Shamir's Secret Sharing.

A threshold cryptographic scheme by Adi Shamir (1979) that splits a secret into n shares such that any k can reconstruct it while fewer than k reveal nothing. It belongs to the Cryptography category of cybersecurity.

A threshold cryptographic scheme by Adi Shamir (1979) that splits a secret into n shares such that any k can reconstruct it while fewer than k reveal nothing.

Shamir's Secret Sharing (SSS), introduced by Adi Shamir in 1979, is a (k,n) threshold scheme based on polynomial interpolation over a finite field. The dealer picks a random polynomial of degree k-1 whose constant term is the secret and distributes n evaluation points as shares; any k shares allow Lagrange interpolation to recover the secret, while k-1 or fewer give no information at all (information-theoretic security). SSS supports refreshing shares without changing the secret and underpins distributed KMS root keys, HashiCorp Vault unseal keys, hardware wallet backups (SLIP-39, Trezor Shamir Backup), multi-party HSM custody, and threshold ECDSA/BLS signing schemes.

Defences for Shamir's Secret Sharing typically combine technical controls and operational practices, as detailed in the full definition above.

Common alternative names include: SSS, Shamir threshold scheme, (k,n)-threshold.