Public-key cryptography is used to transfer data securely over open networks by encrypting the data sent to an address (public key) such that it can only be decrypted using the private key associated with the recipient's public key. There are a few potential problems with this system:
- Lack of security - A single-key wallet is vulnerable to malware and other attacks, especially if the private key is stored online (i.e. hot storage).
- Lack of access control for businesses - A business that transacts in Bitcoin, for example, will be vulnerable to insider theft if multiple people are entrusted with the same private key.
- Lack of recovery options - If the owner of a wallet permanently loses their private key, they will never be able to recover the funds in their wallet.
Multi-Signature wallets require that several private keys (aka digital signatures) are used together in order to authorize a transaction. It is up to the wallet owner to decide how many private keys are created and how many are required to authorize a transaction.
Example 1: If two people who co-own a business that uses Bitcoin want to minimize the need to trust each other, they could create a multi-sig wallet which requires both of their private keys to authorize a transaction moving BTC out of the wallet. This is called a 2-of-2 wallet
Example 2: An individual who's worried about losing their private key could have a multi-sig wallet with 3 private keys that only requires 2 keys to authorize a transaction. That way, he/she could recover the funds in the wallet even if they lose 1 of the private keys. This is called a 2-of-3 wallet.
Example 3: An individual makes their software wallet more secure with two-factor authentication, which requires one private key stored on their computer and one generated by a mobile app on their phone such as Google Authenticator. (2-of-2)
