Excited to share our new paper, "Accountable Liveness", w/ @AndrewLewisPye @Tim_Roughgarden @luca_zanolini. We explore when and how adversarial nodes can be punished if they stall transaction confirmation in blockchains.

RT @socrates1024: Announcing the Financial Cryptography 2026 call for papers. Paper deadline is Sep 16 (not a ton of time!). w/ Co-chair….

Don't miss Aditi's SBC talk today at 10:30 !.

Looking forward to talking about accountable liveness at SBC at 1:30p today! TL;DR:

If you want to know a lot more, including all the nitty gritty technical details, you can find the paper on IACR ePrint 2025/693.

If you want to know more, especially motivation and intuition, check out this video by @Tim_Roughgarden:.

Our results do provide rigorous foundations for liveness-accountability heuristics such as the inactivity leak employed in Ethereum.

You could also ask if the number of adversarial nodes our scheme identifies in case of a liveness violation is "good"? We show that it is "not bad" (and sometimes even optimal), but you see that a small gap between upper and lower bound leaves room for improvement:

In terms of limitations, it is important to highlight that as a first paper on the topic, our primary aim is to explore fundamental limits of Liveness Accountability, and demo its feasibility. We have not taken particular care to maintain low communication complexity for example.

So the aforementioned intuition is correct, that Liveness Accountability is harder to achieve than Safety Accountability due to absence vs presence of messages, and indeed that is the key driver for Theorem 2 in the paper.

2) For Safety, the adversary cannot escape accountability, even if almost all nodes are adversarial. For Liveness, we show that Accountability is impossible if the adversary controls a majority of the nodes.

1) Safety Accountability works irrespective of network timing assumptions. For Liveness Accountability, we show that no protocol can provide it, if the network is "more asynchronous than synchronous", ie, for x-partial-synchrony with x>1/2.

You may not like the two restrictions of Liveness Accountability, 1) on network timing, and 2) on number of adversarial nodes. Afterall, Safety Accountability doesn't come with such restrictions. But we show, on the negative side, that these two compromises are unavoidable:.

The intro of the paper has a cute intuitive yet rigorous argument how our mechanism works.

Specifically, our protocol allows to hold adversaries to account for stalling transaction confirmation if f>1/3.

(To make "more synchronous than asynchronous" precise, we introduce x-partial-synchrony as a network model that interpolates between synchrony (x=0) and partial synchrony (x=1). We think this model may be of independent interest.).

On the positive side, we show how PBFT-style consensus protocols that are Safe and Live under partial synchrony up to 1/3 adversary nodes, can be equipped with Liveness Accountability if a majority of nodes is honest and the network is "more synchronous than asynchronous".

Intuitively, because Liveness violations seem to involve the unexpected *absence* of messages like votes, rather than the unexpected *presence* of messages like equivocating votes, one might guess that Accountability would be more difficult for Liveness than for Safety. .

But what if Liveness breaks?.Our paper extends the idea of Accountability to Liveness. We explore under what circumstances and using what protocol techniques, we can provably identify culprits and slash them, in case transaction confirmation stalls.

To achieve crypto-economic security and better incentive alignment, recent research has strengthened Safety with Accountability: If there are many adversarial nodes, and they cause disagreement so that Safety is broken, we can provably identify many culprit nodes and slash them.

Traditional consensus security demands two properties (assuming there aren't too many adversarial nodes):.- Safety: No two honest nodes ever disagree on the confirmed transactions. - Liveness: Transactions eventually get confirmed by every honest node.