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If you found a distribution pattern in a hash function, it's no longer a cryptographic hash function.

There is no such thing in the real world as continuous, it is impossible to measure or quantify. Saying that this disqualifies the use of "gaussian" for a random distribution over a finite field is not a tenable position due to the nature of computation.

The expression "cryptographic hash function" itself implies apparent continuity of distribution. As soon as the discontinuity is found in the distribution its security is busted.

Pip the WoT guy 2y ago

Yes, no such thing as continuity in the real world, real number are not physically real.

Buuut, they are very useful for making computations easiers.

I never disqualified the utility of the gaussian distribution, I simply pointed out the obvious that Gaussian != Uniform

> the expression "cryptographic hash function" itself implies apparent continuity of distribution.

No, it implies apparent uniformity of disitribution.

Continuity is another (topological) property.

f^(-1) (A) is an open set for every open set A.

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Discussion

ᴛʜᴇ ᴅᴇᴀᴛʜ ᴏꜰ ᴍʟᴇᴋᴜ 2y ago

gaussian is continuous uniform distribution. aliasing is an inherent property of finite fields. if this error of precision says it's not gaussian than what use is the expression "gaussian distribution" anyway?

perhaps ergodicity is a more accurate expression, since this doesn't carry baggage of theoretical and impossible things with it?