This article was originally published on my medium page on 2020-08-18.
This article was amended on 2020–12–20 to improve the description of the P2TR output scripts. Thanks to Matthew Zipkin, for pointing out the prior imprecision.

The Bitcoin community has been abuzz for a few years about bringing Schnorr signatures to Bitcoin. Since then, the idea has evolved into three formal Bitcoin Improvement Proposals: ‘BIP340 — Schnorr Signatures for secp256k1’, ‘BIP341 — Taproot: SegWit version 1 spending rules’, and ‘BIP342 — Validation of Taproot Scripts’. Respectively, they define a standard for Schnorr signatures in Bitcoin, introduce the Taproot construction, and formalize the new Script v1 instruction set. Taproot also iterates on the previous proposal of Merklized Alternative Script Trees (MAST).

This article was originally published on my medium page and hackernoon on 2018-02-03.

If you’re keeping a finger on the pulse of Bitcoin development, you’ve probably already heard about Schnorr signatures and you probably won’t find much new here. You might rather want to check out Pieter Wuille’s recent talk at BPASE18, or Bryan Bishop’s compilation of transcripts of Schnorr signature talks whom this article heavily leans on.

Bitcoin signatures are created using the Elliptic Curve Digital Signing Algorithm (ECDSA). Schnorr signatures are another form of digital signatures. The signatures are based on the same security assumptions as ECDSA and are compatible with the elliptic curve Bitcoin already uses (secp256k1). This means that Schnorr signatures can be created with the same private keys and are compatible with currently used key derivation schemes.