To date, the multisigs described in these documents have been entirely simple, of the m-of-n or n-of-n form. However, you might desire more complex multisigs, where cosigners vary or where different options might become available over time.
A variable multisig requires different numbers of people to sign depending on who is signing.
Imagine a corporation where either the president or two-out-of-three vice presidents could agree to the usage of funds.
You can write this by creating an IF/ELSE/ENDIF statement that has two blocks, one for the president and his one-of-one signature and one for the vice-presidents and their two-of-three signatures. You can then determine which block to use based on how many signatures are in the unlocking script. Using OP_DEPTH 1 OP_EQUAL will tell you if there is one item on the stack, and you then go from there.
The full locking script would be OP_DEPTH 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
If run by the president, it would look like this:
Script: <sigPres> OP_DEPTH 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Stack: [ ]
Script: OP_DEPTH 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Stack: [ <sigPres> ]
Script: 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Running: <SigPres> OP_DEPTH
Stack: [ <sigPres> 1 ]
Script: OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Stack: [ <sigPres> 1 1 ]
Script: IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Running: 1 1 OP_EQUAL
Stack: [ <sigPres> True ]
Because the result is True, the Script now collapses to the IF statement:
Script: <pubKeyPres> OP_CHECKSIGNATURE
Running: True IF
Stack: [ <sigPres> ]
Script: OP_CHECKSIGNATURE
Stack: [ <sigPres> <pubKeyPres> ]
Script:
Running: <sigPres> <pubKeyPres> OP_CHECKSIGNATURE
Stack: [ True ]
If run by two vice-presidents, it would look like this:
Script: 0 <sigVPA> <sigVPB> OP_DEPTH 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Stack: [ ]
Script: OP_DEPTH 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Stack: [ 0 <sigVPA> <sigVPB> ]
Script: 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Running: 0 <sigVPA> <sigVPB> OP_DEPTH
Stack: [ 0 <sigVPA> <sigVPB> 3 ]
Script: OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Stack: [ 0 <sigVPA> <sigVPB> 3 1 ]
Script: IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG ENDIF
Running: 3 1 OP_EQUAL
Stack: [ 0 <sigVPA> <sigVPB> False ]
Because the result is False, the Script now collapses to the ELSE statement:
Script: 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG
Running: False IF
Stack: [ 0 <sigVPA> <sigVPB> ]
Script: OP_CHECKMULTISIG
Stack: [ 0 <sigVPA> <sigVPB> 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 ]
Script:
Running: 0 <sigVPA> <sigVPB> 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> 3 OP_CHECKMULTISIG
Stack: [ ]
You might notice that the President's signature just uses a simple OP_CHECKSIGNATURE rather than the more complex code usually required for a P2PKH. We can get away with including the public key in the locking script, obviating the usual rigamarole, because it's hashed and won't be revealed (through the redeemScript) until the transaction is unlocked. This also allows for all of the possible signers to sign using the same methodology.
The only possible problem is if the President is absent-minded and accidentally signs a transaction with one of his VPs, because he remembers this being a 2-of-3 multisig. One option is to decide that's an acceptable failure condition, because the President is using the multsig incorrectly. Another option is to turn the 2-of-3 multisig into a 2-of-4 multisig, just in case the President doesn't tolerate failure: OP_DEPTH 1 OP_EQUAL IF <pubKeyPres> OP_CHECKSIGNATURE ELSE 2 <pubKeyVPA> <pubKeyVPB> <pubKeyVPC> <pubKeyPres> 4 OP_CHECKMULTISIG ENDIF. This would allow the President to mistakenly sign with any Vice President, but wouldn't impact things if two Vice Presidents wanted to (correctly) sign.
Another multisig possibility involves have a m-of-n multisig where one of the signers is required. This can usually be managed by breaking the multisig down into multiple m of n-1 multisigs. For example, a 2-of-3 multisig where one of the signers is required would actually be two 2-of-2 multisigs, each including the required signer.
