I just recently learned that the SHA-3 finalist Keccak allows for variable length output. As the only answer to this question states, "[it] need to have an output length at least equal to the input length," which I understand just fine. However, I'm curious if this guarantees against collisions.
- Is there any work done to show or prove collision resistance gained by increasing digest length? If so, how dependent is this resistance on the hash function itself? (I'm guessing the answer to this is "highly" or "entirely".)
- What are the other benefits of allowing variable and arbitrary length output?
If the math on these points is still fuzzy, is variable length output just based on the intuition that "larger problem space = harder to attack"?
Note my crypto and math expertise is very low, so please add a 'for dummies' section to any answer you write and I thank you in advance.