# How to compute $r \cdot (a+b+c)$ for random $r$ and secret value$a,b,c$ in MPC?

Suppose Alcie,Bob,and Charlie each has a secret value $$a,b,c$$ respectively. they want to compute a value $$r\cdot (a+b+c)$$ together. $$r$$ is a random value, and all parties know nothing about it.
I tried to use OLE to address this problem,but it works only in two party setting,i.e. $$r\cdot (a+b)$$。So is there any possible solutions?

So is there any possible solutions?

How about: have the party jointly pick a random $$d$$ value, and we are done.

In this case, $$r = d / (a + b + c)$$; as long as $$a+b+c \ne 0$$, it will always exist (assuming that we're working in a field).

No one without knowledge of $$a, b, c, d$$ can know the value of $$r$$, which I believe is what was requested.

Of course, this doesn't work if you're in a ring/field with a nontrivial probability of a random element being noninvertible (e.g. $$\mathbb{Z}/{2^n}$$ or $$GF(2)$$)

• thanks for your answer! Another questioin is if $a,b,c$ was extended to vectors $\vec{a},\vec{b},\vec{c}$,they need to compute $r\cdot (\vec{a}+\vec{b}+\vec{c})$。it seems doesn't work Apr 16 at 13:49
• @RuiT. if that's the scenario you're interested in, you probably should mention it in your question... Apr 16 at 14:11
• sorry about that！！i thought the former scenario could be easily extended to the latter ,so i simplify the question incorrectly。sorry about wasting your time! Apr 16 at 14:44