How Shamir's Secret Sharing Works
6 hours ago
- #cryptography
- #secret-sharing
- #Shamir
- Shamir's secret sharing allows a secret to be split into pieces, requiring a threshold number of pieces to recover it, while fewer pieces reveal nothing.
- The method uses geometry: a secret is hidden as the y-intercept of a line or curve; each share is a point on that line or curve.
- Two points determine a line (2-of-n scheme), three determine a parabola (3-of-n), and in general, a polynomial of degree k-1 requires k shares.
- Implementations use finite-field arithmetic, ensuring that with insufficient shares, every possible secret remains equally likely.
- This concept is applied in practical scenarios like Ente's Legacy Kit, where it enables recovery without exposing permanent keys and allows revocation of shares.