Encrypting a pseudorandom message Does encrypting a pseudorandom message need the same requirements from a block cipher?

For instance, can we decrease the number of rounds of AES if we want to cipher a random block, without any security loss?

Thank you
A message - strange as it may sound - cannot be encrypted by a block cipher. A block cipher is a deterministic keyed permutation. As it is deterministic, it cannot be a CPA secure cipher: identical messages will result in identical ciphertext, leaking information about the message. This is why ECB mode encryption, which consists of block encrypting subsequent blocks of the message, is insecure. A secure mode of operation - CBC, CTR etc. - and an IV are required to turn block ciphers into secure ciphers.

As there is no way of distinguishing the message from random data the cipher doesn't need to be that secure. It is however still required to use a mode of operation and an IV if the block size is small. Otherwise the block cipher must be relatively large (˜256 bits for large messages) so that repetition of blocks in the plaintext cannot be detected.

If there is even a hint of information on the message (a header or the parity bits of a DES key, a slow starting PRNG, a PRNG started with too little entropy in the seed, a non-secure PRNG etc. etc.) then these kind of schemes will fail spectacularly. The scheme would be brittle to the extreme; if anything breaks or if any info leaks it will crumble. Obviously an attacker should certainly not be allowed to control the plaintext, so the scheme would not be CPA secure.

So yeah, you could reduce the number of rounds or even use a repeated XOR cipher. But the risk of leaking info would be huge.