There is another problem in key sharing: after key sharing, if you want to sign with the original key in the future, you need to obtain the sub-key, and then sign it after restoring it to the original key. This process may be used by hackers to steal keys.

Cryptography can solve this problem. If the subkeys are stored on different devices, the original keys can be recovered in a decentralized way instead of being stored on a device. This technology is called threshold signature technology. A typical example is an electronic wallet with dual security mechanisms (N=2 and K=2). If the two subkeys are stored in the personal computer and the mobile phone respectively, you can initiate payment on the computer. At this time, the computer will generate a signature fragment and send it to your mobile phone. Then, the mobile phone will prompt you for payment information (including payee, amount, etc. ) and wait for your confirmation. If you confirm the payment information, at this time, the mobile phone will complete the entire signature with its subkey and then broadcast it to the blockchain. If a hacker takes control of your computer and tries to transfer Bitcoin to his account, you will know that there is a problem according to the payment information on your mobile phone, so you will not confirm the transaction. The mathematical details involved in threshold passwords are complicated, and members can't understand them, so they won't discuss them.

Threshold signature is a technology in cryptography, which divides a key into different segments and stores them separately, and it is not necessary to restore the original key when signing a transaction. Multi-signature is the characteristic of bitcoin script, which gives control of a bitcoin account to multiple keys, and these keys * * * ensure the security of the account. Both threshold signature and multi-signature can overcome the defect of single-point key storage.

There is another way to overcome the shortcomings of single-point key storage, that is, multi-signature, a term that appears in Chapter 3. Through bitcoin scripts, you can directly hand over the control of a bitcoin account to multiple keys instead of sharing keys. These keys can be stored in different places and generate signatures respectively. Of course, the information of the final transaction will still be stored on a device, but even if the hacker controls the device, all he can do is to prevent the transaction from being broadcast to the whole network. Without the participation of other devices, he can't generate effective multiple signatures.

For example, suppose A, B, C, D and E are the founders of a company that has a lot of bitcoins. We may use multiple signatures to protect these bitcoins. Each of these five people has a key, and we can use three of them to protect the cold storage. A transaction requires the signatures of at least three of the five people to complete.

In this way, as long as the five of us are in different places and keep our keys with different security measures, Bitcoin will be quite safe. Hackers have to steal the keys of the three of us to steal bitcoin. Even if one or two of us betray us, they can't run away with the money because they need another signature. At the same time, if one of us loses the key, others can still take out Bitcoin and go to a new account to reset the password. In short, multi-signature can properly manage a large number of bitcoins in the cold storage, and any major event requires the participation of many people.

As mentioned above, people use threshold signature technology to realize double security mechanism or multiple security mechanism, and people use multiple signature technology to realize the same control of the same property by many people. In fact, both technologies can achieve the above two purposes.