How Shamir's Secret Sharing Works

5 hours ago

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.

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