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Is it possible for person A, person B, and person C to create a multiple signature address without one person needing to initially know all three addresses to create that public address in the first place?
Ideally 5 people somehow create an address together, maybe passing it on to each other? But only if 3 out of those 5 private keys are used, can money be gotten out of that wallet?
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You need the public addresses of all persons involved in order to create the multi-sig address. So if you are creating a 3 of 5 multi-sig address you need all 5 public address. In order to retrieve funds from that address you need signatures from 3 of the 5 people (or however many signatures you require). Check out this example here, which was a huge help for me.
bitrated.com and https://coinb.in/multisig/ have open source implementations of this as well.
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When you create a multi-signature address using pay-to-script-hash (p2sh), you create an address by hashing a redeemscript (hence the name). This redeemscript specifies the requirements to spend any funds sent to the resulting address. To lock funds to a quorum of 3-of-5, you will need to include the five public keys of the involved parties in the redeemscript. Therefore, neither addresses nor private keys are needed to generate a multi-signature address, but all five public keys must be known to the party that creates the address. As the redeemscript (and therefore the public keys) is revealed at the time of spending funds sent to the address in the transaction's input script, there is no expectation of keeping the public keys private in the long run.
To maintain privacy, the five participants should each generate a new key pair for this multi-signature address instead of reusing an existing public key. They could however use their existing public keys to authenticate the new public keys by signing a message stating their ownership with their old public key.
