Eth-Gitter-Bridge
@Eth-Gitter-Bridge
Jun 25 03:22
[Vitalik Buterin] so I just realized one issue re griefing analysis
[Vitalik Buterin] an attacker could censor other people's prepares until the epoch ends
[Vitalik Buterin] but then still send their commits
[Vitalik Buterin] then they can include the prepares later to justify their commits
[Vitalik Buterin] aaah right the commits won't get rewarded because they can't get processed unless enough prepares are there
[Vitalik Buterin] but still, this does mean we can't just rule out case 8 in griefing factor analysis
[Chang-Wu Chen] What if there exists a condition, ~1/3 attackers collude to do prepares, though benign validators are not satisfied the prepares, but benign guys do not want to lose their money because of griefing analysis?
[Vitalik Buterin] preparing is always net profitable
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
Jun 25 03:27
[Vitalik Buterin] ie. even if everyone is getting penalized, preparing can reduce your penalties
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
Jun 25 03:33
[Chang-Wu Chen] hmm, even it is net profitable, could I say the maximum profit is to follow the side which has the most prep/commit? If attackers can collude and can do prep/commit fast, they can maintain a orientation.
[Vitalik Buterin] ah I see, you're saying there's an incentive to join the coalition?
[Chang-Wu Chen] yes
[Vitalik Buterin] that's true; I guess the equilibrium is for the coalition to have size 2/3 + 1
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
Jun 25 07:08
[Vitalik Buterin] ok, so another result: if griefing factors for the 2/3 censor case are too high, then the attacker can make a profit by charging others to join the coalition
[Vitalik Buterin] in general, in such a case, griefing factor is 2, so coalition members lose x, others lose 2x, but that's 4x more for non-coalition members
[Vitalik Buterin] so let negative interest rate for a coalition member be p
[Vitalik Buterin] coalition loses p * 2/3
[Vitalik Buterin] others lose 4p * 1/3
[Vitalik Buterin] hence the benefit of being in the coalition is 3p
[Vitalik Buterin] suppose the coalition captures the entire value
[Vitalik Buterin] suppose the attacker captures the entire value of joining the coalition
[Vitalik Buterin] and attacker size is 1/3
[Vitalik Buterin] then attacker loses p 1/3, and gains 3p 1/3
[Vitalik Buterin] actually...
[Vitalik Buterin] wait
[Vitalik Buterin]
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
Jun 25 07:14
[Vitalik Buterin] yeah, so that attack can be profitable
[Vitalik Buterin] attacker losses = p, attacker revenue = 3p
[Vitalik Buterin] that said, that assumes that a coalition can successfully form around a 33% attacker
[Vitalik Buterin] attacker losses = p 1/3, attacker revenue = 3p 1/3
[Vitalik Buterin] attacker losses = p x 1/3, attacker revenue = 3p x 1/3
[Vitalik Buterin] if the attacker has 1/2, then attacker losses = p x 1/2, revenue = 3p x 1/6
[Vitalik Buterin] so that version of the attack breaks even
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
Jun 25 07:20
[Vitalik Buterin] though note that in these kinds of cases, if it's socially obvious that an extortion attack is going on, the minority may want to just rebel
[Vitalik Buterin] and do a minority fork
[Vitalik Buterin] I guess the goal is minimizing the possibility of that happening
[Vitalik Buterin] so if the attacker has 1/2, and the coalition goes up to 2/3, the attacker loses p x 1/2, and extortion revenue is 3p / 6
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
Jun 25 07:29
[Vitalik Buterin] if the attacker has 1/2, and the coalition goes up to 3/4, then the attacker loses p x 1/2, and gains 4p / 4
[Vitalik Buterin] so, the closer these attacks get to extorting everyone, the more profitable they become, and this is unavoidable
[Vitalik Buterin] note that if penalties are purely collective, then there is no benefit to being in a coalition, so individualized extortion is harder to pull off
[Vitalik Buterin] which is an interesting result
NIC Lin
@NIC619
04:20

    [Vitalik Buterin] in general, in such a case, griefing factor is 2, so coalition members lose x, others lose 2x, but that's 4x more for non-coalition members
    whose the others that lose 2x? and why is their loss two times the coalition members' loss?

whose the others that lose 2x? and why is their loss two times the coalition members' loss?
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
04:21
[Vitalik Buterin] others in this case are the victims of the censorship
[Vitalik Buterin] ie. everyone outside the coalition
NIC Lin
@NIC619
05:21
but how is that 4x more for non-coalition members if coalition members lose x
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
05:23
[Vitalik Buterin] because their commits are censored, they pay NCP
[Vitalik Buterin] and NCCP
[Vitalik Buterin] whereas the coalition only pays NCCP
[Vitalik Buterin] since the griefing factor is 2, we know that the non-coalition members as a whole pay 2x more
[Vitalik Buterin] but the non-coalition members are 2x fewer, so each one of them pays 4x more
NIC Lin
@NIC619
07:13
but isn't it true that once the 1/3 not-being-censored member join the coalition, they don't have to pay NCP?
so the attacker pay 1/3 x NCCP and the 1/3 non-coalition members pay 1/3 x NCP + 1/3 x NCCP which is twice the size of attacker's loss
Eth-Gitter-Bridge
@Eth-Gitter-Bridge
07:29
[Vitalik Buterin] ah sorry when I say coalition I mean attacker plus anyone who pays extortion fee