# Adaptor Signature ## Metadata **Status**:: #x **Zettel**:: #zettel/fleeting **Created**:: [[2024-03-06]] **URL**:: [surebits.com](https://suredbits.com/schnorr-applications-scriptless-scripts/) ## Definition Adaptor signature for the message $m$, the key $x$, the one-time key $k'$, and secret $t$ where $T = tG$ is $(R', s', T)$ where, $s = s' + t$, $k = k' + t$, $R'=k'G$ and $ s' = k' + H(X, R' + T, m)x $ ### Repairing Signature Verify that $s'G = R' + H(X, R' + T, m)X$. Compute $ s = s' + t = (k' + t) + H(X, R' + T, m)x = k + H(X, R, m)x $ ### Recover t From Signature $ t = s - s' $ ## Reference - [x] [[Schnorr Signature]] - [x] Surebits series on Schnorr - [x] [What are Schnorr Signatures – Introduction](https://suredbits.com/introduction-to-schnorr-signatures/) - [x] [Schnorr Signature Security: Part 1 – Schnorr ID Protocol](https://suredbits.com/schnorr-security-part-1-schnorr-id-protocol/) - [x] [Schnorr Signature Security: Part 2 – From IDs to Signatures](https://suredbits.com/schnorr-security-part-2-from-id-to-signature/) - [x] [Schnorr Multi-Signatures – MuSig](https://suredbits.com/schnorr-applications-musig/) - [x] [Batch Verification](https://suredbits.com/schnorr-applications-batch-verification/) - [x] [Schnorr Threshold Signatures](https://suredbits.com/schnorr-applications-threshold-signatures/) - [x] [Flexible Round-Optimized Schnorr Threshold – FROST](https://suredbits.com/schnorr-applications-frost/) - [x] [Schnorr Blind Signatures](https://suredbits.com/schnorr-applications-blind-signatures/) - [x] [Taproot Upgrade – Activating Schnorr](https://suredbits.com/the-taproot-upgrade/) - [x] [Schnorr Applications: Scriptless Scripts](https://suredbits.com/schnorr-applications-scriptless-scripts/) - [x] [Andreas Erwig et al. - Two-Party Adaptor Signatures from Identification Schemes](https://eprint.iacr.org/2021/150) [📖 Zotero](zotero://select/items/EDVW2NVF) - [x] [Adaptor signatures by Bitcoin Optech](https://bitcoinops.org/en/topics/adaptor-signatures/) - [x] [Adaptor signature -Schnorr signature and ECDSA by Ichiro Kuwahara](https://medium.com/crypto-garage/adaptor-signature-schnorr-signature-and-ecdsa-da0663c2adc4)