How do I derive a child key pair from a master key pair?

[TechPro424]

I'm trying to create a functional replica of the Bitcoin protocol, albeit at a smaller scale, for an academic project, and I'm trying to generate a unique address for each transaction. According to this answer,
https://bitcoin.stackexchange.com/a/48325/160205

What you can do, is derive additional private keys from a "master private key" with a given derivation rule. These additional private keys obviously correspond to new addresses.

How do I derive such "additional private keys"?

I tried using bcrypt on the master key according to this example
https://www.pycryptodome.org/src/protocol/kdf#bcrypt
and then tried using RSA.import_key() to convert the hash to a new key, for which I got the error ValueError: RSA key format is not supported, which, in hindsight, would obviously have never worked as that function is to be used for importing already exported, valid keys.

[Legrandin]

How do I derive such "additional private keys"?

The key derivation functions in Crypto.Protocol.KDF can only be used to derive new random-like byte strings (derived keys) from an existing random-like byte string (master key).

Elliptic curve keys and RSA have specific structures so a random-like byte string can't be interpreted directly as such kind of keys (with a few exceptions, see below).

There are a few ways to do that.

If your derived key must be an Ed25519 key, you can use a KDF to derive 32 bytes and have that imported as an Ed25519 key with Crypto.Signature.eddsa.import_private_key.

If your derived key must be an X25519 key, you can use Crypto.Protocol.DH.import_x25519_private_key instead.

(similar functions exist for Ed448 and X448)

If your derived key must be a NIST P ECC key or an RSA key, you can use the derived key (byte string) as data for a XOF (like Crypto.Hash.SHAKE256) . Then you pass the method read of that new object as parameter randfunc to Crypto.PublicKey.ECC.generate. That will make the generation of the ECC key deterministic and based on the output of the KDF. This is OK for ECC, but not advisable for RSA.