Here is a solid answer. Can we derive parent’s private key using child’s private key?

Andrew Chow put’s forth a solid answer.

As for the specific questions:

How could that be possible?

Once again, Andrew Chow: Derivation of parent private key from non-hardened child

Furthermore, how can the hardened derivation scheme neutralize this problem by using the parent’s private instead of his public as input for the HMAC-SHA5 functions?

(From the linked post above) Hardened derivation protects against this because it generates the child private key by hashing the parent private key. However this also means that you cannot generate the child public key from the parent public key.

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