The birthday problem?

Well, since i haven't explained it yet. Collision attack are done based on a statistical problem known as the birthday problem. The problem being: What are the chances of two persons having the same birthday in class of certain size. In a class of say 30 people, one would expect 30/365, which is around 8%. However in reality the chances are around 70% and 99.9% for 70 people. This is due to the fact that this applied to any day of the year, not just a specific day. This is same concept is used in collision attack to try to find two identical hash. Due to the nature of this, it is possible to cut the complexity of attack down to 2^(n/2) where n is 256 for 32 bits and 512 for 64 bits.