I have a extended private key, I'm creating multiple child private key / public key pair. If want to verify that the child public is derived from the parent public key. Can I do that? Thanks in advance!
To derive child keys, two conditions have to be met / satisfied:
The extended parent public key is available (public key & chain code)
The derivation path uses non-hardened indexes
(optional) know the derivation path; if you don't know it, it will take you time to iterate through the various combination (i.e. brute force), but typically they are simply incremented, so it shouldn't be costly.
Reference Public parent key → public child key in BIP-0032.