[21496] in cryptography@c2.net mail archive
Re: passphrases with more than 160 bits of entropy
daemon@ATHENA.MIT.EDU (leichter_jerrold@emc.com)
Wed Mar 22 13:49:10 2006
X-Original-To: cryptography@metzdowd.com
X-Original-To: cryptography@metzdowd.com
From: leichter_jerrold@emc.com
To: aramperez@mac.com
Cc: cryptography@metzdowd.com
Date: Wed, 22 Mar 2006 13:32:51 -0500
| 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
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