For people who understand this better. When mining, isn’t it better to stick with a template for a relatively longer time, and not keep adding removing transactions from it?
This question has nothing to do with the options above.
I was just wonder, because when I look at the Ocean dashboard, the template changes every second. And for some reason I feel it is more probably to hit a block if the template doesnt change for say 3 minutes.
Might be completely wrong but that’s why I’m asking.
I think you are wrong because the probability of finding a valid block at trial number N should follow a Geometric Distribution.
The Geometric Distribution has the property of being "memoryless".
Correct, it makes no difference. This indifference is part of what makes a hash function a "cryptographic hash function". The distribution is nearly gaussian, close enough to call it random.
you probably wanted to say uniform distribution.
Hash function have the design goal of inducing a probability distribution on their image which is closer to a uniform distribution as possible.
So the probability that h(X) = k is the same for every k.
continuous uniform distribution
https://en.wikipedia.org/wiki/Probability_distribution#Absolutely_continuous_probability_distribution which is commonly associated with gaussian normal distributions.
of course it's discrete integers but continuous implies total randomness since all bits are at play and not any holes in it or symmetries.
I don't understand why you say Gaussian, when it actual fact is uniform.
Also, it's discrete and not continuous, because the Image of all hash functions is discrete (countable infinity of rational numbers).
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.
The other thing that you can't say either is that it's not deterministic, because without determinism the hash function is not useful.
Yeah yeah, in this we agree. I was just lazy.
One should say:
X is a random variable representing the choice of a message at random (under probability distribution PX).
Then h(X) is a random variable, that induce a different probably distribution bla bla.
it's super magical stuff anyway. non-crypto people don't get it.
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.
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?
The template has to be at least subtly different for every hash (which a mining chip does billions of every second)
I’ve never heard of this before, why would the template have to change each hash?
Interesting. I didn’t know that. Thank you.
