Shamir's Secret Sharing

Shamir's Secret Sharing (SSS) is a method for dividing a secret into multiple pieces, called shares, such that a specified minimum number of shares (called the threshold) are required to reconstruct the original secret. This can be useful in the context of seed phrases for secure backup and recovery of self-custody wallets.

For example, let's say you have a secret 12-word seed phrase for your bitcoin wallet, and you want to use Shamir's secret sharing to divide it into five shares. You could divide the seed phrase into five shares such that any three of the shares are required to reconstruct the original seed phrase. This means that you could give one share to each of three different trusted friends, and as long as any three of them are able to get together and combine their shares, they will be able to recover the original seed phrase and access your bitcoin wallet.

This can be a more secure way to back up your seed phrase because it reduces the risk of a single point of failure. If you were to just give a copy of your seed phrase to one friend, and something were to happen to that friend or their copy of the seed phrase, your wallet would be at risk of being lost forever. But with Shamir's secret sharing, as long as any three of your five friends still have their shares, you can recover your wallet.