Re: AES and Diehard

From: Mok-Kong Shen (mok-kong.shen_at_t-online.de)
Date: 09/14/03 

Date: Sun, 14 Sep 2003 18:50:57 +0200

"Douglas A. Gwyn" wrote:
>
> Mok-Kong Shen wrote:
> > Knuth uses 'random' almost synonymously with 'pseudo-random'.
>
> No, he doesn't:
> "How can a sequence generated in such a way be random,
> since each number is completely determined by its
> predecessor? ... The answer is that the sequence *isn't*
> random, but it *appears* to be. ... Sequences generated
> in a deterministic way such as this are often called
> *speudorandom* or *quasirandom* sequences in the highbrow
> technical literature, but in most places of this book we
> shall simply call them random sequences, with the
> understanding that they only *appear* to be random."
> I.e., he explicitly establishes that he is using an
> informal term solely within the context of the book.
> Presumably that was simply to improve readability, since
> the entire chapter was concerned with generation of
> pseudorandom sequences, testing them against the random
> model, and generating nonuniformly distributed variates.
>
> If you want to determine what "random" means in general,
> you have to look outside a context where it has explicitly
> be introduced as shorthand for the technically correct
> "pseudorandom". Any decent textbook on statistics ought
> to provide a suitable definition, although most likely
> it will be of "random variable" rather than "random" as
> such. A *random sequence* is a sequence of values of a
> random variable, and can be thought of as outcomes of a
> sequence of executions of some definite experiment where
> each execution has exactly the same initial context.
> Pseudorandom sequences do not have the same context for
> production of each value and thus are not random
> sequences.

Mmm. Look at how the statisticians work. Look at any
numerical libraries for statistical applications.
Do they use any 'true randomness'? If pseudo-randomness
couldn't be (practically) a substitute of the theoretical
(perfect) randomness, then they would have got stuck. I
mentioned in a previous post a book where 'random' is
used implicitly for 'peudo-random'. To be definite, here
is the title of it:

  J. Dagpunar, Principle of random variate generation.
  Clalendon Press.

M. K. Shen

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