Shamir's Secret Sharing
A cryptographic scheme that splits a secret into N shares such that any threshold M can reconstruct it but fewer cannot.
Shamir's Secret Sharing (SSS) is the math behind splitting a Bitcoin seed (or any secret) into multiple shares such that any M of N shares can reconstruct it, but any M-1 reveal nothing. Named for cryptographer Adi Shamir, who published the construction in 1979.
In Bitcoin practice, the standard form is SLIP-39: a wordlist-based SSS scheme for BIP 39 seeds. Trezor implements it natively; SeedSigner can produce SLIP-39 shares from any seed. Typical configurations: 2-of-3 or 3-of-5 shares distributed across geographic locations or trusted parties.
The full discussion of SSS in Bitcoin - including the crucial caveat that SSS is not the same security model as multisig, because key reconstruction at signing time momentarily holds the full key on one device - lives at key-split.
Key takeaways
- Standard math for splitting a seed across multiple locations
- Standardized for BIP 39 seeds as SLIP-39 (Trezor supports natively)
- Not equivalent to multisig - see key-split for the security caveat