I wonder if there is a known hash function that for any $x$, $y$ which are numbers in a certain range with certain accuracy (I guess one can think of them as integers?), you can define two functions corresponding to addition and multiplication such that:
$h(x) \# h(y) = h(x+y)$
$h(x) \cdot\cdot h(y) = h(x \cdot y)$.
Edit: I now see it is slightly duplicated with Is it possible to subtract/multiply numbers using homomorphic encryption?