Shamir’s Secret Sharing Explained: How 2-of-3 Keys Work

The idea in one picture

Two points define a straight line. Hide your secret as the place where a randomly chosen line crosses the vertical axis, then give each person one point on the line. Any two points recover the line — and the secret. A single point tells you nothing, because infinitely many lines pass through it.

Why not just make copies?

• Every copy is another way to steal the secret.
• A single copy is another way to lose it.
• Splitting reduces both risks: theft needs several holders to cooperate, loss needs several to disappear.

Choosing the threshold

• 2 of 3: easy to arrange and tolerant of one lost share
• 3 of 5: safer against collusion, needs more people to be reachable
• The higher the threshold, the harder it is to steal — and the easier it is to lose access

What it does not do

It cannot help if too many holders lose their shares, and it protects the secret only as well as each holder protects their share. It also does not decide when the shares should be released — that is the job of a careful switch and clear instructions.

How Wirātha uses it

Each vault has its own key pair. The private key is split into three shares, each sealed to one holder with that holder’s own key, and the whole key is then discarded. Any two holders can open the vault; Wirātha stores only the sealed shares.