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A multi-signature address is an address that is associated with more than one ECDSA private key. The simplest type is an m-of-n address - it is associated with n private keys, and sending bitcoins from this address requires signatures from at least m keys. A multi-signature transaction is one that sends funds from a multi-signature address.

The primary use case is to greatly increase the difficulty of stealing the coins. With a 2-of-2 address, you can keep the two keys on separate machines, and then theft will require compromising both, which is very difficult - especially if the machines are as different as possible (e.g., one pc and one dedicated device, or two hosted machines with a different host and OS).

It can also be used for redundancy to protect against loss - with a 2-of-3 address, not only does theft require obtaining 2 different keys, but you can still use the coins if you forget any single key. This allows for more flexible options than just backups.

It can also be used for more advanced scenarios such as an address shared by multiple people, where a majority vote is required to use the funds.

Multi-signature transactions are often conflated with BIP 16 and 17. In fact they are not directly related. Multi-signature transactions have been supported by the protocol for a long time; but implementing them would require a special output script.

What BIP 16/17 do is offer a standard way to encapsulate a script within an address; this makes it easier to use advanced scripts, with the most prominent example being multi-signature transactions.

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And for the parts that are missing yet: Needed in the client yet are "RPC calls to implement BIP 10 or something like it" - bitcointalk.org/index.php?topic=82213.msg906833#msg906833 - en.bitcoin.it/wiki/BIP_0010 –  Stephen Gornick May 18 '12 at 20:37
    
So as of now multisignatures are not supported and non-standard. –  Jus12 Mar 19 at 13:08
    
@Jus12: They're supported (Bitcoin Core raw transaction API) and AFAIK standard. –  Meni Rosenfeld Mar 19 at 17:06
    
Multisig transactions are indeed standard, you can see several of them being created on the blockchain. To build one easily see: dev.blockcypher.com/#multisig –  Matthieu Jul 1 at 19:55

Enjoy!

"Bitcoin Faucet Hacked" How a future version of the Faucet will work to prevent a similar incident:

"BIP 16 / 17 in layman's terms"

"The Truth behind BIP 16 and 17"

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Multisig have lots of uses, wallet sharing, increased security and escrow to say the first that come to mind.

Increased security: 2FA purposes or even help provide services like double spend prevention and instant confirmation.

If you want to try an open source wallet with all these features in action try https://greenaddress.it

It allows you to smoothly create P2SH Multisig transaction but with a simple intuitive interface that hides all the complexity.

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