Why should hard be secure enough? Information and non-invertibility
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Re: Why should hard be secure enough? Information and non-invertibility
#2I 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?
Re: Why should hard be secure enough? Information and non-invertibility
#3This 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.
Re: Why should hard be secure enough? Information and non-invertibility
#4"...if we have zero information concerning the value of x, than we are also clueless in what concerns the value of, say, x^2"
But that is not true, we have -some- information concerning the value of x, namely that the value of x is equiprobable.
Re: Why should hard be secure enough? Information and non-invertibility
#5While 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.
Re: Why should hard be secure enough? Information and non-invertibility
#6If 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. Rather than hiding "what value does x take", we can hide "what probability distribution does x come from". That's one level up. (Then you could ask what the likelihood of x having a given probability distribution is, and so on -- zero information is having none of this information, all the way up.)
Re: Why should hard be secure enough? Information and non-invertibility
#7While 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.
Re: Why should hard be secure enough? Information and non-invertibility
#8While 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.
Well, I was criticising the article in a condescending way, on very similar grounds, so you make a fair point ;)
Re: Why should hard be secure enough? Information and non-invertibility
#9I 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.
Re: Why should hard be secure enough? Information and non-invertibility
#10I 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?
It's confusing to me why the author is confused by these. As you say, he's literally saying "if I know nothing about x, then I should also know nothing about 0x". Wtf? No.