Independent parameters basis for torsion-groups in SIDH: Is the Weil-pairing necessary?
As you mentioned, computing the discrete logarithm is an easy way to check for linear dependency. The usual way to compute discrete logs over elliptic curves relies on some pairing, but there are ways to do so without any pairing. See for instance &quot;Isogeny-based key compression without pairings&quot; at PKC'21 (https://eprint.iacr.org/2021/272.pdf), where pairing-less discrete logs are used for key compression.