# are deterministic pseudorandom based hash functions chaotic?

Im looking into "bitcoin like" mining processes. Say a security process uses a hash of data as proof that the data was known at some point in time.

from what I understand, hash functions are pseudorandomly generated based on the initial seed (the raw data).

if the hash function is chaotic, then the seed data should have strange attractors. if so, then i may be able to map a seed to its attractor and "pre-mine" using attractor buckets.

Are these pseudorandom functions deterministic chaos?

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"chaos", "deterministic chaos" - that's not a useful concept in crypto (they're buzzwords). Anyway, you haven't defined those terms. I suggest you edit your question to provide a precise technical definition of what you mean by chaos, and what the motivation/context for the question is, and what problem you're actually trying to solve. –  D.W. May 12 at 22:14
its not a buzzword at all. "Small differences in initial conditions (such as those due to rounding errors in numerical computation) yield widely diverging outcomes for such dynamical systems, rendering long-term prediction impossible in general.[1] This happens even though these systems are deterministic, meaning that their future behavior is fully determined by their initial conditions, with no random elements involved.[2] In other words, the deterministic nature of these systems does not make them predictable.[3][4] This behavior is known as deterministic chaos, or simply chaos. " –  jaybny May 12 at 22:17
Again, I suggest you edit your question to try to provide a precise technical definition. You might start by quantifying what "small" means in this context, and what you mean by a "difference", and what you mean by "initial conditions", in this specific context. If you can't do that.... you might want to re-think your "not a buzzword" stance. This site is best used for well-posed technical questions, not for open-ended or subjective discussions, so it's important to spend a lot of thought into how to frame a precise technical question. –  D.W. May 12 at 22:20
for example a tent map is chaotic. en.wikipedia.org/wiki/Tent_map –  jaybny May 12 at 22:23
@D.W. im asking how the pseudorandom functions work, and my hunch is that its chaotic. do you know the answer? –  jaybny May 12 at 22:31

For instance, the graph of a random function $\{0,1\}^n\to \{0,1\}^n$ typically has the following form: there is a single large cycle of length $\Theta(2^{n/2})$, such that most inputs eventually lead to the cycle. Starting from a random input, the length of the path that leads to that large cycle is typically $\Theta(2^{n/2})$. This does not break standard schemes for hash-chaining, proof-of-work, Bitcoin, etc., as the parameters for their hash function is chosen to take this structure into account.