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Is it possible to create a multi-signature contract that would not require a transaction for every signature (since this is quite expensive for a higher number of transactions)?

Is it possible to collect signatures offline and broadcast all of them in one on-chain transaction?

Thanks

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Yes. You can achieve this by using signatures of the member keys instead of transactions.

To achieve this, each members of the multisig can sign a message attesting that they approve of the transaction. They can then give their signatures to a single entity who broadcasts the transaction that includes all the signatures as data. On-chain, the smart contract will take each signature and recover each of the signers original addresses and compare that to a mapping of addresses stored in a mapping.

Gnosis Safe does it here.

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There's Simple Multisig, by Christian Lundkvist, that requires sending all signatures in a single transaction.

It has a execute function that validates the signatures and executes the operation requested:

function execute(
    uint8[] sigV, 
    bytes32[] sigR, 
    bytes32[] sigS, 
    address destination, 
    uint value, 
    bytes data, 
    address executor, 
    uint gasLimit) public

There's an article by the author for the previous version: Exploring Simpler Ethereum Multisig Contracts.

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