Re: What is md5sum?
From: Micha³ Kosmulski (M.Kosmulski_at_NOSPAM.elka.pw.edu.pl)
Date: 06/30/04
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Date: Wed, 30 Jun 2004 15:15:07 +0200
>>A dramatic misunderstanding ! One doesn't have to show them to prove
>>they exist.
>
>
> Oh, yes one does. What makes you think you don't? (you are supposed to
> think about how you may convince me).
Well, then let us play by your own rules. If you insist that to prove
something you have to "show" it, please convince us that no two files
have the same md5sum, as you claim. This ought to be fairly simple: just
create all possible files and their MD5 sums and send them to this
newsgroup, so we can read through the list and check for ourselves that
actually no two items in the list share the same MD5 sum. Then I'll agree ;]
> Fantastic, so even though you "know" that there "are" two files with
> the same md5sum, you find yourself curiously unable to CHOOSE a pair to
> show me!
Have you never seen a proof of a mathematical theorem done by showing
that if we assume the theorem false, we get a contradiction ? If I can
show that nonexistance of a number with some property X leads to a
logical contradiction, then a number with property X does exist, even
though I may be unable to show it to you. Of course, we can change the
starting set of axioms, or perhaps even the logic we use. But then we
have to consider, what value such reasoning would have for learning
anything about our world.
Of course, mathematics is only a model etc etc; but thus far it has
provided us with quite a lot of good ideas and has found a few uses in
different branches of science and technology. If someone invents a
better tool for this job, I'll switch immediately :)
Then again, there is one more thing nobody has pointed out so far. All
our estimations of how probable a collision in MD5 is were based on the
assumtion that MD5 is a really perfect hash function. The sad truth is
that it is not perfect (probably neither is anything else we can come up
with) and so collisions or reversing the function may happen to be much
easier than we assume - if someone finds a vulnerability.
If hash functions we create were perfect, we wouldn't be using MD5 - we
would still use MD2 or MD1 (I'm not sure if there was and MD1 but MD2
was there). Even MD4 showed to have some weaknesses and was replaced by
MD5. And notice that most digital signature algorithms use SHA-1, not
MD5. If our hash functions were perfect, nobody would care about one
function giving 128 bits long hashes and another 160 bits, since the
probability of a collision or reversing the function would be negligible
even for the most important tasks with less than even 128 bits. But
since the hash functions created by humans are not perfect, some are
better than others - and SHA-1 is considered more secure than MD5.
Michal
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