additive hash function Do functions with the following properties exists for x being arbitrary stream of bytes:


op(f(x1), f(x2))=f(x1+x2) and op(f(x1), f(x2))!=f(x2+x1) given that x1!=x2 where plus denotes concatenation and op is an easily computable operation
f(x) is fixed length of about 160-512 bytes
f does not need to be hard to revert, but should be useful at finding transmission errors or duplicates.


Could you provide any names/articles/pointers?
Try the CRC hash; it has this property.  You can also look at Merkle tree hashing.

See also https://crypto.stackexchange.com/q/24622/351, Which fingerprinting/hashing algorithms support compounding?, https://crypto.stackexchange.com/q/6497/351.