Entropy Definition (was Re: passphrases with more than 160 bits of entropy)

[Aram Perez]

On Mar 22, 2006, at 2:05 PM, Perry E. Metzger wrote:

> Victor Duchovni <Victor.Duchovni at MorganStanley.com> writes:
>> Actually calculating the entropy for real-world functions and  
>> generators
>> may be intractable...
>
> It is, in fact, generally intractable.
>
> 1) Kolmogorov-Chaitin entropy is just plain intractable -- finding the
>    smallest possible Turing machine to generate a sequence is not
>    computable.
> 2) Shannon entropy requires a precise knowledge of the probability of
>    all symbols, and in any real world situation that, too, is
>    impossible.

I'm not a cryptographer nor a mathematician, so I stand duly  
corrected/chastised ;-)

So, if you folks care to educate me, I have several questions related  
to entropy and information security (apologies to any physicists):

* How do you measure entropy? I was under the (false) impression that  
Shannon gave a formula that measured the entropy of a message (or  
information stream).
* Can you measure the entropy of a random oracle? Or is that what  
both Victor and Perry are saying is intractable?
* Are there "units of entropy"?
* What is the relationship between randomness and entropy?
* (Apologies to the original poster) When the original poster  
requested "passphrases with more than 160 bits of entropy", what was  
he requesting?
* Does processing an 8 character password with a process similar to  
PKCS#5 increase the entropy of the password?
* Can you add or increase entropy?

Thanks in advance,
Aram Perez

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