I am preparing for an exam and trying to solve the following question I found on the internet:
Let $F_k$ be a pseudorandom function. Show that the following MAC for messages of length $2n$ is insecure. The shared key is a random key $k \in \{0, 1\}^n$.
$\operatorname{Mac}_k(m_1||m_2) = ⟨F_k(m_1), F_k(m_1 \oplus \overline{m_2})⟩$
where $m_1, m_2$ are binary strings of length $n$ and $\overline{m_2}$ is $m_2$with all its bits inverted. What is the minimum number of queries that the adversary has to make to the MAC-oracle to forge a MAC?
To solve both questions I have tried to construct two messages for which the attacker requests tags and then combine the messages and corresponding tags in a way that gives a valid message and tag. Regrettably, this didn't work out since the second part of the tag combines both parts of the original message. Am I on the wrong track with my approach?