# Efficient universally composable protocols for aggregate statistics

Let's say we have multiple parties $$P_1, \dots P_n$$ that gather personal data, and a party $$C$$ that is interested in aggregate statistics on these data, i.e. the average value.

An ideal functionality $$\mathcal{F}$$ would allow $$C$$ to register a subset of parties $$\mathbf{P}$$ linked to some kind of abstract data identifier $$id$$. $$\mathcal{F}$$ would collect data from all parties of $$\mathbf{P}$$ corresponding to $$id$$, calculate the average and return it to $$C$$.

I specifically mention the average as the protocol should not necessarily provide the option to do any sophisticated computation on the data. It would completely suffice do "easy math" on the data and maybe therefore having a higher efficiency of the protocol.

Are there any efficient universally composable protocols for aggregate statistics of this kind (ideally in the CRS-model) ?

I somehow fail to find any protocols specific to this obvious scenario. Generally I would assume that a combination of a universal composable secret sharing protocol and a homomorphic encryption scheme could do the job.

• Secure multiparty computation (MPC), mental poker, socialist millionaires, etc. There exists many schemes in this spirit of distributed computation. SCALE-MAMBA is one of the more recent implementations (Turing complete), but might have too much overhead for your usecase? Possibly something simpler like elgamal homomorphic encryption (using simple addition) with multiple parties, average by dividing the result? – Natanael Apr 11 at 14:18
• @Natanael I would like to avoid the overhead of these protocols. It would not even be necessary to deal with floating point numbers or division. The secure multiparty computation could be a simple addition of the values of the parties with the number of summands as a "public part" to let C do the division by itself. The key point is, that it should be an efficient universally composable secure multiparty protocol of this dead simple computation. – bit Apr 11 at 14:57
• then look into the elgamal version that I mentioned – Natanael Apr 12 at 16:08