Hi g0b1e,
I wanted to add to this excellent summary that there is a trade off here.
The harder you make payment correlation the easier you make channel
jamming. If payments can not be correlated at all it's possible to make
payment paths that cycle through the same nodes many times over. This
Using payment correlation attacks adversary can try to link the sender and
receiver of payment by observing traffic from the potential sender to the
potential receiver. Such observations can be made by the adversary nodes if
they are present on the payment path or if the adversary is able to