Stateless and deterministic number generation
I want a stateless deterministic pseudorandom generator.


I don't see how that can work.

"Stateless" - the generator is always in the same state

"Deterministic" - given the same state (and inputs, but there's no inputs here), the generator always generates the same output.

Hence, you end up with something that always generates the same output; hardly pseudorandom.

The comparison with SPHINCS doesn't appear to be quite valid; the original SPHINCS is not deterministic (it selects the path through the hypertree randomly); you could make it deterministic (by depending on the message being signed to seed your randomness), but that's making it depend on an input that your pseudorandom number generator doesn't have.