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?
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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 $GF(2)$)
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$\begingroup$ 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 $\endgroup$– Rui T.Commented Apr 16 at 13:49
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$\begingroup$ @RuiT. if that's the scenario you're interested in, you probably should mention it in your question... $\endgroup$– ponchoCommented Apr 16 at 14:11
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$\begingroup$ 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! $\endgroup$– Rui T.Commented Apr 16 at 14:44