Would it be secure to encrypt a sequence of blocks by having the next integer be H(k) — such that the random integer for block number i is H applied to the original random integer (k) i times? Thus needing only an initial random integer from which all subsequent random integers are derived.
The general idea is to create a PRNG using the cryptographic hash. Since these hashes generally produce far more bits than needed for scalars (64 bits), you can mix the extra bits for the next cycle of the PRNG and emit (say) 64 bits per cycle. The sequence of the PRNG output is the 'pad'.
