[Lightning-dev] An Idea to Improve Connectivity of the Graph

Christian Decker decker.christian at gmail.com
Fri Apr 6 12:23:45 UTC 2018

ZmnSCPxj via Lightning-dev <lightning-dev at lists.linuxfoundation.org>
> In a retaliation construction, if a party misbehaves, the other party gets the entire amount they are working on together, as disincentive for any party to cheat.
> That works for the two-party case A and B.  If A cheats, B gets money.
> How do you extend that to the three-party case A B C?  If A cheats, what happens?
> Suppose the correct current state is A=2, B=99, C=3.  Suppose A cheats
> and attempts to publish A=102, B=1, C=1.  C detects it because B is
> asleep at that time.  Does C get to claim the money that A claimed for
> itself, basically 101+1 and thus 102?  But the correct state has
> almost all of the money assigned to B instead.  Obviously that is
> unjust.  Instead C should get to claim only 3 from A (its 3 in the
> final state) in addition to its 1 in the published state, and should
> give the 99 to B.  So now B also needs another retaliatory
> construction for the case "A cheated first and C found out and and
> also cheated me", and a separate construction for "A cheated but C was
> honest".  And that is separate construction for the case "C cheated
> first and A found out and also cheated me" and a separate construction
> for "C cheated but A was honest".
> As should be obvious, it does not scale well with number of
> participants on a single offchain "purse"; it quickly becomes complex
> fast.

The need to identify the misbehaving party and punish just that one
party could be addressed by having pre-committed retaliation
transactions. However this results in a large number of pre-committed
transactions that need to be carried around just for the case that
someone really misbehaves. In addition colluding parties may be able to
punish each other when an cheat attempt seems doomed to fail, which
reduces the cost of the attack. This could also be partially fixed by
pre-committing retaliation transactions that split the misbehaving
party's funds. Overall a very unsatisfactory solution.

> Retaliatory constructions however have the major advantage of not
> imposing limits on the number of updates that are allowed to the
> offchain "purse".  Prior to Rusty shachains it was thought to require
> storage linear in the number of updates (which could be pruned once
> the channel/"purse" is brought onchain), but Rusty shachains also
> require O(1) storage on number of updates.  Thus retaliatory
> constructions are used for channels.
> Note that channel factories, to my understanding, can have the Duplex
> construction near the root of the initial onchain anchor transaction,
> but be terminated in Poon-Dryja retaliatory channels, so that a good
> part of the current LN technology has a good chance of working even
> after channel factories are implemented.  This strikes me as a good
> balance: restructuring channels is expected to be much rarer compared
> to updating them normally for normal usage, so each construction plays
> its own strengths: the Decker-Wattenhofer construction which imposes a
> limit on the number of updates, but has no limit on number of
> participants, is used for the rarer. massive "channel restructuring"
> operations, while the Poon-Dryja construction which imposes a
> practical limit on number of particiapnts, but has no limit on number
> of updates, is used for "day-to-day" normal operation.

That's not as bad a tradeoff as people usually interpret, the DMC
construction has parameters that allow tweaking the number of
invalidations, and with parameters similar to LN we can have 1.4 billion
updates. Which is years of operation without need to
re-anchor. In addition penaltyless invalidation has a number of
advantages, for example it doesn't have the state asymmetry inherent in
LN and there is no toxic state information that, when leaked, results in
your funds being claimed through a retaliation. This happened to me btw
last month when I accidentally restored a wallet from backup and
attempted to reconnect.


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