Re: More about MT19937 in crypto

From: Mok-Kong Shen (mok-kong.shen@t-online.de)
Date: 03/06/03 

From: Mok-Kong Shen <mok-kong.shen@t-online.de>
Date: Thu, 06 Mar 2003 10:01:33 +0100

Mok-Kong Shen wrote:
>
> Benjamin Goldberg wrote:
> >
> [snip]
> > You're given input bits; take them two at a time, and process them as
> > follows:
> >
> > A B
> > 00 - 0
> > 01 1 -
> > 10 0 -
> > 11 - 1
> >
> > The bits of the A column get outputed directly, and the bits of the B
> > column get sent to the next computation unit to be unbiased in an
> > identical manner.
> [snip]
>
> No question that this processing is o.k. I just want
> to say that the above table reminds me of some
> similarity (not identity!) with that of JK-flipflop
> which I vaguely remember was mentioned somewhere
> as a way of postprocessing bit streams. (It certainly
> hasn't the good theoretical basis as the above, if
> I don't err.)

I do think now that one could give a rationale for
the scheme as follows: Let's suppose that all the
bits emitted by the device up to a certain point are
unbiased. If the following input is 01 or 10, then
one adds one unbiased bit according to von Neumann.
If the following input is 00 or 11, with probabilities
unequal, say, q and 1-q, and let the last emitted
bit be u, then one has probability of q to add
a bit the same as u and probability of 1-q to add
a bit that is the complement of u. But u is by
assumption unbiased, hence the bit added is also
unbiased. (cf. xoring a sequence of uniform
distribution with one of arbitrary distribution
results in a uniform distribution.)

Could the above argument be o.k.? If yes, then the
scheme seems to have the advantage of simpler
implementation and higher efficiency than the
two-level von Neumann. (Would someone already having
the needed testing software and materials at hand
like to give it a trial?)

M. K. Shen

Relevant Pages

  • Re: HUP Fails Via Nonexistent Distributions 2: The Uniform Claim
    ... > Max Jammer's The Philosophy of Quantum Mechanics, Wiley: ... Also, the probability that q is in [L1, ... > The uniform probability distribution in mathematical ... the graph of a uniform distribution is a horizontal line ...
    (sci.physics)
  • HUP Fails Via Nonexistent Distributions 2: The Uniform Claim
    ... Max Jammer's The Philosophy of Quantum Mechanics, Wiley: ... Also, the probability that q is in [L1, ... The uniform probability distribution in mathematical ... the graph of a uniform distribution is a horizontal line ...
    (sci.physics)
  • Re: Simulated Annealing
    ... The thing on the right is the probability of a change. ... > has a higher probability then pure chance (uniform distribution) then ...
    (sci.math)
  • Re: Probability in an infinite sample space
    ... It is often assumed that if no distribution is specified, ... no such thing as a uniform probability distribution on a countably ... example, there is a uniform distribution on the unit interval, ... I can't form the sum of the probability of a randomly selected element ...
    (sci.math)
  • Re: Pigeons, People, and Priors
    ... the variance of the probability generator go to zero you have a continuum ... a random-interval 60 s schedule is not. ... The Exponential Distribution ... I probably should have used the phrase "statistical learning theory" rather ...
    (comp.ai.philosophy)
Quantcast