Re: What is md5sum?

From: P.T. Breuer (ptb_at_oboe.it.uc3m.es)
Date: 06/30/04 

Date: Wed, 30 Jun 2004 23:41:29 +0200

John Hasler <john@dhh.gt.org> wrote:
> P.T. Breuer writes:
> > When you say that md5sum does not identify a files contents uniquely.
> > Show us the counterexample!
>
> Collisions are theoretically possible: just too unlikely to be of practical
> concern. This follows logically from the fact that, in general, the md5sum
> is shorter than the file.

The problem is that the argument "not possible that all different
implies there exists some the same" is not constructivist. It fails in
many many many logics and in many domains (constructivist logic is
minimalist in the sense that only constructive proofs of existence
claims are allowed, so it tends to be the case that if something is
constructively provable, it is true in all decent logics ...).

It's rather a bad idea to have faith in it for the real world - the
kibosh here comes when you realize that to have any decent chance of
finding a collision even under classical mathematics via statistics, you
would have to explore at least a 100th part of the search space.
Unfortunately, at a millijoule or so per file tested, you have zero
chance of completing that project in the next few centuries, because it
would require more than the sun's complete power output during that
entire period.

If you try and drop below the picojoule per file tested range in order
to try and rescue the construction, you are getting into quantum stuff,
and we know what happens there ... logic goes non-classical too.

Well, maybe we could build a quantum computer which produced the md5sum
of an input file as a certain energy level which could only be occupied
by one particle at a time. Then maybe we could detect two file inputs
with the same md5sum via quantum exclusion effects, or something.

Peter

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