Update EIP-7594: Polish EIP, expand rationale #9588
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still reviewing the security section with @fradamt and @MarcoPolo |
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The commit 63cae7d (as a parent of 2e44014) contains errors. |
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| Validators are assumed to have marginally higher requirements to participate on the network. PeerDAS introduces a custody requirement that scales with the validator count so that nodes with more resources can contribute to a more stable backbone that makes the global network more robust. | ||
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| ### Column sampling vs row sampling |
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Would add that extending columns (including proof computation) has to be done just in time, in the critical path, whereas rows can be extended in advance and the proof computation can even be outsourced to the senders, as we do in the previous section
| | $\epsilon$ | $n\epsilon$ (nodes) | Upper bound on $\mathbb{P}$ | | ||
| |:-----------:|:---------------------:|:---------------------:| | ||
| | 0.0 | 0 | 2.36*10^37 | | ||
| | 0.1 | 1 000 | 10^-960.9 | | ||
| | 0.2 | 2 000 | 10^-2607.9 | | ||
| | 0.3 | 3 000 | 10^-4536.5 | | ||
| | 0.4 | 4 000 | 10^-6674.8 | | ||
| | 0.5 | 5 000 | 10^-8995.6 | | ||
| | 0.6 | 6 000 | 10^-11491.3 | | ||
| | 0.7 | 7 000 | 10^-14169.4 | | ||
| | 0.8 | 8 000 | 10^-17057.3 | | ||
| | 0.9 | 9 000 | 10^-20226.8 | | ||
| | 1.0 | 10 000 | 10^-24045.0 | | ||
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I'd prioritize values in the most interesting range, i.e. small and near the transition from unsafe to safe. These are the log2 values of the bound for [0.01, 0.02, 0.03, 0.04, 0.05]:
127.43879660818209
-66.57921254923122
-337.35094215358595
-658.5475731661436
-1017.6532434515411
In other words, these parameters are good for epsilon >= 2-3%, depending on the failure probability you're ok with
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Alternatively, could show (as an image or table) the minimum number of samples to achieve a certain failure probability for a given epsilon, e.g. this plot is with failure probability 2^-128, n = 10k
| | $\epsilon$ | $n\epsilon$ (nodes) | Upper bound on $\mathbb{P}$ | | ||
| |:-----------:|:--------------------:|:-----------:| | ||
| | 0.01 | 1 00 | 10^38.36 | | ||
| | 0.02 | 2 00 | 10^-20.04 | | ||
| | 0.03 | 3 00 | 10^-101.55 | | ||
| | 0.04 | 4 00 | 10^-198.24 | | ||
| | 0.05 | 5 00 | 10^-306.34 | |
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| | $\epsilon$ | $n\epsilon$ (nodes) | Upper bound on $\mathbb{P}$ | | |
| |:-----------:|:--------------------:|:-----------:| | |
| | 0.01 | 1 00 | 10^38.36 | | |
| | 0.02 | 2 00 | 10^-20.04 | | |
| | 0.03 | 3 00 | 10^-101.55 | | |
| | 0.04 | 4 00 | 10^-198.24 | | |
| | 0.05 | 5 00 | 10^-306.34 | | |
| | $\epsilon$ | $n\epsilon$ (nodes) | Upper bound on $\mathbb{P}$ | | |
| |:----------:|:-------------------:|:---------------------------:| | |
| | 0.01 | 100 | $10^{38}$ | | |
| | 0.02 | 200 | $10^{-20}$ | | |
| | 0.03 | 300 | $10^{-101}$ | | |
| | 0.04 | 400 | $10^{-198}$ | | |
| | 0.05 | 500 | $10^{-306}$ | |
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