Add Golden blog post#3836
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| For reconstruction, we rely on the property that given any $t$ points $p_i$, | ||
| the values $f(p_i)$ determine $f$ completely. | ||
| In fact, given any large enough subset of the $n$ players, each player | ||
| can *locally* convert their share $s_i$ into a share $s'_i$, such that: | ||
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| \sum_{i \in P} s'_i = s | ||
| $$ | ||
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| How exactly this reconstruction works isn't essential for this post; we just | ||
| care about what the sharing looks like. |
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Can we just explain lagrange interpolation here? Also can we define P?
If it's the subset of parties reconstructing, then the transformation to s_i' changes when P changes right?
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We could, but then we wouldn't reference this process at any other point in time, so I thought it was worth a bit of vagueness here to avoid going into detail.
| There are some other details that aren't too important to us, like how you | ||
| don't need to include every dealer, depending on your trust assumptions, | ||
| and how you can preserve the value of $f(0)$ across multiple rounds, so that | ||
| the secret stays static. |
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I think we can drop the secret staying the same part as the blog is only focused on dkg. But I think we should at least briefly explain that at least one honest dealer must contribute who doesn't collude with other parties and deletes their share
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Maybe we can structure as: present the semi-honest construction first where all dealers follow the protocol, but collude and we still want security.
Then explain what can go wrong if a dealer deviates before going into how golden/other work handles this
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Do you actually need dealers to delete their polynomials? If you require t different dealers, then I don't think you get much out of the dealers not deleting their polynomials, you still need t of them.
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| Let's look at how to address this. | ||
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| # The Two Round Approach |
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Should we shorten this section to just say there exist two round protocols but here are the issues? It feels like a distraction from the one round DKG approach which is the focus of this blogpost
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Perhaps, but I think it's not too much to explain the two round approach that we implement ourselves, and it could be a useful reference, because we don't have a blog about it already. It's also hard to understand some of the purported issues in the abstract, I think.
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patrick-ogrady
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just editorial comments (modulo the citation)!
| katex: true | ||
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| We've completed an initial implementation of the [Golden protocol](https://eprint.iacr.org/2025/1924), |
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I prefer focusing on "no synchrony/publicly verifiable" rather than 2->1 round but your call!
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love the new title
Also cleans up the generation of math in blog posts.
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Also cleans up the generation of math in blog posts.