Hash function based cryptographically secure pseudo random number generator

I once read/heard that one could generate a cryptographically secure pseudo random number generator based on two cryptographically secure hash functions.

The algorithm goes this way:

• Let $$f$$ and $$g$$ be two independant cryptographically secure hash functions of block size $$s$$.
• This algorithm outputs blocks of $$s$$, the block $$n$$ is defined as: $$output[n \times s; (n+1) \times s] = f(g_{n}(seed))$$
• The function $$g_{n}(seed)$$ is defined as $$g_{n} = g_{n-1}(seed)$$ where $$g_{0}(seed) = g(seed)$$.

Concretely, the first block is generated with $$f(g(seed))$$, the second block with $$f(g(g(seed)))$$, then $$f(g(g(g(seed))))$$, and so on...

I've been looking around for any paper, or anybody mentioning this algorithm and/or trying to do cryptanalysis of this algorithm, but I haven't found anything.

Cryptographically strong seeded pseudo random number generator suggests the same algorithm, but only uses one hash function contrary to what I'm suggesting. The selected answer says to use two hash functions, but I couldn't find more details in the literature.

Is this algorithm real? What is the name of it?

• A couple of examples Can a cryptographic hash be used as a cryptographic RNG? . Using a hash function as a random number generator, Would it be secure to generate random number using AES? Where see NIST SP 800-90 for hash (and HMAC) based RNGs Commented Oct 10, 2021 at 19:02
• The question is what the conditions on $f$ and $g$ are. In general it's clearly false, just choose $f=g$. Commented Oct 11, 2021 at 14:31
• @Maeher I edited the question. The condition on $f$ and $g$ is that they are unrelated/independant from each other. Commented Oct 11, 2021 at 20:03
• If f and f are independent random functions, this shouldn't be tricky to prove. I'm not sure if there's a weaker condition that allows a proof though. Commented Oct 13, 2021 at 10:12