# Partial collisions of hashes, why is this important?

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?

• If we think about the hash function $h:\{0,1\}^* \rightarrow \{0,1\}^n$ as $n$ boolean functions, $f_i:\{0,1\}^* \rightarrow \{0,1\}$, then finding a collision method for some output bits is a kind of divide and conquer attack. Dec 14 '18 at 16:52