There's a lot of work finding "partial collisions" in hashes, and "Parallel Collision Search with Cryptanalytic Applications" seems to be the go-to paper for this work. I'm trying to understand why finding partial collisions, particularly by brute force, is such a topic of interest. As an example, let's say we have a 256-bit hash, and the last 4 bytes are the same for two message.
Is the interest in this work just because it's a useful segue to understand how to make collision? Is there a condition where one would truncate a longer hash that would cause a partial collision to be a problem?