I've been wanting something like a "commutative cryptographic hash function" (or just a "rolling cryptographic hash function") that would allow us to compute a cryptographic hash of some data M given subchunks M_0 ... M_n and/or sub-hashes H_0 ... H_n. I.e. allowing us to quickly compute the hash of the final data from combining most existing hashes with the hash of the newly created chunk.