passphrases with more than 160 bits of entropy
Perry E. Metzger
perry at piermont.com
Wed Mar 22 13:58:32 EST 2006
leichter_jerrold at emc.com writes:
> | Let me rephrase my sequence. Create a sequence of 256 consecutive
> | bytes, with the first byte having the value of 0, the second byte the
> | value of 1, ... and the last byte the value of 255. If you measure
> | the entropy (according to Shannon) of that sequence of 256 bytes, you
> | have maximum entropy.
>
> Shannon entropy is a property of a *source*, not a particular sequence
> of values. The entropy is derived from a sum of equivocations about
> successive outputs.
>
> If we read your "create a sequence...", then you've described a source -
> a source with exactly one possible output. All the probabilities will
> be 1 for the actual value, 0 for all other values; the equivocations are
> all 0. So the resulting Shannon entropy is precisely 0.
Shannon information certainly falls to zero as the probability with
which a message is expected approaches 1. Kolmogorov-Chaitin
information cannot fall to zero, though it can get exceedingly small.
In either case, though, I suspect we're in agreement on what entropy
means, but Mr. Perez is not familiar with the same definitions that
the rest of us are using.
Perry
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