# "Homomorphic" one way function for public/private key pairs

Is there a signing scheme relying on a secret key $s_k$ and public key $p_k$ for which we can find a one way function $h$ such that we can efficiently calculate the public key associated with $h(s_k)$ from $p_k$.

For instance, with the ElGamal signing scheme, we'd be looking for a one way function $h$ such that for all $g$ and $s$ in $\mathbb{Z}/p\mathbb{Z}$ we can efficiently compute $g^{h(s)}$ from $g$ and $g^s$.

Alternatively, being able to verify that a given value is indeed the public key associated with the hash of the secret key would be enough.

(The goal is to get some kind of non interactive forward secrecy with certain properties.)

the public key associated with $h(s_k)$" without even needing $s_k$'s public key.