From: Hartmut (hartmut@ccc-hanau.de)
Date: Tue Sep 24 2002 - 16:09:36 MDT
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gts wrote:
> > but random is not only defined over an equal outcome of 1's
> > and 0's. You need also to take into account all sequences like
> > 00, 01 and so on (sequences of three bit ...). So if there exist more
> > long-short outcomes, then you will, because of the determined changing
> >
> > of the rule, get more sequences of 01 or 10 than 00 or 11. But for
>
> each
>
> > of the four sequences should be the probability 1/4.
>
> I don't believe that is true. If a given number in the final unbiased
> sequence has equal probability of being 1 or 0 (as is the case) then
> each of the two possible outcomes for a given trial has probability 1/2.
> It follows that each of the four possible outcomes for two successive
> trials has probability 1/4.
Sorry, but that is not correct. You can't say, that if 0 and 1 have
probability 1/2, the probablity distribution also holds for longer subseries.
Consider the following sequence: 010101010101 .... (only long-short events, I
know, this won't happen :-) )
Here 0 and 1 each have probability 1/2, but, depending on where you do the
cut, 01 and 10 each have probability 1/2 and 00 and 11 each have probability
0.
This is holds for longer sequences too as you can see here: 001100110011 .....
Now all sequences of two digits have probability 1/4 and 1 and 0 have
probability 1/2 but as you can see the sequence is also easily predictable,
because the groups of three following digits don't have equal probability.
010 and 101 for example do have probability 0.
As short-long would have a higer probability than long-short, there would be a
higher probability for series of 101... (this is symetric -> also if
long-short gets more percent). This would effectivly help a cryptattacker as
for this person the space of random numbers created by your method got a
little bit narrower.
Your method would only work, if 0s and 1s got each 50% probability, but then
it won't be neccessary to switch after each event.
Bye
Hartmut
- --
"The only purpose for which power can be rightfully exercised over any
member of a civilized community, against his will, is to prevent harm to
others. His own good, either physical or moral, is not a sufficient
warrant." --John Stuart Mill
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