I'm looking for a hash function and a related function or operator such that:

```
H(string1 . string2) = f(H(string1), H(string2))
H(string1 . string2) = H(string1) op H(string2)
where:
H() is the hash function
string1 is a string
string2 is a string
. is the string concatenation operator
f() is a function
op is a binary operator
```

Any suggestions?