[aklug] Re: [OT] Re: random bits vs random Hex

On Tue, May 28, 2013 at 10:25 PM, <bryanm@acsalaska.net> wrote:

> That brings up an interesting point (which was not part of the original
> post). What if you change to a base that doesn't match so well? For
> example, take a random string of bits, group them into triplets, and
> convert each one to a decimal digit.
>
> 001 011 000 110 111 010 010 101
> ..1 ..3 ..0 ..6 ..7 ..2 ..2 ..5
>
> If the original string of bits is random, each new bit is equally likely
> to take either of the possible states {0,1}. When converted to decimal,
> though, each new digit is equally likely to be one of 0 through 7, but
> it will never be 8 or 9. Whether that is useful information, of course,
> depends on the application.
>

I'm fairly certain changing the base is irrelevant. Entropy doesn't change
with a base change; the number of possible states (i.e., base) is not a
measurement of the entropy in a given string.

At its simplest, a pile of coin flips {0,1} could be just as random as a
game of Mastermind. More, in fact.

The idea of changing bases is intriguing, though. Weak steganography; and
one of my favorite bits of smartness, Huffman coding, is essentially a
variable base, explicitly for entropy encoding.

jermudgeon

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Received on Tue May 28 22:51:23 2013