""" A much faster solution would be the same approach rsync takes with its "rolling checksum." """

I know this function is attributed to Bernstein and it's called Bernstein hash [0]. You're describing the Rabin-Karp string matching algorithm [1].

[0] http://fr.wikipedia.org/wiki/Table_de_hachage#Fonction_de_Ha...

[1] http://en.wikipedia.org/wiki/Rabin-Karp_string_search_algori...