I have some issue to understand the verify round of the KZG polynomial commitment scheme. The following diagram is associated to the scheme. I appreciate any help.
To verify, the verifier should compute the pairing of $e(g^{f(\tau)-f(u)}, g)$ and $e(g^{\tau-u}, g^{q(\tau)})$.
However, to compute these pairings, verifier should compute $g^{f(\tau)-f(u)}$ and $g^{\tau-u}$ first. So, we see that $g^{f(\tau)-f(u)}=g^{f(\tau)}/g^{f(u)}$ and this is division of two points of the elliptic curve! However, the division of two elliptic curve points is not defined! We have the same issue with computing $g^{(\tau-u)}$ which is equal to $g^\tau/g^u$.