I\'m looking into \"bitcoin like\" mining processes. Say a security process uses

Question

I'm 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 chaotic systems?

Explanation / Answer

In chaos theory the defining attribute of a chaotic system is that small changes in the starting state tend to compound. If you look at the internal round structure of many hash functions, you will see a similar phenomenon: a single bit's change in the input will spread more and more evenly to all the state bits as you go through the rounds, until it is (assumed to have) evenly spread to all the bits.

If you iterate further, taking a hash of a hash etc., you would eventually find attractors. Both fixed points and cycles are possible. However, the mathematical structure of a hash function has been designed to resist analysis trying to find these attractors and the time to find them or end up in them by brute force is huge for secure-sized hash functions. If would on average take approximately 2n/2 iterations to end up in a cycle.

Now, those attractors do not matter in the least for most applications of hash functions, including the proof of work used in cryptocurrencies. Only one or two iterations of the hash function are used in the proof of work. The output image of a 256-bit hash only loses around a bit of its size from two iterations, so it is nowhere near to getting to those attractors.

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