Re: Good enough for crypto?

On Fri, 28 Nov 2003 21:58:02 +0000, Scott Wilber wrote:

> In my opinion, there are three types of entropy that are commonly in
> use.  Only Quantum Entropy, deriving from a pure quantum process, is a
> true entropy source.  The purest (theoretically simplest) type of
> quantum entropy is produced by "splitting" a single polarized photon
> with a polarization beam splitter rotated to produce an exact 50/50
> probability of the photon exiting either the vertical or horizontal
> port. The photons are detected by one of two single-photon detectors
> located at each of the output ports.  Of course, there is no such
> thing as a split photon; this is a mathematical abstraction describing
> the photon's probability function or "quantum wave".
> 
> The second type of entropy is actually chaotic complexity.  This is
> the most common "entropy" source used in true (non-deterministic)
> random number generators.  Examples are, as mentioned; Lavarand, pure
> thermal noise, mechanical lottery machines and chaotic analog
> circuits.  There is little to no true entropy produced by these
> sources; however, they do generally meet the present criteria for true
> randomness.  This is because the level of chaotic complexity is so
> high that consecutive points become theoretically unpredictable.
> (See Lyapunov Exponents http://hypertextbook.com/chaos/43.shtml )
> This does not mean that these systems will always remain entirely
> unpredictable; only that our level of mathematical sophistication and
> physical measurement are too limited to do so today.

In general, your statement that physical chaotic systems do not
contain real entropy is wrong. A fundamental characteristic of all
chaotic systems is that infinitesimal changes in the initial
conditions will eventually lead to macroscopic differences. When the
system does not contain any entropy, as you claimed, it should be
possible to fully predict all outputs. But because the system is
chaotic this is only possible when the initial state (plus all other
external inputs) is completely known. But for virtually all relevant
physical systems it is fundamentally impossible to know the initial
state completely, because of Heisenberg's uncertainty relation.  Any
advances in mathematics or physics can only reduce our estimation of
the actual entropy in a given sample of such a physical chaotic
system, but they will never be able to reduce the entropy to zero.

greetings,

Ernst Lippe