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How Shamir's Secret Sharing Works Explained

A secret becomes points on a random polynomial; any threshold of shares reconstructs the line — and fewer shares reveal nothing at all.

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Reconstruct: Two Points, One Linetwo-wayrecovery dayinstanttrustees reuniteinterpolationdisaster recovery
Split: Points on a Lineone-waysplit oncenoneany channel, any trusteepolynomial of degree K−1key recovery + custody