What cryptographic operations are performed on the 3 public keys to produce a multisig (2 of 3) address?

Question

I'm just getting a handle on multisig, so sorry about that. I don't really get how, (what operations are performed) on the inputs (3 public keys, right?) to generate a multisig address. Or is it some simple concatenation operation?

Answer 1

To better understand multisig addresses and transactions, it's useful to read BIP 0013 and create a multisig address using https://coinb.in/multisig/

If I want to create a multisig that requires signatures from 2 of the 3 following pubkeys:

04c96a8b79aff49f36766b7827308bb5d6dc031e4e9112b785201a9a61821d2a336dbb7fa69f44c2dc76dee8fa7ed8fee2958f4a86a3dbb7ebf3eeb790cd464db9
04fd6c4db8841f7370a0cdc464a58b3e2a0da5b6566e0502a9cf583360bcdd16e8453a0a8da0fba0ff26e40c1f8c55f8cd0ad61988b7d4418b504264be8a9cef59
04c41b31403f24ef79e9c7dcfb67ea0341fcb986e9555123b022258a92d2bade3674574bf3de7affe93706399d9eb76d04f05213cda8b8e8bb8541533c39f244a9

The resulting multisig script is this: (broken down by OP code)

52 OP_2, meaning you need two signatures
41 push 65 bytes
04c96a8b79aff49f36766b7827308bb5d6dc031e4e9112b785201a9a61821d2a336dbb7fa69f44c2dc76dee8fa7ed8fee2958f4a86a3dbb7ebf3eeb790cd464db9
41 push 65 bytes
04fd6c4db8841f7370a0cdc464a58b3e2a0da5b6566e0502a9cf583360bcdd16e8453a0a8da0fba0ff26e40c1f8c55f8cd0ad61988b7d4418b504264be8a9cef59
41 push 65 bytes
04c41b31403f24ef79e9c7dcfb67ea0341fcb986e9555123b022258a92d2bade3674574bf3de7affe93706399d9eb76d04f05213cda8b8e8bb8541533c39f244a9
53 OP_3, meaning there are three public keys
ae OP_CHECKMULTISIG described at https://en.bitcoin.it/wiki/Script

And the page tells me the address for it is 3K6sEDqXaSFKjcq8PUKNsGbxXjBR8QmBWr

The hash of this script, along with a version number (to make the starting character 3) and checksum (to ensure that a misentering of data is not likely to go through) is what makes up the multisig address:

base58-encode: [one-byte version][20-byte hash][4-byte checksum]

You can verify this by comparing the hash160 value shown at https://blockchain.info/address/3K6sEDqXaSFKjcq8PUKNsGbxXjBR8QmBWr and the result of the following short C# program: they are both befcdceed8cbf0d74d9d58bf8e30ce027e8a9b56

var data = new byte[] { 0x52, 0x41, 0x04, 0xc9, 0x6a, 0x8b, 0x79, 0xaf, 0xf4, 0x9f, 0x36, 0x76, 0x6b, 0x78, 0x27, 0x30, 0x8b, 0xb5, 0xd6, 0xdc, 0x03, 0x1e, 0x4e, 0x91, 0x12, 0xb7, 0x85, 0x20, 0x1a, 0x9a, 0x61, 0x82, 0x1d, 0x2a, 0x33, 0x6d, 0xbb, 0x7f, 0xa6, 0x9f, 0x44, 0xc2, 0xdc, 0x76, 0xde, 0xe8, 0xfa, 0x7e, 0xd8, 0xfe, 0xe2, 0x95, 0x8f, 0x4a, 0x86, 0xa3, 0xdb, 0xb7, 0xeb, 0xf3, 0xee, 0xb7, 0x90, 0xcd, 0x46, 0x4d, 0xb9, 0x41, 0x04, 0xfd, 0x6c, 0x4d, 0xb8, 0x84, 0x1f, 0x73, 0x70, 0xa0, 0xcd, 0xc4, 0x64, 0xa5, 0x8b, 0x3e, 0x2a, 0x0d, 0xa5, 0xb6, 0x56, 0x6e, 0x05, 0x02, 0xa9, 0xcf, 0x58, 0x33, 0x60, 0xbc, 0xdd, 0x16, 0xe8, 0x45, 0x3a, 0x0a, 0x8d, 0xa0, 0xfb, 0xa0, 0xff, 0x26, 0xe4, 0x0c, 0x1f, 0x8c, 0x55, 0xf8, 0xcd, 0x0a, 0xd6, 0x19, 0x88, 0xb7, 0xd4, 0x41, 0x8b, 0x50, 0x42, 0x64, 0xbe, 0x8a, 0x9c, 0xef, 0x59, 0x41, 0x04, 0xc4, 0x1b, 0x31, 0x40, 0x3f, 0x24, 0xef, 0x79, 0xe9, 0xc7, 0xdc, 0xfb, 0x67, 0xea, 0x03, 0x41, 0xfc, 0xb9, 0x86, 0xe9, 0x55, 0x51, 0x23, 0xb0, 0x22, 0x25, 0x8a, 0x92, 0xd2, 0xba, 0xde, 0x36, 0x74, 0x57, 0x4b, 0xf3, 0xde, 0x7a, 0xff, 0xe9, 0x37, 0x06, 0x39, 0x9d, 0x9e, 0xb7, 0x6d, 0x04, 0xf0, 0x52, 0x13, 0xcd, 0xa8, 0xb8, 0xe8, 0xbb, 0x85, 0x41, 0x53, 0x3c, 0x39, 0xf2, 0x44, 0xa9, 0x53, 0xae, };
var sha256 = System.Security.Cryptography.HashAlgorithm.Create("SHA256");
var ripe = System.Security.Cryptography.HashAlgorithm.Create("RIPEMD160");
Console.WriteLine(string.Join("", ripe.ComputeHash(sha256.ComputeHash(data)).Select(x=>x.ToString("X2"))).ToLower());

Then when you want to pay that address, you use pay-to-script-hash output instead of a pay-to-pubkey-hash.