passphrases with more than 160 bits of entropy

| 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.

							-- Jerry

------------------------------------------------------------
---------
The Cryptography Mailing List
Unsubscribe by sending "unsubscribe
cryptography" to majordomometzdowd.com

leichter_jerroldemc.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

------------------------------------------------------------
---------
The Cryptography Mailing List
Unsubscribe by sending "unsubscribe
cryptography" to majordomometzdowd.com