Part A : Shamir secret sharing scheme (SSSS)
SSSS is a way where you can split some data into m of n parts called secrets where if you bring m or more parts, you can reconstruct the original data. If you have m-1 or lesser parts you get no information of the original data. 2/3 SSSS applied on ‘hello’ gives the following secrets:
Clearly, knowing one part gives you no information about the original data i.e. ‘hello’.
For crypto asset security, SSSS is applied on a user’s 12/24 word wallet mnemonic phrase. Eg: For a 2 of 3 SSSS, someone having access to one part, wouldn’t be able to deduce anything about your wallet phrase. This is how a sample wallet mnemonic phrase looks like:
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1) No need to get signatures from multiple devices for doing every transaction
Think of SSSS as a backup mechanism, you generate secrets of your wallet mnemonic phrase and distribute them among a set of trusted devices & friends. In case you lose your phone, your phone gets damaged etc., you gain access to a new phone and recover your mnemonic using the backed up secrets and hence gain access to your funds. Your crypto assets always stay on your main device and relevant transactions can be made from the device itself.
2) Advanced sharing schemes like 6/11, 26/51
SSSS utilizes polynomial mathematics and there is no limitation on m & n in a m of n scheme. In the extreme case, one can use schemes like 26/51 with the 51 parts stored in places like bunkers, bank lockers, although I envision people not going over 6/11 scheme especially if they are using phones/hardware devices for storing the secrets. For a multi-sig based setup, there are limitation on m & n. Eg : For a P2SH multisig with uncompressed public keys, n can be upto 7, refer this.
3) Ability to support multiple coins
SSSS can be applied on any data to create relevant secrets. If applied on a BIP39 mnemonic, the secrets can be used to generate back the mnemonic phrase which can then be used to regenerate the private keys of all the coins.
This mnemonic serves as the “root” of the tree and it can be algorithmically converted into the all the relevant private keys. This is why all wallet providers only require you to right down your mnemonic phrase and not private keys of the individual coins. This means SSSS can be used for backing up all crypto assets like BTC, ETH, XMR, DOGE etc. as well as all your other altcoins.
1) Funds have to be on one device
One security issue with SSSS is that your crypto assets stay on one device itself, the other devices holding the relevant secrets just serve as a backup of the funds and are not required for doing any transaction. Although, if you are using a non-custodial mobile wallet like Coinsafe for storing your crypto assets & say your device gets stolen, the thief would require some time to brute force your phone PIN as well as your wallet PIN to gain access to your funds. During this time, you can move your funds to a new wallet.