Also covering 2pECDSA and Two-Party ECDSA (2pECDSA)

Scriptless multisignatures are digital signatures created using two or more private keys which can be verified using only a single public key and a single signature.

Scriptless multisignatures can be compared with scripted multisig, the use of public keys and signatures with Bitcoin’s OP_CHECKMULTISIG and OP_CHECKMULTISIGVERIFY opcodes (and the OP_CHECKSIGADD opcode proposed for tapscript). Multisignatures have the advantage that only a single key and a single signature are published onchain when they are used in a Bitcoin transaction, allowing an unlimited number of signers to pay the same amount of transaction fee that a single signer would pay for an otherwise identical transaction. Multisignature payments being indistinguishable from single-signature payments also gives the creators of both types of payments greater privacy.

It’s possible to create multisignatures for the ECDSA algorithm supported by all versions of Bitcoin, although it’s easier to create multisignatures for schnorr signatures and several algorithms for that are known, with MuSig having been specifically created for the needs of Bitcoin users.

Terminology: the following table summarizes the differences between multisignature and related terms.

Term Private keys Messages
(e.g. tx inputs)
Published pubkeys Signatures Signers required Notes
Scripted multisig m 1 m k where k<=m k Uses Bitcoin Script multisig opcodes
Scriptless multisignatures m 1 1 1 m Indistinguishable onchain from single-sig
Threshold signature m 1 1 1 k where k<=m Indistinguishable onchain from single-sig

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