You have a 2048 bit private key, which is 2,048 randomly generated bits. It is not an RSA or ECC key. It is the master key that is used for every message. You receive a message to encrypt and generate an IV for it. Next, you take the first block of plaintext and SHA256(IV + 2048 bit key). You use that hash as a key to encrypt the first block of plaintext using AES-256. Then, you SHA-256(IV + 2048 bit key + previous round key) and use that hash to encrypt the second block. This is done for every block afterwards, always generating each block key with SHA-256(IV + 2048 bit key + previous round key). When finished, you store the ciphertext and the IV.
Would the attacker have to brute force every block one at a time and would it make it more difficult for the attacker to, most importantly, recover the original key itself? You could parallelize and pre-emptively generate the keys because they are based on a hash of the IV, the 2048 bit key, and previous round key. You're only suffering the SHA-256 and AES key setup penalty every round in terms of performance.