All-out Attack: Optimal Block Withholding Under Pay-Per-Share Scheme

Introduction to the show: ident: Security Radio. Generated commentary on the latest security and cryptography papers.

Nadia: We're looking at the paper: "All-out Attack: Optimal Block Withholding Under Pay-Per-Share Scheme".

Elias: The gist: The optimal strategy for a Block Withholding (BWH) attacker under Pay-Per-Share (PPS) schemes in Nakamoto-style blockchains is an All-out Attack (AoA),

Nadia: First, who's behind it and why it matters.

Title and authors: Nadia: So we're looking at this paper today, "All-out Attack: Optimal Block Withholding Under Pay-Per-Share Scheme." It tackles a specific scenario in blockchain mining where pools get paid immediately for submitting shares instead of waiting for the actual block to be found.

Elias: Right. What’s the main idea here? Basically, they're looking at how an attacker can still make money even when you're using these share-based reward systems, which is different from the older block-dependent schemes we usually see discussed in classical BWH studies.

Nadia: Exactly. The core claim is that under Pay-Per-Share or PPS, the traditional way of thinking about Block Withholding doesn't hold up as expected because of how those shares are paid out right away.

Priya: So, if I understand correctly, this paper is arguing that you can actually profit from withholding blocks in a PPS setup where the old literature suggested you couldn't?

Elias: That’s right. They prove that the optimal strategy for a Block Withholding attacker in this PPS environment is what they call an All-out Attack or AoA, which involves allocating all your hashpower to the victim pool.

The paper's summary: Nadia: Let's unpack what that All-out Attack actually means in practice for someone listening. It means the attacker commits their entire mining power to that one pool and submits only partial Proof-of-Work shares, while they keep all the actual valid blocks.

Elias: That’s because this attack exploits how the difficulty adjustment mechanism works after you start mining. The idea is that by withholding those full Proof-of-Work shares, you initially take no money from the victim pool operator.

Priya: So, what happens once that first difficulty adjustment kicks in? Does the attacker suddenly start making money, or does something else happen?

Nadia: After the adjustment, because fewer blocks are mined per time unit, if you maintain a constant ratio of partial shares to full shares being mined by the pool, then those partial share rewards also decrease.

Elias: That decrease in difficulty means the attacker can generate revenue even after the adjustment period because they exploit that change in block mining difficulty >

Priya: So, what’s the payoff compared to just waiting for a normal block? What are they showing us about how much extra money you can actually get?

The paper's improvements: Nadia: The paper points out that the authors showed this All-out Attack is actually better than other methods, and they also looked at advanced BWH variants like Fork After Withholding or FAW.

Elias: They found that those advanced variants, like FAW, don't actually yield any additional profit in a PPS scheme; they don't give you any extra revenue compared to the basic AoA.

Priya: And what about the other side of things? The paper talks about how you can make this attack even more effective if you use variable share difficulty, which is called vardiff.

Nadia: Vardiff helps maintain a steady rate of share submissions, and under that condition, they determined the optimal way to split your power to maximize your revenue change. They found the math points toward the All-out Attack being optimal in most practical situations when you look at parameter q.

Elias: The paper also suggests scaling up by using multiple Sybil identities, which effectively reduces that parameter q by dividing it by the number of identities, which helps keep the All-out Attack optimal even when alpha is less than one over two.

Conclusion: Nadia: So, to wrap up on "All-out Attack: Optimal Block Withholding Under Pay-Per-Share Scheme," the paper confirms that this strategy is the best way to attack PPS schemes because it aligns with the theoretical upper bound of what you can get from optimal selfish mining.

Elias: They show that after one difficulty adjustment, you achieve a post-adjustment reward rate of alpha to the power of one minus alpha per target epoch, which matches the theoretical maximum for selfish mining under perfect network influence <ref:2607.01209#pg1>.

Priya: From my side, I see this as important because it shows that even in these share-based systems where operators take all the risk associated with block mining time variance, an attacker still has a way to extract a measurable profit.

Nadia: It confirms that the All-out Attack is optimal, meaning you should put one hundred percent of your hashpower into the victim pool for maximum gain >

Elias: The analysis shows that all mining entities benefit by the same magnitude per unit of hashpower they control, while the victim pool operator incurs a loss >