Secret Sharing — Shamir's Scheme

Also Known As

TL;DR

Explanation

Shamir's Secret Sharing (1979) splits a secret S into N shares using polynomial interpolation — any K shares reconstruct S; K-1 shares reveal nothing (information-theoretic security). Use cases: root CA private keys (3-of-5 ceremony), disaster recovery keys (2-of-3: company safe + lawyer + escrow), cryptocurrency wallet seeds, HSM master keys. AWS CloudHSM and HashiCorp Vault implement secret sharing for key material ceremonies.

Common Misconception

Why It Matters

Common Mistakes

• Threshold K too low (1-of-N) — defeats the purpose
• All shares stored in the same location or with the same person
• Not testing reconstruction before destroying the original
• Using secret sharing for routine operations — it is for disaster recovery, not daily use

Code Examples

// Single root key — single point of failure:
$rootKey = file_get_contents('/etc/app/root.key');
// Compromised: all encrypted data exposed
// Lost: all encrypted data permanently unrecoverable

// Shamir's 3-of-5 distribution:
$shares = SecretSharing::split($rootKey, shares: 5, threshold: 3);
// Share 1: CTO (sealed envelope in office safe)
// Share 2: Company lawyer (offsite)
// Share 3: Company safe (separate location)
// Share 4: Escrow service
// Share 5: Backup HSM
// Any 3 parties must cooperate to reconstruct — no single point of failure

References

• ↗ https://en.wikipedia.org/wiki/Shamir%27s_secret_sharing

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