Hi,

Trying to educate myself about tapscripts, Schnorr signatures and taproot in general. My understanding is that taproot Merkle trees have the advantage of being able to reveal only the used path of the tree when signing a transaction. I am trying to understand if this can be leveraged at all for a k of n threshold scheme. For example, I would have expected that for a 2 of 3 with keys A, B and C, we would want to use 3 script paths:

- A and B
- B and C
- A and C

However, from what I have seen it seems that this is not how it is done, and even that using the same key more than once is not allowed, which would not even make it possible to do.

Am I understanding this properly? If so, why would a single script path be preferable for a threshold scheme? Finally, why isn't it allowed to reuse the same key within multiple script paths?

Thanks!