# Necessity of Randomness when Privately Computing a Sum

I want to show that no 1-private deterministic protocol exists for calculating a sum of $n \geq 3$ parties (within the realms of Perfect rather than Computational Security). I'm having trouble showing that as I have to show that for any protocol, meaning I've no idea what messages are being sent.

I thought about showing privacy violation by showing that knowing the sum, a party may gain information about others, but obviously a Simulator could do that as well.

• SMC is also my interest. However, I have not understood your problem. You should re-define this issue to clearly make it. – HienVD Jun 2 '18 at 15:18
• For the private case of $n=3$, let $f(x_1, x_2, x_3) = (\sum_{i=1}^3 x_i, \sum_{i=1}^3 x_i, \sum_{i=1}^3 x_i)$. Show that there's no deterministic protocol computing $f$, perfectly secure against a passive adversary controlling a single participant. – leopoldsatz Jun 2 '18 at 15:41