Proof of Stake Censorship Oracle

This censorship oracle is based on an eth research post by Ed Felten.

The idea is that ETH Proof of Stake consensus chains, eg Ethereum mainnet and Gnosis Chain, contain enough information in block headers to make statistical conclusions about censorship --- critical when determining the challenge period in optimistic mechanisms (eg rollups, economic games about data curation).

X-posting from Ed's post,

Assume that each slot is assigned to a non-censoring validator with probability p . Then the probability of seeing k or fewer non-censored blocks in n blocks is equivalent to the probability of getting k or fewer heads when flipping a biased coin that comes up heads with probability p .

The cumulative distribution function is

$$ \operatorname{Pr}(X \leq k)=\sum_{i=0}^k\left(\begin{array}{c} n \\ i \end{array}\right) p^i(1-p)^{n-i} $$

which we can calculate numerically in practical cases.

For example, this implies that with n=688 and p=0.1 , we can conclude that Pr(X≤34)<10−6 .

In other words, if we see 34 or fewer missing blocks out of 688 slots, we can conclude that a non-censored block was included with very high confidence. 688 slots is about 2 hours, 18 minutes.

Alternatively, if we see 4 or fewer missing blocks out of 225 slots, we can conclude that a non-censored block was included with very high ( 10−6 ) confidence. 225 slots is 45 minutes. Observed rate of missing blocks

Over a recent series of 500,000 blocks, 3346 blocks were missing, a rate of 0.67%.

Over a series ~1,975,776 blocks since the merge, ~90,000 blocks were missing, a rate of 4.3%.

Over ~7,405,227 blocks missing since the merge, a rate of 4.2%