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

1. op(f(x1), f(x2))=f(x1+x2) and op(f(x1), f(x2))!=f(x2+x1) where plus denotes concatenation and op is an easily computable operation
2. f(x) is fixed length of about 160-512 bytes
3. 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?

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

1. 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
2. f(x) is fixed length of about 160-512 bytes
3. 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?