VEYRNOX · Learn · Shamir Secret Sharing
Shamir Secret Sharing
Shamir Secret Sharing is a cryptographic scheme that splits a secret into N shards such that any T of them can reconstruct the secret, but fewer than T reveal nothing. Adi Shamir published the scheme in 1979; it is provably information-theoretically secure.
How it works
The scheme uses polynomial interpolation over a finite field. The secret is encoded as the constant term of a random polynomial of degree T-1; each shard is one evaluation of that polynomial at a distinct point. Any T shards uniquely determine the polynomial (and therefore the secret), while T-1 or fewer shards are consistent with every possible secret — the leakage is exactly zero, not just computationally hard. Practical implementations use a 256-bit prime field and a small integer shard count (typically 2-of-3 or 3-of-5).
Why it matters
Shamir gives a wallet a way to survive single-point-of-failure loss without depending on a single custodian. A 2-of-3 split across device, personal cloud, and paper means loss of any one shard leaves the wallet recoverable, and no single shard reveals the seed. Compared to MPC (Multi-Party Computation), Shamir is simpler, standard, and does not require a live counterparty during signing.
Related concepts
- Seed Phrase — A seed phrase — also called a recovery phrase or mnemonic — is a human-readable list of 12 or 24 words that encodes the entropy behind every private key in a wallet.
- KEK (Key Encryption Key) — A KEK — Key Encryption Key — is a cryptographic key used to encrypt other keys rather than user data directly.
- MPC Wallet — An MPC wallet uses Multi-Party Computation to compute signatures without any single party ever holding the whole private key.
- Self-Custody — Self-custody is the practice of holding your own cryptographic keys rather than delegating custody to an exchange or custodian.
Frequently asked questions
Is Shamir Secret Sharing quantum-resistant?
Yes. The scheme is information-theoretic; no computational assumption backs it, so quantum computers give no advantage.
What is the difference between Shamir and MPC?
Shamir splits a static key; MPC computes signatures without ever reconstructing the key. MPC needs live parties; Shamir does not.
Is Shamir the same as multisig?
No. Multisig is on-chain (multiple signatures on a transaction); Shamir is off-chain (one key, reconstructed from shards).
In Veyrnox
Veyrnox splits the seed with a 2-of-3 Shamir scheme across device, your personal cloud (iCloud today, Google Drive on Android), and a KEK-protected server shard. See the Shamir wallet page for the full recovery model.