As describe by Maxwell here in HD wallets assuming we have a key pair with private key
SK.a and public key of
PK.a and a seed
s and a generator point
G, we can generate a new key pair of
(SK.b, PK.b) as follows:
PK.b = PK.a + sG SK.b = SK.a + s
The advantage with this method is that a service provider can generate new public keys without knowing the clients private key. My question is that, why don't we multiply the seed and private key rather than adding them?
PK.b = PK.a * s SK.b = SK.a * s
Is there any problem with the later method that I suggested?