How Shamir's Secret Sharing Works

Some secrets are too important to trust to one person, and too important to lose if that person disappears.

A company wants three officers present before the master key is used. A family wants account recovery to need more than one envelope. A team wants a backup that survives a missing member without handing anyone the whole thing.

Adi Shamir (the S in RSA), published a way to do this in 1979. Split a secret into pieces so that some number of them can recover it, and any smaller number reveals nothing at all. Not "is hard to crack." Reveals nothing.

The core idea fits on a page.

Two points make a line

Start with something you already know: two distinct points determine exactly one straight line.

A single point does not. Infinitely many lines pass through one point, and each line crosses the…