How to retrieve extended private key from extended public key + master seed / root private master key

Question

I have a master seed (I use a hardware wallet). I know how to transform it into a (root) private key. I have also several public keys, which all was obtained by derived a private/public keys of the root private key.

Questions:

• How can I get all the private keys corresponding to the public keys mentioned above?
• What is the best tool to do this thing ?

In otherm term, I want to retrive derivated private key like that:

derivated private key = function(derivated public key, master root key)

My ultimate goals is then to import all these private keys in a Electrum wallet for instance.

Answer 1

If you already have the seed phrase (aka mnemonic) then all you have to do is import that into Electrum.

1. Click File > New/Restore (ctrl+N)
2. Set a name
3. Select Standard wallet
4. Select I already have a seed
5. Enter seed phrase then click option and select BIP39 seed and the other checkbox only if you had used a passphrase to extend this seed
6. Choose the address type that were created by this seed and modify the derivation path if needed

Now if you want an individual private key, simply go to Addresses tab and select any address there, right click and choose Private key.
If you want to know the underlying methods used to derive the keys then check out BIP-39 and BIP-32.