Addressing systemic risks – discouragement attacks against centralized validator sets

This is a minority discouragement attack, the topic first described here (note that the correlated reward reduction in Eq. 41 is only relevant if the attack is constant and ongoing across the epoch, otherwise it becomes smaller; h/t Francesco). I recently also discussed minority discouragement attacks here and here, since it is a relevant topic in terms of issuance policy. In particular, note the recent specific discussion on censorship of the attestation containing the head, source and target vote here. Unfortunately, I have not yet had time to publish the paper.

This would need to be analyzed in the context of a sizeable attack where missing attestations are just not spurious but systematic and significant. This gives incentives for later proposers to try to pick them up, and of course, the attacked party will be particularly incentivized to try to recoup them. I have not studied this dynamic, so if you can perform a more detailed study on how the specific process of recouping such attestation could play out (or not play out), it would be very welcome!

Note that focusing on missed rewards as in your post does not give the full picture. Penalties must also be accounted for, as in previous links. The attacked party will not only lose out on rewards, it will get penalized if the source and target votes are not included. The correct griefing factor if all votes indeed would be dropped (which I would suggest cannot be counted on), while ignoring the correlated reward reduction for simplicity, is then

G= \frac{14+26\times2+26\times2}{(14+26+26)/7}\approx12.5

It should be noted, as described here, that targeting sync-committee attestations gives a griefing factor of G=14, and that these cannot be picked up later.

Finally, a minority discouragement attacker is still susciptible to social slashing, and would need to make some calculus as to the risks before proceeding. But it is indeed true that these attacks exist, and it is important to keep them in mind in the design of Ethereum’s micro incentives going forward.

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