Re: Does good compression = good encryption?

Dennis Clark (dennis@nospam.ilanet.slnsw.gov.au)
Thu, 16 Nov 1995 10:51:45 +1100 (EST)

In previous mail, Cameron Hutchison wrote:
>
> Once upon a time Dennis Clark said...
> >
> > A clearer way of saying that they "reduce redundancy" is to say that
> > they increase the entropy (randomness) of a message.
>
> I was going to say this too, but then I decided to look it up.
> Compression does not increase the entropy of a message. The entropy is
> related to the message; compression does not change the message, just
> its representation. Also, entropy is the "amount of information" in
> a message, not its randomness.

Serves me right for using terminology I'm not totally familiar with.
What I meant was the "average entropy per byte" (there's a special
term for that I'm sure, it was covered in the subject "Communications
Software"). This _DOES_ equate to a sort of "randomness", ie. if a single
byte contains a high amount of information, it is because it shares less
in common with the other bytes in the message, and is therefore "more
random".

Looking at what you said, its obvious that this average entropy per byte
_DOES_ increase by compression (if total entropy stays the same, but the
number of bytes decreases, then average entropy _MUST_ rise).

I can only assume that encryption increases total entropy of a message
(where would the extra "information" come from, tho?). If this is the
case, the average entropy per byte would also increase with encryption
(because most ciphers keep the total message size the same).

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Dennis Clark | Email: dennis@nospam.ilanet.slnsw.gov.au
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