Re: MD5 is 1=>1?

[wcs@anchor.ho.att.com (bill.stewart@pleasantonca.ncr.com +1-510-484-6204)]

> >     Are there 128 bit messages 
> > in MD4 which hash to the same value, and if so, what insight into the 
> > cycle leingth vs string leingth would it give us.
> If there are, then you have broken MD4!  This is the definition of
> breaking a Hash: finding two strings (of *any* size) that hash to the
> same value.

There are different kinds of brokenness.
- There's being able to find the original input to match any output
  (not a problem here, though finding the shortest ASCII input would
  certainly be interesting...)
- There's being able to find at least one input to match any given output;
  that's pretty broken.  For MD5, it's assumed that the probability
  is 2**-128 of an input producing any given output.
  If you can do this, it's easy to abuse protocols using the hash.
- There's being able to find two input strings with the same output,
  excluding some easily identified set of "weak" inputs; 
  for MD5 this is presumed to take about 2**64 tries with the usual
  birthday problem math.  Occasionally this can be useful for
  abusing protocols that use the hash, though not too often.
  It might be one way to cheat at net.gambling, for instance....
- There's being able to find two input strings through careful
  analysis; I don't remember if MD4 has any, but MD5 has a few.
  A carefully designed protocol can avoid accepting these outputs
  if there's a small set of them.

			Bill