does extended public key derivation go both directions I understand that unhardened extended public child keys may be derived from any unhardened extended public key without access to any private keys.

Is the reverse also true -- can a parent extended public key be derived from a child extended public key?
Is the reverse also true -- can a parent extended public key be derived from a child extended public key?


No. BIP 32 uses hash functions in order to derive the child keys. In order to be able to derive the parent key from the child key, you should need to be able to reverse the hash function, which is currently impossible (I say currently because some vulnerability could be discovered which allows it to be reversed, but that is unlikely to happen).

Furthermore, the child key derivation also involves calculating a public key from a private key (that private key is basically temporary and doesn't actually reveal anything about the child private key). You would need to reverse that too, but doing so is also currently impossible (it is theoretically possible with a quantum computer).