Multisignature (often called “multisig”) refers to requiring multiple keys to spend funds in a Bitcoin Cash transaction, rather than a single signature from one key. It has a number of applications and allows users to divide up responsibility for possession of coins.
Multisignature scripts set a condition where N public keys are recorded in the script and at least M of those must provide signatures to unlock the funds. This is also known as M-of-N multisignature scheme, where N is the total number of keys and M is the threshold of signatures required for validation. The signatures used can either be ECDSA signatures or Schnorr signatures.
Multisig schemes can be built with the opcodes
OP_CHECKMULTISIGVERIFY, two opcodes of the Bitcoin Cash scripting language.
OP_CHECKMULTISIGVERIFY has the same implementation as
OP_CHECKMULTISIG, except OP_VERIFY is executed afterward.
OP_CHECKMULTISIG can be included in all sorts of scripts. The minimal locking script using
M <pubkey1> ... <pubkeyN> N CHECKMULTISIG
This script creates a P2MS (raw multisig) output. It can also be used as a redeem script for a P2SH output.
The unlocking script corresponding to the previous locking script is:
<dummy> <sig1> ... <sigM>
Upon script execution, this will act like:
<dummy> <sig1> ... <sigM> M <pubkey1> ... <pubkeyN> N CHECKMULTISIG
Due to a historical bug (the original implementation of
M+N+3 items on the stack instead of
M+N+2), an extra unusued value called the
dummy element was included in the script. This was usually done via
OP_0. Since the HF-2019115 Bitcoin Cash upgrade, this element has been repurposed as a trigerring and execution mechanism.
In particular, the value of the
dummy element determines whether ECDSA or Schnorr signatures have to be used. If
0 (i.e., an empty byte array), then all signatures must be produced by ECDSA. If
dummy is not
0, then all signatures must be produced by the Schnorr algorithm and the
dummy element is interpreted as a bitfield called
OP_CHECKMULTISIG execution, the ECDSA mode (
dummy = 0) is:
The Schnorr mode (
dummy = checkbits > 0) operates similarly, but only checks signatures as requested, according to the
checkbitsis set, then the first signature is checked against the first public key.
checkbitsis bit-shifted to the right (
checkbits := checkbits >> 1).
checkbitsvalue is non-zero, then
Because public keys are not checked again if they fail any signature comparison (in both cases), signatures must be placed in the unlocking script using the same order as their corresponding public keys were placed in the locking script (P2MS) or redeem script (P2SH).
Note that the
checkbits element is encoded as a byte array of length
floor((N + 7)/8) (the shortest byte array that can hold N bits) and must have exactly M bits set to ensure that all signatures are checked against public keys.
To know more about the Schnorr mode, see the specification.
The most commonly used scheme is the 2-of-3 multisig scheme:
2 <pubkeyA> <pubkeyB> <pubkeyC> 3 CHECKMULTISIG
where 2 out of 3 participants (Alice, Bob and Carol) can sign a transaction from the shared account.
Let’s say Alice and Carol want to spend funds. If they want to use ECDSA, they have to sign the transaction with this algorithm and build the following script:
0 <sigA> <sigC>
If they want to use Schnorr, they have to sign the transaction with this algorithm and build the following script:
5 <sigA> <sigC>
The value of the
dummy element is 5, whose binary representation is
0b101. This ensures that Alice’s signature (
sigA) is checked against her public key (
pubkeyA), that Carol’s signature (
sigC) is not checked against Bob’s public key (
pubkeyB) but against her public key (
N-of-N multisig schemes can also be implemented in P2PKH outputs, using the Schnorr aggregation property.
By combining the public keys of the cooperating parties, a combined public key can be created and used in a locking script.
When spending the output, the parties can jointly create a signature that will validate as a normal Schnorr signature for the combined public key in the locking script.
For more details, see MuSig.