Suppose that I have an AES key $K$, and I'm instructed to find a plaintext such that the first 32 bits of the plaintext are some string of bits $S_1$, and the last 32 bits of the ciphertext once the plaintext has been encrypted with $K$ are another string of bits $S_2$.
Is this difficult? Is there a known attack against this that's faster than just fixing one of the $S$'s and brute-force searching for a text with the other $S$?