What Is Schnorr Signature?
Also known as: Schnorr Signatures, BIP340, BIP 340, Schnorr Signature Scheme
In short
A Schnorr signature is a digital signature scheme named after mathematician Claus-Peter Schnorr, known for its simple structure and well-analyzed mathematical security; it was added to Bitcoin with the 2021 Taproot upgrade.
For many years, Bitcoin used only ECDSA signatures. Schnorr signatures work on the same elliptic curve (secp256k1) but have a linear mathematical structure: multiple public keys and signatures can be combined into a single key and a single signature. Its implementation in Bitcoin is defined by BIP340 and it was activated together with Taproot in November 2021.
This property makes a difference especially in multisignature scenarios. With protocols such as MuSig2, for example, a spend from a wallet jointly controlled by three people appears on-chain as a single signature. This both reduces transaction size and fees and improves privacy, because an outside observer cannot tell that the transaction is multisig. Thanks to batch verification, nodes can check many signatures faster.
Compared with ECDSA, Schnorr signatures have a simpler security proof and are resistant to the signature malleability problem. However, the correct implementation of key aggregation protocols is critical; mistakes such as reusing random values (nonces) can lead to the leak of the private key. Threshold signature schemes also take advantage of similar mathematical structures.
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