Shamir Secret Sharing

Shamir Secret Sharing (SSS) divides a secret, like a crypto wallet seed, into multiple shares. A threshold number of shares reconstructs it, enhancing security as in SLIP-39 backups.

Security

Updated: Mar 19, 2026

Also known as: SLIP39 Shamir backup SSS

What Is a Shamir Secret Sharing?

A Shamir Secret Sharing (SSS) splits a secret into multiple shares. A predefined threshold number of shares reconstructs the secret. Fewer shares reveal nothing. Developers use it for secure backups, like cryptocurrency wallet seeds.

SSS relies on polynomial mathematics. The creator picks a secret as the constant term of a random polynomial of degree t-1, where t is the threshold. They generate n shares by evaluating the polynomial at n distinct points. Each share is a pair (x, y).

To recover the secret, combine any t shares. Use Lagrange interpolation to rebuild the polynomial. The y-intercept gives the secret. For example, split a 12-word wallet seed into 7 shares with a 4-of-7 threshold. Lose 3 shares? Still recover it safely.

SSS provides information-theoretic security. Even infinite computing power cannot crack it with fewer than t shares. In crypto, SLIP-39 applies SSS to mnemonic phrases for hardware wallets like Trezor. It beats single-seed backups by avoiding single points of failure. Users store shares separately, like with family or safes.

Key traits include customizable t-of-n schemes and perfect secrecy. Synonyms cover SLIP-39, Shamir backup, and SSS.

Real-World Examples

Example 1: Hardware Wallet Backup

Trezor users enable SLIP-39 to split a 20-word recovery seed into 33 shares with a 3-of-33 threshold. Store shares in separate locations, like home safes and bank vaults. Lose two shares? Combine three to recover the wallet.

Example 2: Family Inheritance

A crypto holder creates a 7-of-11 Shamir backup of their wallet seed. Give one share to each of five family members and store three in trusted safes. After passing, heirs gather seven shares to access funds without trusting a single person.

Example 3: Enterprise Key Management

A company splits a master encryption key into 5-of-9 shares using SSS. Distribute shares to executives. Any five can reconstruct the key for operations, but no single executive or small group holds full control.