Shamir's Secret Sharing, explained simply

← Blog · July 3, 2026 · Capsulene Team

How do you store a secret so that no single person — not you, not the service, not your heir — can be the weak point? In 1979, cryptographer Adi Shamir answered with a scheme that still underpins serious key management today: split the secret into shares, where enough shares reconstruct it perfectly and fewer reveal nothing at all.

The intuition: a line through a point

Two points define a line; one point defines nothing — infinitely many lines pass through it. Hide your secret as the spot where a line crosses the y-axis, hand out points on that line, and you've built a 2-of-N scheme: any two points recover the line (and the secret); a single point is mathematically worthless. Shamir generalized this with polynomials — need k shares, use a curve of degree k−1 — but the line picture is the whole idea.

Not encryption — something stronger, differently

An encrypted file with one key has one weak point: the key. Split that key with Shamir 2-of-3, and there is no single thing to steal. One share leaks? The thief has a point on an unknown line: nothing. One share burns in a fire? Any two of the remaining still recover. Security and redundancy, from the same math.

Why 2-of-3 fits inheritance perfectly

The inheritance problem is a trust triangle: you, your heir, and a service. Nobody should hold the whole key alone; no single loss should destroy it. Capsulene's key capsules encrypt contents in your browser, then split the key 2-of-3 — one share to you, one to your recipient, one to Capsulene:

Capsulene alone: nothing. Zero-knowledge isn't a promise, it's arithmetic.
Your heir alone, today: nothing — no early peeking.
Heir + Capsulene, after the dead-man trigger fires: two shares — the capsule opens exactly when it should.
Capsulene disappears: you + your heir hold two shares — the secret survives the service.

See the key-share exchange in the guide, or the full crypto-inheritance walkthrough.

Protect a key with 2-of-3 secret sharing — free to start.

Create a key capsule