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

Question

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?

Answer 1

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.