It is possible to use the Ueli Maurer s Diffie Hellman reduction to transfer the discrete logarithm problem from an elliptic curve to a finite field?

The [original paper](https://crypto.ethz.ch/publications/files/Maurer94.ps) ("Towards the equivalence of breaking the Diffie-Hellman protocol and computing discrete logarithms") solves the discrete logarithm problem using a Diffie-Hellman oracle and auxiliary groups. It also transfers the problem from a finite field to solving the discrete logarithm on an elliptic curve. It was since extended for transferring the problem from an elliptic curve to a different elliptic curve which isn't isomorphic to the original.

*Would it be possible to perform the reverse operation? That is, from the elliptic curve, to transfer the problem to a finite field, and possibly do it to an additive group?*

Of course, the MOV attack already allows that, but the interest here would be to use the oracle in order to bypass the embedding degree restrictions.

*If possible, what would be the exact steps to perform it?*