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THE MATHS, GENTLY

Schnorr signatures

Taproot introduced Schnorr signatures: a fixed 64 bytes, simpler maths, batch verification and multi-party key aggregation. Learn what changed.

What changed

Schnorr signatures arrived with Taproot in November 2021 (BIP 340).

ECDSASchnorr
Size71–72 bytes64 bytes
Public key33 bytes32 bytes (x-only)
MalleableYes, needed fixesNo
Batch verificationNoYes
Easy key aggregationNoYes

Linearity: the big win

Schnorr's maths is "linear": signatures and keys can be added together. With protocols like MuSig2, several people can combine their keys into one public key and jointly produce one signature.

Key aggregation: three signers, one key and one signature on-chainAlice keyBob keyCarol keyOnecombined keylooks like a single user
Key aggregation: three signers, one key and one signature on-chain

On-chain, a 3-of-3 multisig spend looks exactly like an ordinary single-signature spend: smaller and more private.

Batch verification

A node can check many Schnorr signatures together faster than one by one, which helps during Initial block download (IBD).

Why it took until 2021

Schnorr signatures were invented by Claus-Peter Schnorr around 1989, but a patent covered them until 2008. When Bitcoin launched, ECDSA was the standardised, patent-free option. Adding Schnorr later needed a soft fork, which arrived with Taproot.

MuSig2 and FROST

  • MuSig2: n-of-n signing, where all parties combine into one key.
  • FROST: threshold signing (like 2-of-3) that still produces one ordinary-looking signature.

Both make shared custody cheaper and more private on-chain.

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Key takeaways

  • Schnorr signatures are 64 bytes and arrived with Taproot.
  • They are non-malleable and support batch verification.
  • Key aggregation lets many signers look like one on-chain.

Common questions

Do Schnorr signatures use a different curve?

No, they use the same secp256k1 curve as ECDSA.

Can I use Schnorr with my old address?

No, only Taproot (bc1p) outputs use Schnorr signatures.

Are Schnorr signatures more secure than ECDSA?

They have a cleaner security proof and no malleability. Both are considered secure today.

Do Schnorr signatures save fees?

Yes, slightly per signature, and greatly when many signers aggregate into one.