Derive new public keys from a public key?
Is there a kind of homomorphism between the set of private keys and public keys?


Yes. You can think of f: G -&gt; H being the function that derives a public key (i.e. something from the set of H) from a private key (something from the set of G).

More to the point, f(a + b modulo n) = f(a) # f(b)

(I'm using the # symbol above to mean 'secp256k1 elliptic curve point addition')


  Because the article says that you can either sum before or after the public key is generated.


That's accurate.