# Eliptic curve verifiable secret sharing

I am implementing the following the algorithm instructions as shown in 1 (section IV, B).

When trying to verify the share given the commits, $a_jG$ verifier $i$ checks whether $f(i)G=\sum_{j=0}^{t} (x_i)^ja_jG$. The phrasing of the verification is unclear to me, on the left side of the equation there is a scalar on the elliptic curve, on the right side there is a a polynomial. Should the polynomial on the right be evaluated at point $i$?

A robust threshold elliptic curve digital signature providing a new verifiable secret sharing scheme

I cannot access the linked document, but I think that $G$ is a generator point of the elliptic curve, so you will have points on both sides.