Suppose I run a multiparty protocol. At the output stage, I have the function output in a secret shared manner among all parties.
Now I want all the parties to commit to their value of the secret shares
In essence, suppose every party $P_i$ has a share $Y_i$.
Every party should commit their value = $Com(Y_i)$
My problem is that I want to ensure that party $P_i$ doesn't commit to an incorrect value
$Com(Y'_i)$ s.t $Y'_i \not= Y_i$
before moving to the next stage in the protocol. I also do not want to reconstruct the output value until a later stage in the protocol.
Is there any efficient way in which you can perform such a commitment while ensuring that every party commits to the right value?