Kurihara backup

[qlrd]

Reference PR: #883 (comment)

From what i got, it's a similar idea to Hamming XOR n-of-m backup¹. Similar to CC n-of-n.

Already used once and experimented with reference implementation. Was nice.

So i think that the academic references (what is good) could be interpreted as "Hamming with steroids". As my epistemological mother is experimental music, i would experiment with this. But experiment a lot, because any other wallet AFAIK implemented that.

I once talked about this with @oleonardolima from BDK and IIRC he liked the idea but said me that almost no one knows that.

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Footnotes

1. https://cp4space.hatsya.com/2021/09/10/hamming-backups-a-2-of-3-variant-of-seedxor/ ↩

[CaverneCrypto]

Thanks for the Hamming-backups pointer — it's a fair comparison in spirit: both are XOR-based, loss-tolerant, and produce valid BIP39 shares.

The key difference is generality. Hamming backups (Gassmann / cp4space) are a clever but fixed 2-of-3 construction built on a parity/Hamming structure. Kurihara is a general ideal (k, n)-threshold scheme: you pick any n-of-m, every share is exactly the size of the secret (the "ideal" property), and it comes with information-theoretic confidentiality proven for every coalition below the threshold. So "Hamming with steroids" captures the vibe, but it's really a different, more general construction — arbitrary thresholds + formal security proofs, not just 2-of-3.

Fully agree it's under-explored — which is exactly why a working, tested reference implementation helps. There's now a full split/restore UI up in #883 if you'd like to try it. Appreciate the thoughtful framing. 🙏