Here's a simple way to script that:
OP_3DUP
2 <pubKeyRequired> <pubKeyA> 2 OP_CHECKMULTISIG
NOTIF
2 <pubKeyRequired> <pubKeyB> 2 OP_CHECKMULTISIG
ENDIF
The unlocking script would be either 0 <pubKeyRequired> <pubKeyA> or 0 <pubKeyRequired> <pubKeyB>.
First the Script would check the signatures against <pubKeyRequired> <pubKeyA>. If that fails, it would check against <pubKeyRequired> <pubKeyB>.
The result of the final OP_CHECKMULTISIG that was run will be left on the top of the stack (though there will be cruft below it if the first one succeeded).
We've talked a lot about escrows. Complex multisigs combined with timelocks offer an automated way to create them in a robust manner.
Imagine home buyer Alice and home seller Bob who are working with an escrow agent. The easy way to script this would be as a multisig where any two of the three parties could release the money: either the seller and buyer agree or the escrow agent takes over and agrees with one of the parties: 2 <pubKeyA> <pubKeyB> <pubKeyEscrow> 3 OP_CHECKMULTISG.
However, this weakens the power of the escrow agent and allows the seller and buyer to accidentally make a bad decision between themselves — which is one of the things an escrow system is designed to avoid. So it could be that what we really want is the system that we just laid out, where the escrow agent is a required party in the 2-of-3 multisig: OP_3DUP 2 <pubKeyEscrow> <pubKeyA> 2 OP_CHECKMULTISIG NOTIF 2 <pubKeyEscrow> <pubKeyB> 2 OP_CHECKMULTISIG ENDIF.
However, this doesn't pass the walk-in-front-of-a-bus test. If the escrow agent dies or flees to the Bahamas during the escrow, the buyer and seller are out a lot of money. This is where a timelock comes in. You can create an additional test that will only be run if we've passed the end of our escrow period. In this situation, you allow the buyer and seller to sign together:
OP_3DUP
2 <pubKeyEscrow> <pubKeyA> 2 OP_CHECKMULTISIG
NOTIF
OP_3DUP
2 <pubKeyEscrow> <pubKeyB> 2 OP_CHECKMULTISIG
NOTIF
<+30Days> OP_CHECKSEQUENCEVERIFY OP_DROP
2 <pubKeyA> <pubKeyB> 2 OP_CHECKMULTISIG
ENDIF
ENDIF
First, you test a signature for the buyer and the escrow agent, then a signature for the seller and the escrow agent. If both of those fail and 30 days have passed, then you also allow a signature for the buyer and seller.
BIP 112 offers a different example of this sort of escrow that doesn't have the extra protections to prevent going around the escrow agent, but which does give Alice total control if the escrow fails.
IF
2 <pubKeyA> <pubKeyB> <pubKeyEscrow> 3 OP_CHECKMULTISIG
ELSE
<+30Days> OP_CHECKSEQUENCEVERIFY OP_DROP
<pubKeyA> OP_CHECKSIGNATURE
ENDIF
Here, any two of the three signers can release the money at any time, but after 30 days Alice can retrieve her money on her own.
Note that this Script requires a True or False to be passed in to identify which branch is being used. This is a simpler, less computationally intensive way to support branches in a Bitcoin Script; it's fairly common.
Early on, the following sigScript would be allowed: 0 <signer1> <signer2> True. After 30 days, Alice could produce a sigScript like this: <sigA> False.
More complex multisignatures can typically be created by combining signatures or multisignatures with conditionals and tests. The resulting multisigs can be variable, requiring different numbers of signers based on who they are and when they're signing.
🔥 What is the power of complex multisig scripts? More than anything we've seen to date, complex multisig scripts are truly smart contracts. They can be very precise in who is allowed to sign and when. Multi-level corporations, partnerships, and escrows alike can be supported. Using other powerful features like timelocks can further protect these funds, allowing them to be released or even returned at certain times.
Continue "Designing Real Bitcoin Scripts" with §13.3: Empowering Bitcoin with Scripts.