LearnBitcoin

Glossary

Shamir's Secret Sharing

A cryptographic scheme that splits a secret into N shares such that any threshold M can reconstruct it but fewer cannot.

Shamir's Secret Sharing (SSS) is the math behind splitting a Bitcoin seed (or any secret) into multiple shares such that any M of N shares can reconstruct it, but any M-1 reveal nothing. Named for cryptographer Adi Shamir, who published the construction in 1979.

In Bitcoin practice, the standard form is SLIP-39, which splits a wallet's BIP 32 master seed into shares written as words from its own 1024-word list. It is not a wrapper around BIP 39: it was proposed by BIP 39's own authors as a successor, and the two are mostly not compatible. Turning an existing 12 or 24 word phrase into SLIP-39 shares is possible only by splitting the derived 512-bit seed, which makes every share 59 words long, and the spec advises moving funds to a fresh SLIP-39 wallet instead. Trezor implements SLIP-39 natively and has made it the default backup type on its Safe devices since 2024. Common configurations: 2-of-3 or 3-of-5 shares distributed across geographic locations or trusted parties.

The full discussion of SSS in Bitcoin - including the crucial caveat that SSS is not the same security model as multisig, because key reconstruction at signing time momentarily holds the full key on one device - lives at key-split.

Key takeaways

  • Standard math for splitting a seed across multiple locations
  • Standardized for wallet seeds as SLIP-39, which replaces BIP 39 rather than wrapping it (Trezor supports it natively)
  • Not equivalent to multisig - see key-split for the security caveat

Related chapters

Corrected

  • Was: The entry said SLIP-39 is a wordlist-based Shamir scheme for BIP 39 seeds, and that SeedSigner can produce SLIP-39 shares from any seed.

    Now: SLIP-39 splits a wallet's BIP 32 master seed using its own 1024-word list and was proposed by the BIP 39 authors as a replacement for BIP 39; the two are mostly not compatible, and converting an existing phrase yields 59-word shares. SeedSigner's published feature list does not include SLIP-39, so that claim was removed. Details

Sources (4)

Related terms (4)

Published . Revised . One correction logged for this page.

Edit this page on GitHub