Exploring the advantages of multisig tapscripts

Hey everyone, I’m trying to wrap my head around tapscripts, Schnorr signatures, and taproot in general. From what I gather, taproot Merkle trees can show only the specific path used in a transaction when signing. I’m curious if this can be applied to a k of n threshold setup (setting aside FROST for now, whenever that’s ready). For instance, with a 2 of 3 scenario involving keys A, B, and C, I thought we’d have three distinct script paths: - A and B - B and C - A and C But from what I’ve come across, it looks like that’s not the case, and using the same key multiple times seems to be off the table, which makes that setup impossible. Am I getting this right? If so, what’s the reasoning behind using just one script path in a threshold scheme? And why can’t you reuse a key across different script paths? Appreciate any insights!

Anyone knows about this? If my question does not make sense, please let me know!

The essence of Taproot is to improve privacy and efficiency and it's most efficient when you are using script path or non. Though using what you mentioned above is correct in a traditional of K of n scheme, But not quite the most efficient in Taproot. In taproot rather than using all the combination as seperate script path, multisig( a schnorr based signature that allows multiple keys to produce a single aggregated public key and signature) is quite more efficient. Yes you have it right. Now the reason for using a single script and not using same key more than once is for security purposes. Using a single script is more efficient(reduces the size of the transaction since only one public key is needed) ,secured( improves privacy since specific private keys used is not shown) and not to mention simpler (since you using an aggregated script rather than multiple script). It does.