Signature

A signature, in bitcoin, is a cryptographic proof that the holder of a private key authorized a specific transaction. Produced with ECDSA since 2009 and additionally with the 64-byte Schnorr scheme since the Taproot upgrade of 2021, it can be verified by anyone using the corresponding public key, without the key holder revealing the secret itself.

Why it matters

Signatures are the entire basis of ownership in bitcoin. There is no registry of names, no account recovery, and no institution that decides disputes: coins move if and only if a valid signature satisfies the script guarding them, and every one of the network's nodes checks every signature independently. The same mechanism proves authorship off-chain, since a message signed with an address's key demonstrates control of that address, a technique used in proof of reserves attestations and in settling public disputes about who controls famous coins.

How it works

The wallet hashes the relevant parts of the transaction into a digest, then combines the digest, the private key, and a random nonce into a pair of numbers that satisfy a curve equation on secp256k1. Verifiers plug the signature, digest, and public key into the same equation. The nonce must never repeat: reusing one across two signatures exposes the private key algebraically, an error that has drained real wallets and famously broke the PlayStation 3's code signing in 2010. Deterministic nonce generation is now standard practice to eliminate the risk.