Re: 31 bit pseudo-random number gen in C, C++ & d*** assembly code

From: Will Dickson (wrd_at_glaurung.demon.co.uk)
Date: 10/09/05

  • Next message: obie: "Re: Help needed to evaluate crypto software" 
    Date: Sun, 09 Oct 2005 02:56:26 +0100

    On Sat, 08 Oct 2005 18:28:03 -0400, John E. Hadstate wrote:

    >> Claude Shannon didn't pick the term 'entropy' by
    >> coincidence. Thermodynamic entropy and cryptographic entropy are both
    >> the same function of the probabilities of a system being in each of its
    >> possible states.
    >>
    >>
    > What does it mean for a continuous, physical system to be "in each of
    > its possible states"? So far as I know, thermodynamics pre-dates
    > quantum theory and, as such, views the physical world as a continuum.

    There is a "macroscopic" expression of thermodynamics which considers the
    behaviour of the system in terms of a set of "state variables", which are
    continuous. However, there is also a "microscopic" expression which views
    the system in terms of the statistics of a very large collection of very
    small things, which each hold differing amounts of energy, momentum etc.
    (This is not even close to a real quantum-mechanical treatment - it's much
    simpler.) It can be shown that the two expressions are equivalent - you
    can derive one from the other.

    The microscopic-viewpoint definition for thermodynamic entropy is of the
    same form as the definition of cryptographic entropy.

    I have it on good authority (one of my erstwhile physics lecturers,
    although chasing this up has been on my to-do list for years now, and I
    don't know the detailed argument) that the relationship between
    informational and thermodynamic entropy goes deeper than this. The example
    I was given is that this relationship is required in order to analyse
    systems such as Maxwell's Demon.[1]

    Will.

    [1] A thought-experiment. This demon guards a tiny hole in a partition
    separating two containers of gas at equal temperature. When a particularly
    fast molecule heads for the hole in one direction, the demon opens the
    hole and lets the molecule through. When a particularly slow molecule
    approaches the hole from the other side, the demon opens the hole and lets
    that through as well; otherwise it keeps the hole closed. In this way it
    makes one side hotter and the other colder.

  • Next message: obie: "Re: Help needed to evaluate crypto software"
    • Quantcast