Why is CBC-MAC with length appended not secure?

Question

I've just read about CBC-MAC for the authentication of arbitrary length messages. In particular I cannot figure out why appending the message length before computing the MAC yields a non-secure MAC. I've already read other topics on crypto about this problem, but i did not find a rigorous proof.

Answer 1

I'll give you a hint, and you can work out the details yourself.

Take any $m_1,m_2,m_3$ of length $n$ (where $n$ is the block length), with $m_1\neq m_2$. Query the oracle with $m_1$, then query the oracle with $m_2$, and finally query the oracle with $m_1\|n\|m_3$.

Work through this, and you can find a message and its forgery.