# Are modes like CBC, OFB, CFB subject to chosen plaintext attacks?

I haven't found much info on the internet about the weakness of modes to chosen plaintext attacks, but from what I understand of them, there seem to be some trivial attacks, so I'm a bit confused. For example, let's encrypt 2 blocks of plaintext with value 0 with CBC:

C0=Ek(P0+IV)=Ek(IV)

C1=Ek(P1+C0)=Ek(Ek(IV))

But then we have a double encryption of IV, which should be subject to a Meet in the Middle attack. Is there something wrong with my reasoning or are chaining modes of operation inherently weak against chosen plaintext attacks?

CBC, OFB, CFB, CTR modes resist chosen plaintext attack, if the underlying block cipher is secure, and the Initialization Vector is uniformly random and unpredictable, and the total amount of blocks stays below $$\sqrt{\|B\|}\,\epsilon^{-2}$$ blocks, where $$\|B\|$$ is the size of the block space and $$\epsilon$$ is the desired residual probability of success of adversaries.
Getting $$\mathsf{IV}$$, $$E_K(\mathsf{IV})$$ and $$E_K(E_K(\mathsf{IV}))$$, as we can have with CBC mode under chosen plaintext attack, does not allow to mount a Meet in the Middle attack. Argument: such attacks require that the key can be divided into segments that allow a meaningful calculation, and here $$K$$ remains a single entity.