Re: Who's familiar with random oracle model?

From: Anton Stiglic (astiglic_at_okiok.com)
Date: 11/01/04 

Date: 1 Nov 2004 06:15:06 -0800

"D. J. Bernstein" <djb@cr.yp.to> wrote

> If X is a countable set, here's what a ``distribution on X'' is: it's a
> function f from subsets of X to nonnegative real numbers, satisfying the
> axioms f(X) = 1 and f(S_0 union S_1 union ...) = f(S_0) + f(S_1) + ...
> whenever S_0, S_1, ... are disjoint subsets of X.
>
> Consider, for example, the function f on subsets of {heads,tails}
> defined by
>
> f({}) = 0,
> f({heads}) = 1/3,
> f({tails}) = 2/3,
> f({heads,tails}) = 1.
>
> This function is a distribution on {heads,tails}.
>

I looked at your defintion and the definitions at MathWorld:
http://mathworld.wolfram.com/DistributionFunction.html
http://mathworld.wolfram.com/ProbabilitySpace.html

but I am still confused on when you should talk about a distribution
function or when it is more appropriate to talk about a probability
space.

Based on the definition from MathWorld, a distribution function
relates to a variate (which is a set of random variables that obey a
given probability law???) and a function P that defines a probability
law, while on the other hand the definition of probabilistic space
(given at MathWorld) relates to a triple S, S', P where (S, S') forms
a mesurable space (is this the sample space??) and P defines a
probability law. Is there some definition that gives a bit more of
intuition for non mathematicians?

I found that in crypto papers they often use bad terminology, and that
doesn't help me (I get slumpy with the terms). Could you shed some
lite?

--Anton

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