Understanding sha-1 collision weakness

Question

According to various sources, attacks looking for sha-1 collisions have been improved to 2^52 operations:

http://www.secureworks.com/research/blog/index.php/2009/6/3

Answer 1

Well good hash functions are resistant to 3 different types of attacks (as the article states).

The most important resistance in a practical sense is 2nd pre-image resistance. This basically means given a message M1 and Hash(M1)=H1, it is hard to find a M2 such that Hash(M2)=H1.

If someone found a way to do that efficiently, that would be bad. Further, a preimage attack is not susceptible to the birthday paradox, since message M1 is fixed for us.

This is not a pre-image or second pre-image attack, merely a collision finding attack. To answer your question, No a brute force attack does NOT have a higher chance of finding collisions. What this means is that the naive brute force method, combined with the researchers methods result in finding collisions after 2^52. A standard brute force attack still takes 2^80.