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In following paper, written by Christian Decker et al., there is a paragraph that is not clear to me.

eltoo: A Simple Layer2 Protocol for Bitcoin

"The central idea of Lightning is to invalidate an old state by punishing the participant publishing it, and claiming all the funds in the channel. This however introduces an intrinsic asymmetry in the information tracked by each participant. The replaced states turn into toxic information as soon as they are replaced, and leaking that information may result in funds being stolen. The asymmetry also limits Lightning to two participants."

There are following points that are not clear to me:

(1) Does asymmetry mean the information tracked by each participant (payer and recipient) are NOT the same (or are NOT equal)?

(2) What is the reason of this asymmetry?

(3) What does "turn into toxic information" mean?

(4) The last sentence: "asymmetry also limits Lightning to two participants", Does it mean that we can expect a payment transaction can have more than two participants? since a payment logically has only two participants: a payer and a recipient.

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When two channel participants open a channel or update it, they exchange commitment transactions. Each of these commitment transactions allows one 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 The lock on the closing party's funds gives the counterparty time to impound the closing party's funds if an outdated state was broadcast.

Once a channel is updated, the outdated channel state is "toxic" in the sense that (accidentally) using the outdated commitment transaction to close the channel will cost the user all their funds in the channel.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 on a multiparty setup, it would be extremely complex. In Eltoo broadcasting an outdated state is dealt with by updating to the latest state. Since channel state can thusly be symmetric, it is trivial to have channels with more than two parties. This could take the form of e.g. 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 the other participants, 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.

  • Thank you. Just when you say we can have channels with more than two parties, do you mean that we can have a bidirectional payment channel between e.g. 4 participants (payer/recipient) like this figure? ( imgur.com/5KVLP6G ) Or do you mean something else? And does eltoo such a capability? Thanks – Questioner Jan 2 at 16:39
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    with the current lightning network multiparty channels are theoretically possible but not implemented. in eltoo these channels are much easier to implement because all parties share the same state and update / settlement transactions. Therefor if we switch to eltoo channels one day we will most likely get multiparty channels implemented – Rene Pickhardt Jan 2 at 18:06
  • And in that case (having multiparty channels), we can establish a large channel between participants, such that they do not need to do multi hop payments since a direct link exists between them and therefore we do not need to do a routing process, isn't it? Do you agree? Thank you. – Questioner Jan 2 at 19:25
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    I've amended my answer to give more details on some potential applications for Eltoo. – Murch Jan 3 at 6:52

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