To describe the Dual Target game:

- Challenger receives two group elements G, H. Sends (G, H) to the adversary.
- Adversary sends back (H, G). I rename these values to H_k and G_k.
- Challenger chooses a random y. Sends to Adversary.
- Adversary chooses an x value which satisfies the following conditions:

- y * (H_k - xG) == 0
- y * (H - xG_k) == 0
- H_k != xG or H != xG_k