[21510] in cryptography@c2.net mail archive
Entropy Definition (was Re: passphrases with more than 160 bits of entropy)
daemon@ATHENA.MIT.EDU (Aram Perez)
Wed Mar 22 21:45:09 2006
X-Original-To: cryptography@metzdowd.com
X-Original-To: cryptography@metzdowd.com
In-Reply-To: <87y7z2rv86.fsf@snark.piermont.com>
From: Aram Perez <aramperez@mac.com>
Date: Wed, 22 Mar 2006 15:29:07 -0800
To: Cryptography <cryptography@metzdowd.com>
On Mar 22, 2006, at 2:05 PM, Perry E. Metzger wrote:
> Victor Duchovni <Victor.Duchovni@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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