Secret Sharing Schemes Référence
Référence pour Shamir et autre threshold secret sharing schemes pour distributed clé custody.
Shamir Secret Sharing
Shamir's scheme splits a secret into n shares such that any k shares reconstruct the secret, but k-1 shares reveal nothing. The construction uses polynomial interpolation over a finite field: a random degree-(k-1) polynomial with the secret as the constant term. The scheme is information-theoretically secure, relying on no computational assumptions. It is widely used for key custody and MPC ceremonies.
- threshold
- k-of-n reconstruction
- field
- Finite field arithmetic
- security
- Information-theoretic
any k shares sufficeGF(p) for prime pno computation assumptionVariants and Applications
Verifiable secret sharing adds commitments allowing shareholders to verify share consistency. Packed secret sharing packs multiple secrets into one polynomial for efficiency. Proactive secret sharing refreshes shares periodically without changing the secret to defend against mobile adversaries. Applications include threshold cryptography, secure multiparty computation, and key escrow.
- verifiable
- Share validity checks
- packed
- Multiple secrets per polynomial
- proactive
- Periodic share refresh
Feldman/Pedersen VSSamortized costmobile adversary