Attacks on the RawCBC-MAC if the final step of encrypting with a second key isn't done This is from Boneh's lecture ECBC-MAC

Here is also a link to the lecture itself - https://www.coursera.org/learn/crypto/lecture/QYT6i/cbc-mac-and-nmac
CBC-MAC with $(K_1, K_2)$ on a message $M$ applies RawCBCMAC with $K_1$ to message $M$ &amp; takes the output tag &amp; runs the PRF on the tag using a second key $K_2$
Boneh explains a chosen message attack on RawCBCMAC

Ask the oracle for the tag on a 1 block message $m$. Let's say the tag is $t$.
Now the same tag $t$ will also be the tag for a 2nd message $ (m || t \oplus m)$

Yes, this will indeed work.
I can think of another attack on the RawCBCMAC

Ask the oracle for the tag on a message $m$ (can be any number of blocks). Let's say the tag is $t$.

Ask the oracle for the tag on a single block message ($w \oplus t$). Let's say the tag is $t'$

Now the tag for the message $(m || w)$ is same as $t'$


Is this also a valid attack on RawCBC or am I missing something?
Is this also a valid attack on RawCBC [...]?

Yes. Writing down the expressions, we get $t=F(k,m)$ and $t'=F(k,w\oplus t)$ - while abusing notation and meaning RawCBCMAC for multi-block invocations of $F$. Now the actual tag for $(m\|w)$ would be $t''=F(k,F(k,m)\oplus w)=F(k,t\oplus w)$ which is equal to $t'$.