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Why should hard be secure enough? Information and non-invertibility
11–20 of 48 posts
Re: Why should hard be secure enough? Information and non-invertibility
#12There are some technical issues with the article, but the point the author makes (hashes are imperfect since they carry some information, but it is really hard or even impossible to do something better) still stands.
Re: Why should hard be secure enough? Information and non-invertibility
#13I don't understand why the x^2 thing is interesting at all. If I multiply x by 0, the distribution is now just 0. If I take abs(x) now it is positive. Are these confusing to anyone?
In code: i(x) = x // We know i is uniformly distributed just as x is - preserve "unknowability" f(x) = x^2 // We know f has higher probability between [0,1] than [1,2] g(x) = 1 // We know g is always 1. Just because your inputs are random, doesn't mean your output is - the implementation matters.
... which is exactly what I said. What are you adding here?
Re: Why should hard be secure enough? Information and non-invertibility
#14While I like the style of writing very much, I don't like the pseudo-scientific take on the 'problem'. In any probability class, you will learn that you can't have an uniform distribution on an infinite set.
Nitpicking, but you can have a uniform distribution on the unit interval, which is infinite :). What you cannot have is a uniform distribution on an unbounded set. Edit: As pointed out, the correct assumption is not unboundedness, but having infinite measure (since then no normalization constant exists). I thought they were equivalent, but a simple counterexample is [0,1] \cup Z.
It's an interesting exercise in measure to figure out what falls apart between a uniform distribution on [0,1] and the lack of one on [0, inf]. (Adding a point at infinity to compactify the set, which makes the two intervals topologically equivalent.)
Re: Why should hard be secure enough? Information and non-invertibility
#15While I like the style of writing very much, I don't like the pseudo-scientific take on the 'problem'. In any probability class, you will learn that you can't have an uniform distribution on an infinite set.
Which aspect of the writing style appealed to you?
Re: Why should hard be secure enough? Information and non-invertibility
#16diogomonicapt writes
"Light does not travel at the speed of light (no pun intended) because it is hard for it to do otherwise. No. It travels (and does so at that particular speed), because it is impossible for light to do otherwise."
Actually,the speed of light in a vacuum is an upper bound. The actual speed of light can be substantially slower. https://en.wikipedia.org/wiki/Slow_light
Some cosmological theories do not require the speed of light to be constant and fixed, and replace that axiom with requirements on the relationship of the speed of light with other physical parameters.
Re: Why should hard be secure enough? Information and non-invertibility
#17This article takes a very long time to make an elementary point: if x is a uniformly distributed random variable, f(x) is not a uniformly distributed random variable if f is non-linear.
Which is visualized nicely in these 20 second videos.
Non-linear transform of a random variable:
https://www.youtube.com/watch?v=hQjk4ClpuUk
Linear transform of a random variable:
Re: Why should hard be secure enough? Information and non-invertibility
#18If we have any probability distribution, that tells us something about x. If someone tells us that license plates numbers are uniformly distributed, we can pretend to be a license plate maker by sampling from a uniform distribution, and nobody else could tell the difference by looking at the license plate numbers we make. Zero information is more like not knowing what probability distribution a variable comes from. R…
Uniform distribution gives minimum information, assuming the range is known. Any other distribution will give more information. Talking about information capacity of coded messages, here.
I think what you are saying when you use the phrase "zero information" is really "zero knowledge".
Re: Why should hard be secure enough? Information and non-invertibility
#19While I like the style of writing very much, I don't like the pseudo-scientific take on the 'problem'. In any probability class, you will learn that you can't have an uniform distribution on an infinite set.
Nitpicking, but you can have a uniform distribution on the unit interval, which is infinite :). What you cannot have is a uniform distribution on an unbounded set. Edit: As pointed out, the correct assumption is not unboundedness, but having infinite measure (since then no normalization constant exists). I thought they were equivalent, but a simple counterexample is [0,1] \cup Z.
Mathematician here. You can't have a uniform distribution on a set with infinite measure. Unbounded sets are fine as long as they have finite measure.
Re: Why should hard be secure enough? Information and non-invertibility
#20diogomonicapt writes "Light does not travel at the speed of light (no pun intended) because it is hard for it to do otherwise. No. It travels (and does so at that particular speed), because it is impossible for light to do otherwise." Actually,the speed of light in a vacuum is an upper bound. The actual speed of light can be substantially slower. https://en.wikipedia.org/wiki/Slow_light Some cosmological theories do…
He didn't say "the speed of light in a vacuum", he just said "the speed of light". And in the next sentence he said
> … it is simply not possible for light to be still, or even propagate at a different speed in the same medium.
So he's already acknowledged the fact that the speed of light depends on the medium. His point, though, is that light must still travel at this speed (even though the speed itself depends on the medium).