# Some misunderstanding on the Security Proof with Oracle

I have a question about the security proof. Suppose that I proved the following relations. That is, I proved that $$Adv_A \le Adv_A^{O} \le Adv_B$$, where A,B are some cryptographic schemes and O is an oracle. I also suppose that the oracle O has a very strong property. For example, the O can solve DLP in polynomial time.

On the other hand, there is an attacker $$\mathcal{A}$$ which can break the scheme A. That is, $$Adv_A$$ is not negligible in the security parameter.

Even though $$Adv_B$$ is also non-negligible, but we do not have the oracle O. In this setup, how to break the scheme B using $$\mathcal{A}$$?

You have to look in more details the proof of the inequality $$Adv^{O}_A \leq Adv_B$$.
The proof will give you explicitly how to construct $$\mathcal{B}$$ from $$\mathcal{A}^O$$. It should be written how to simulate the experiment with $$A$$ and the powerful oracle $$O$$, by only having interaction with the experiment with $$B$$. And how to use the output of $$\mathcal{A}$$ to win the game against $$B$$.