Are there any alternatives to ElGamal that would be resistant/annoying to quantum machines?
I would like to preserve public key derivability/verifiability -- ability to ensure existence of corresponding private keys for made-up public-keys.
I've looked up several other cryptosystems from NIST proposals of post-quantum cryptography, but by directly reading the papers it looks like they lack this property.
For instance NTRUencrypt is a lattice-based cryptosystem. As it operates under a lattice field in theory public keys could be randomly generated without private ones. But I'm not sure that there would be a way to ensure existence of private keys and possibility of decryption (although the private key space could be large enough and this assumption would somehow hold).