MPC servers would get the (secret-shared) inputs, and 
then instead of just adding them and publishing the result, they would perform 
an MPC computation on them.

Now, we could in theory improve Data Collectors so that they can obliviously 
maintain statistics that aren’t just counts. For example, this would enable us 
to store a maximum of observed values (e.g. most streams per circuit seen over 
all circuits through that exit). How that could be done with adequate 
efficiency isn’t clear to me, though (it seems like a research question).

Best,
Aaron
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