passphrases with more than 160 bits of entropy

leichter_jerrold at leichter_jerrold at
Wed Mar 22 13:32:51 EST 2006

| 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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