passphrases with more than 160 bits of entropy

Victor Duchovni Victor.Duchovni at
Wed Mar 22 16:46:19 EST 2006

On Wed, Mar 22, 2006 at 01:58:26PM -0600, Matt Crawford wrote:

> If you have a generator of 8-bit random numbers and every sample is  
> independent and uniformly distributed, and you ran this for a  
> gazillion iterations and wrote to the list one day saying the special  
> sequence { 0, 1, 2, ..., 255 } had appeared in the output, that's a  
> different story.  But still, we would talk about the entropy of your  
> generator, not of one particular sequence of outputs.

We may want to cut the OP some slack... When a sequence is computed
from output of a generator, it is meaningful to ask how much entropy the
sequence retains... If regardless of the generator output the sequence
is { 0, 1, ..., 255 }, we have zero entropy. Otherwise (and in any case)
the entropy can in theory be computed from the probability distribution
of the possible output sequences which is in principle available from
the distribution of the generator outputs and the deterministic functions
that create the sequence.

Actually calculating the entropy for real-world functions and generators
may be intractable...


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