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Re:Yahoo discloses hack of 1B accounts by manarth on Thursday December 15, 2016 @02:49AM (#13183139)

  > the complexity involved in finding a collision for a specific hash
If it can be shown that a preimage collision can be computed in less time than an exhaustive search, the algorithm is generally regarded as having a weakness, even if the given "less time" is still a very very long time.

The theoretical complexity of MD5 is 2^128, but a preimage attack was discovered in 2009 which showed that a collision can be found in 2^123.4. [1]

Collision attacks against MD5 have become more practical, there are even frameworks for it [2]. The complexity of 2^123.4 still makes a preimage attack against MD5 computionally unfeasible, but given that it's been shown to be weaker than its theorerical 2^128, it's possible that MD5 has other weaknesses which would allow the complexity to be reduced to a level that is computationally feasible.

[1] https://www.iacr.org/archive/eurocrypt2009/54790136/54790136...

[2] https://marc-stevens.nl/p/hashclash/

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