Secret sharing, or secret splitting, divides a secret into multiple private shares. The secret might be a symmetric key or signing private key; each share is useless alone, reducing the risk of targeting one participant. section 8.8
A typical process works in three steps:
- A dealer generates the secret, splits it, distributes the shares, and deletes the original. section 8.8
- When the secret is needed for encryption or signing, share owners return their private shares to the dealer. section 8.8
- The dealer reconstructs the original secret from the returned shares, concentrating reconstruction at one place. section 8.8
The polynomial picture
Shamir’s Secret Sharing represents a secret as a polynomial. A degree-one line can be recovered from any two points; a degree-two curve needs any three. More generally, recovering a degree-n polynomial requires n + 1 points. section 8.8
