Which private key is used in Taproot transactions?

Question

The transaction only has one input, where its scriptPubKey is --> Op_1 Q , where Q is the tweaked public key.

Let p = private key, P = Public key, q = p + tweak, Q = tweaked Public key

To create the transaction you have to populate the witness field:

1. Key Path Spend: Do you use q (the tweaked private key) to sign the transaction?

   That is, s = k + H(R,Q, txdata)q and sig is (R,s) where k is the nonce

2. Script Path Spend: Do you use p (untweaked internal private key) to sign the transaction

   That is, s = q + h(Q,P, txdata)p and sig is (Q,s) where q is now the nonce

I am not a coder so trying to find the answer to this has been difficult given that I think you would need to code to understand how the mechanics works.

Answer 1

In a key path spend, you always sign with the private key corresponding to the output key. If that key is a tweaked public key (it's recommended to always use a tweaked key), you will also need to tweak the private key.

In a script path spend, the internal (untweaked) key is used to prove the committment to a script tree. The actual script will contain its own public keys that may be unrelated to the internal or output key, and producing signatures for them will require their corresponding private keys.

You may wish to read BIP341: Script validation rules to make sure you understand how exactly Taproot inputs are validated.