This property is not observed in MuSig2’s key generation, as it uses additive secret sharing and randomization.
18.01.2025 08:37 — 👍 0 🔁 0 💬 0 📌 0This property is not observed in MuSig2’s key generation, as it uses additive secret sharing and randomization.
18.01.2025 08:37 — 👍 0 🔁 0 💬 0 📌 0ChillDKG uses this property to commit its threshold public key to an unspendable script path, making it Taproot-safe.
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Proof by Lagrange interpolation
While reviewing the ChillDKG BIP, I noticed a neat property: In a t-of-n Shamir sharing scheme, where combining shares s1, s2, and s3 gives a secret c. If you offset these shares by adding a constant k (i.e., s1 + k, s2 + k, s3 + k), the result will be an offset secret c + k.
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