[Cryptography] Entropy is forever ...
ray at unipay.nl
Fri Apr 17 17:19:33 EDT 2015
> Agreed. It is a fool's errand to assess the randomness
> of a "random number". For starters, there is no such
> thing as a "random number".
> -- If it's a number, it's not random.
> -- If it's random, it's not a number.
> -- You can have a random /distribution/ over numbers,
> but then the randomness is in the distribution, not
> in any particular number that may have been drawn
> from such a distribution.
On the other hand, there is a notion of algorithmic complexity of an
individual string, i.e., the length of the shortest program that
produces it in some universal programming language. In this sense,
most strings are (Kolmogorov) random but those easy to generate (e.g.,
all nines, or the digits of pi) are not.
There are formal relationships between K-randomness and entropy. And
also with computational complexity, e.g., a K-random oracle separates
P and NP.
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