1650s, "to hack, chop into small pieces," from French hacher "chop up" (14c.), from Old French hache "ax" (see hatchet). Hash browns (1926) is short for hashed browned potatoes (1886), with the -ed omitted, as in mash potatoes. The hash marks on a football field were so called by 1954, from their similarity to hash marks, armed forces slang for "service stripes on the sleeve of a military uniform" (1909), which supposedly were called that because they mark the number of years one has had free food (that is, hash (n.1)) from the Army; but perhaps there is a connection with the noun form of hatch (v.2).
"a stew of meat cut into small pieces," 1660s, from hash (v.). Meaning "a mix, a mess" is from 1735. Cryptographic use in computing is by 1979.