When performing Shamir secret sharing I'm trying to find $z_i$, such that $z = x + y$. Where $n = 6$ and $t = 3$.
I believe this would be the correct solution (correct me if I'm wrong):
- Each party computes $x_i + y_i = z_i$
- Each party shares $z_i$ with the other 2 parties
- Each party uses Lagrange basis polynomials to compute the secret (using the 2 obtained values).
My question is this: if the shares are in the form $(i, f(i))$ (for $1$ to $i$) my assumption is that the involved parties can use Lagrange basis polynomials because they will know the "$i$" of the other parties that sent them their computed $z_i$. Is that correct?