Three secret sharing schemes, side-by-side — security model, verifiability, traceability guarantees, and suitability for distributed protocols.
| Property | Shamir SSS | Feldman VSS | Traceable Shamir |
|---|---|---|---|
| Evaluation points | Fixed integers 1, …, n | Fixed integers 1, …, n | Random xᵢ ←$ 𝔽* |
| Threshold | (t+1)-of-(n−1) | (t+1)-of-(n−1) | t-of-n |
| Share verifiability | None | Per-share group check | None (combinable with Feldman) |
| Dealer must be trusted | Yes | No — commitments are public | Yes |
| Identify leakers | Impossible | Impossible | Yes — up to f < t parties |
| Trace key | — | — | tk = (H(x₁),…,H(xₙ)) |
| Extra public data | — | t+1 group elements | — |
| Oracle access needed | — | — | Black-box reconstruction oracle |
| Info-theoretic security | Yes | Yes (DLog for verifiability) | Yes |
| Suitable for DKG | Risky | Yes | Yes (random points compatible) |