In Elliptic Curve Cryptography (ECC) assuming user A has a private public key pair of $S$, $P$ accordingly with generator point $G$ which as we know is: $$P=S*G$$
Assuming that user A wants to generate multiple key pairs deterministically to manage them easier and there is a user B who should be involved in the process to reduce single point of failure. Each time user A wants to generate a new key pair he needs to ask user B to provide him some secret so that user A can generate the new private key.
There are two requirements for the whole scenario:
- User B should not be able to generate any of the user A's private key at any point.
- User A and B can generate future public keys without even knowing their corresponding private keys.
The second part can be done easily if we have only one users:
$$S_{i} = S_{i-1}+X$$ then: $$P_{i} = P_{i-1}+X*G$$ So anyone who knows $X*G$ now can generate the next public key. So in the scenario that was mentioned, user B by giving part of $X$ should help user A to construct the next private key but then they cant know what the next public key will be since they both need to generate X and until then they cant generate $X*G$.
So the question is how we can make this work if user A needs some secrets from user B to construct the key pairs? (I assume we might need something similar to shamir secret sharing at some point)