A homomorphic hash function is a function $H : A \to B$ between two sets with some algebraic structure $(A, *)$ and $(B, \star)$ such that
- $H$ is collision resistant, i.e. it is hard to find $x \neq y$ such that $H(x) = H(y)$ and
- $H$ is a homomorphism, i.e. $H(x * y) = H(x) \star H(y)$.
Are there any practical realizations of such a homomorphic hash function, or even a homomorphic signature scheme (i.e., where we can "add" valid signatures to get a signature of the "sum" of two messages)?
Even better, are there even any libraries implementing this?