I want to implement a PRG (Pseudorandom Generator). As AES is implemented in hardware, I am planning to use AES for efficiency. I am planning to use:
$(AES_k(seed) \| AES_k(seed+1) \| AES_k(seed+2) \|....)$
as a PRG ($k$ represents the key of AES). The receiver of this sequence does not know the random seed, but knows the AES key $k$. So, is this sequence a provably secure PRG, when the AES key is known (at least in ideal cipher model)?