Re: What is distribution ensemble ?



On Oct 1, 9:00 pm, Amit <amitabh...@xxxxxxxxx> wrote:
On Oct 2, 2:09 am, Ilmari Karonen <usen...@xxxxxxxxxxxxxx> wrote:





On 2008-09-30, Sergei <silent...@xxxxxxxxx> wrote:

Not quite sure that this is correct. As far as I understand, the
definition of indistinguishability of distribution ensembles has
nothing to do with convergence of these sequences. It is just a
statement that random variables X_k and Y_k (the k are the same, of
course) are indistinguishable. The ensembles are introduced to work
with cryptographic primitives without a fixed length of the output
(e.g. 1, ...,n, n+1, etc.).

So, let say that we have distribution ensembles X={X_1, X_2,...} and
ensemble Y={Y_1, Y_2, ...} and they are computationally
indistinguishable, then X_1 is computationally indistinguishable from
Y_1, X_2 from Y_2, etc.

From what little I've read, I doubt that (though it would be nice if
someone could give a definitive answer).

It's not even clear to me what the notion of two distributions (rather
than ensembles) being indistinguishable (while not being identical)
would mean: to have (either statistical or computational)
indistinguishability, you need _something_ to be a negligible function
of _something_, and I'm not sure what that second something would be,
if not the index to the ensemble.

--
Ilmari Karonen
To reply by e-mail, please replace ".invalid" with ".net" in address.

Imagine two experiments (1) tossing a die and (2) tossing 6 coins at
once.
Let the outcome of (1) be the number on the die and that of (2) be the
sum of heads on each toss.
Consider the sequence of outcomes of both experiments repeated
infinite times. Each sequence is an ensemble.. They are
distinguishable in this case - Given the two ensembles, it is possible
to decide which was from which experiment.- Hide quoted text -

- Show quoted text -
I think this is someway right... but the problem is we have only one
random variable when tossing a die...even if u toss infinite number of
times...
Any thoughts to the definition/explanation that I had provided
earlier...

(just reworded)
That is ensemble is a sequence of random variables defined over the
sample space...
as mentioned earlier

Event : Roll die say n times..

For example rolling a die :
X_1 = o/p of a die
X_2 = avg. of rolling a die
X_3 = sum of rolls is even or odd

etc....

Similary we can define the other ensemble for Y for another event ...

what say ?


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