CRYPTO LAB A share is not a slice.
One share does not reveal one piece of the message. With correctly randomized Shamir sharing, fewer than the threshold reveal no information about the secret.
A game of shared trust
Secret Council.
One secret. No single keeper.
Build a council that can keep a secret and bring it back.
CHAPTER 01 / 06BEST —
The council chamber
3 / 3 shares assignedTHE CITY’S SECRETSEALEDShared trust begins here
ArchiveHarborTower
Select keepers to give each one a distinct share. Select again to remove.
One secret. Shared responsibility.
The first oath
The threshold is how many distinct shares must come together.
Prepare for these trialsEach is independent
Take your time. Your decisions count, not your speed.
A charter that lasts
The secret is in good hands.
The idea behind the game
Trust, shared.
Power, balanced.
A share is a mathematical point. Enough distinct points recover the secret. A smaller collection leaves every possible secret open.
Higher is a tradeoff.
A larger threshold makes a larger coalition necessary to recover the secret. It also means fewer keepers can be absent. A council needs to plan for both.
Different people. Shared risks.
Two keepers in the same building may disappear in the same outage. The later chapters ask you to distribute shares across independent locations.
Optional · no algebra needed to playWhy aren’t fewer shares enough?
Try a separate, freshly randomized 3-of-5 example. Everything is calculated modulo 17: numbers wrap around after 16.
Choose a possible secret. The plot shows one compatible polynomial’s points. With fewer than three shares, each of the 17 secrets is compatible; the number of matching coefficient choices is equal for every secret.
○ Compatible values● Visible shares◆ Candidate secret at x = 0
| Share x | Value y |
|---|