Re: Other Efforts

Eating Before Swimming (mathboy@sizone.org)
Wed, 11 Jun 1997 15:42:50 -0400 (EDT)


then saurvok@exo.com's all..

> So we could gamble and hope the this one time the key is closer to the
> front than the back and save time, or use the random method at get the 50%.

Ahem. How come there's no chance that your random method wont pick the
key LAST?

Lets say there are 10 possible keys. Lets say the solution is key 8.
Linear would suck: we'd have to search 80% of the keyspace to find the key.

So instead we do it randomly. We randomize the keys and hand them out in
this order:

9 7 1 4 5 2 10 3 6 8

Then your random method would lose out, having to search 100% of the key
space to find the key.

Of course the order we hand out the keys is random. So over many many
tries, the random method would average 50% searched before solution.

And, as you've already agreed, over many many tries the linear search
will average out to 50% as well.

Since we have NO knowledge of where they key is (too bad, huh? :),
starting anywhere in any order is just as good as anywhere else. For
every example you give which foils the linear search, I can give an exactly
equally probable scenario which foils your random search just as well
(and, in fact, EXACTLY as well).

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I suggest that if you want to continue this discussion you DO make an
attempt to understand the simple proof that Justin already outlined instead
of just saying "well, I dont get it, so, back to my version of the
argument".

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Another thing that irks me is this concept of "start" and "end" and to
a lesser extent, "order of keys". There is no real "linear order" at
all. There is no NATURAL order to the keys in the first place unless
you impose your own; in this case you might be thinking of ascii as an
ordering system. Now lets pretend you've worked black magic to run
Deschall under AIX properly niced (poke, poke! :) and it uses EBCDIC
instead of ascii... Just kidding!! (EBCDIC was an early form of
encryption known as a Ceasar cipher. Just kidding again! It was IBMs
own character numbering system.) Then, where do you start? Whats linear?

Since checking a key NEAR the solution key gives NO advantage to your search,
it doesnt matter what "order" you check it in. In fact there is no order
at all to the keys. Consider the keys to be a big messy moving jumbled
mass floating around. There's no order in that, and you just reach into
the mass and hand out keys to check in order, like pulling one name out of
a hat. You cant pull names out of a hat and say "we're getting closer!"
because you saw "joe" and think that that means "steve" is likely to
come next. If that is the case then the hat isnt a gged randomizer.

You cant say yer getting closer except by refering to te fact that
there are fewer keys left to check, as Rocke's updates tell us.

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I've been reading alot of cosmology/quantum theory (just the theory,
not the math! Im a wuss! :) lately... it seems to help one lose not
only your anthropomorphic points of view, but this euclidian sense of
"order" and "start"/"end" or "begginings" and "endings" of things...
not to mention "straight lines" (or sequential time for that matter!).
Abstract math is all the same huge beast no matter how you slice it,
cryptographically or cosmologically! There are some subtleties to wrap
the mind around and make sure you dont fall into the trap of false
assumptions which otherwise usually apply in everyday life.

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Mebbe some one can write a more formal proof for the gunk I expressed
in this message, or clean up any loose ends I've left...

/kc

--
Ken Chase mathboy@sizone.org Sonic Interzone $free$ email/news Toronto Canada
------------------------------------------------------------------------------
Join the DES Challenge! Wake up the US Govt!   www.frii.com/~rcv/deschall.htm

NB:Only 16000 P200-months CPU req'd to recover 56-bit IBM alliance keys! ** U.S. EXPORT LAWS MAY NOT APPLY TO YOUR COUNTRY: DEVELOP YOUR NATIONS' OWN CRYPTO-EXPORT INDUSTRY! USE 2048bit KEYS FREELY! FLAUNT YOUR SOVEREIGNTY! **

-- 
Ken Chase mathboy@sizone.org Sonic Interzone $free$ email/news Toronto Canada
------------------------------------------------------------------------------
Join the DES Challenge! Wake up the US Govt!   www.frii.com/~rcv/deschall.htm

NB:Only 16000 P200-months CPU req'd to recover 56-bit IBM alliance keys! ** U.S. EXPORT LAWS MAY NOT APPLY TO YOUR COUNTRY: DEVELOP YOUR NATIONS' OWN CRYPTO-EXPORT INDUSTRY! USE 2048bit KEYS FREELY! FLAUNT YOUR SOVEREIGNTY! **