How Shamir's Secret Sharing Works

Shamir's Secret Sharing, published in 1979, is a cryptographic method that splits a secret into pieces where any k pieces can reconstruct it, but fewer than k pieces reveal nothing about the secret. The technique uses polynomials of varying degrees—a line for 2-of-n sharing, a parabola for 3-of-n sharing, and higher-degree curves for larger thresholds—where the secret is hidden at a specific point on the curve and each person receives one point. Ente's Legacy Kit employs this scheme as part of a larger recovery system that allows distributed secret reconstruction without creating a permanent vulnerability if individual shares are lost.