When two channel participants open a channel or update it, they exchange commitment transactions. These commitment transactions allow each party to unilaterally close the channel.
The commitment transactions are asymmetric in that they lock the closing party's funds when broadcast, i.e. Alice's commitment transaction locks Alice's funds, Bob's commitment transaction locks Bob's funds. The counterparty's funds are immediately available for spending. The lock on the closing party's funds (the "breach remedy") gives the counterparty time to impound the closing party's funds via a "punishment transaction" if an outdated state was broadcast.
Commitment Transaction (via Elle Mouton): Alice's output to herself (
to_local) in her commitment transaction is encumbered with a Revocable Sequence Maturity Contract (RSMC) which allows her to revoke the commitment transaction later, while the output to Bob (
to_remote) is a simple send, vice versa for Bob's transaction.
When a payment is made in the channel and the channel is updated with new commitment transactions, the outdated channel state is revoked by revealing the secrets to spend the old commitment transactions (dB1 and dA1 in the graphic). This makes the old state "toxic" in the sense that (accidentally) using the outdated commitment transaction to close the channel will cost the closer all their funds in the channel.
Updating a channel to make a payment in the punishment-based channel setup requires a procedure with multiple roundtrips in a specific order to ensure that there is no disadvantageous intermittent state for either party. If it were possible to map this onto a multiparty setup, it would be extremely complex.
In Eltoo, commitment transactions are shared across the participants. Broadcasting an outdated state is corrected by overwriting it with the latest state. Since the channel state is symmetric, it is trivial to have channels with more than two parties. This could take e.g. the form of four parties creating a four-of-four multisig output to anchor a channel. Each party would have a balance in the channel which they could use to send funds to another channel participant, or other network participants. With Schnorr signatures and key aggregation, such channels would be extremely efficient as they could still fit in the size of a singlesig output. Practically, the number of participants would still be limited as any channel update would have to be agreed upon by every participant, and any one participant wanting to close the channel would close it for all. Possibly, this could be used as a liquidity pool or for channel factories among large players that can guarantee continuous availability.