Bilinear map assumpion
It's unlikely that you'll be able to prove unforgeability from Discrete Log alone. You might need a new assumption altogether on bilinear maps.

Also, in the bilinear world, assuming discrete log is usually not enough to prove security. You need stronger assumptions such as Bilinear Diffie-Hellman or XDH, or the bilinear generic group model (see Appendix A of BBG05).