A thread on how taproot improves bitcoin privacy:

Right now in Bitcoin there are a bunch of different kinds of multisig (graph here https://txstats.com/dashboard/db/p2sh-repartition-by-type?orgId=1) All this leaks privacy-relevant information. Taproot allows us to do multisig but where all that information is hidden and it looks exactly the same as a single-sig.

LN channels will look just like schnorr single-sigs (right now they are 2of2 multisig) So we'll get into nice situation that many random txes out there "could have been" LN channels which actually transport coins off-chain, hugely boosting privacy even for people who dont use LN

Taproot allows scriptless scripts, which mean that in a Lightning payment there's no longer a common hashlock value along a Lightning route, so it will no longer be obvious to different Lightning nodes along a route that they're all part of the same payment.

Scriptless scripts also mean that unilateral LN channel closes will become undetectable. Right now these transactions publish a visible contract on-chain. After taproot these contract can be indistinguishable from any other schnorr. Again, any tx out there could've been LN

It's great to see how far we've come even with the last soft fork of Segwit which allowed Lightning to come to bitcoin. That's a huge privacy benefit. Just think of the millions of off-chain transactions that were made and aren't stored forever in public view on the blockchain