Comment by hinoki

4 years ago

The summary says that it works if it is a measurable function [0], which is structure preserving. So sha256 would scramble the input too much for it to be detected here.

[0] https://en.m.wikipedia.org/wiki/Measurable_function

I've not yet read the article, just the abstract. But the abstract is pretty precise, and being "measurable" is a very weak constraint. For (computationally) complex functions like a hash, my first guess is the "escape clause" is in the number of samples needed for the statistic to converge to its expected value.

Any function that can be implemented in a computer is a Lebesgue measurable function.

  • I don't doubt it, but I don't immediately see the proof either. What's the key idea?

    • Most spaces that computers deal with are basically discrete.

      Technically this may not always be the case but it's very hard to construct a convincing counter example.