# Re: What is distribution ensemble ?

*From*: crypter <crypter00@xxxxxxxxx>*Date*: Thu, 2 Oct 2008 13:57:52 -0700 (PDT)

On Oct 1, 9:00 pm, Amit <amitabh...@xxxxxxxxx> wrote:

On Oct 2, 2:09 am, Ilmari Karonen <usen...@xxxxxxxxxxxxxx> wrote:I think this is someway right... but the problem is we have only one

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 -

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 ?

.

**References**:**Re: What is distribution ensemble ?***From:*Ilmari Karonen

**Re: What is distribution ensemble ?***From:*Amit

- Prev by Date:
**Re: Is fast variant of Paillier insecure?** - Next by Date:
**Re: Universally composable protocol....** - Previous by thread:
**Re: What is distribution ensemble ?** - Next by thread:
**Re: What is distribution ensemble ?** - Index(es):