passphrases with more than 160 bits of entropy

Perry E. Metzger perry at piermont.com
Wed Mar 22 12:04:15 EST 2006


Aram Perez <aramperez at mac.com> writes:
>> Entropy is a highly discussed unit of measure.
>
> And very often confused.

Apparently.

> While you do want maximum entropy, maximum
> entropy is not sufficient. The sequence of the consecutive numbers 0
> - 255 have maximum entropy but have no randomness (although there is
> finite probability that a RNG will produce the sequence).

One person might claim that the sequence of numbers 0 to 255 has 256
bytes of entropy.

Another person will note "the sequence of numbers 0-255" completely
describes that sequence and is only 30 bytes long. Indeed, more
compact ways yet of describing that sequence probably
exist. Therefore, we know that the sequence 0-255 does not, in fact,
have "maximum entropy" in the sense that the entropy of the sequence
is far lower than 256 bytes and probably far lower than even 30 bytes.

Entropy is indeed often confusing. Perhaps that is because both the
Shannon and the Kolmogorov-Chaitin definitions do not provide a good
way of determining the lower bound of the entropy of a datum, and
indeed no such method can exist.

Perry

---------------------------------------------------------------------
The Cryptography Mailing List
Unsubscribe by sending "unsubscribe cryptography" to majordomo at metzdowd.com



More information about the cryptography mailing list