Mathematical implementation of polynomial secret splitting over Galois fields, enforcing split-knowledge key custody.
HSMSafe divides 256-bit symmetric master keys and elliptic curve private keys by evaluating random polynomials of degree M-1 over Galois Field GF(2^8). Each share is cryptographically authenticated using HMAC-SHA-256 to detect fraudulent or corrupted shards before reconstruction begins.
By requiring 3-of-5 or 5-of-8 geographic stakeholder presence to authorize master recovery operations, HSMSafe guarantees that no single compromised executive, rogue administrator, or physical extortion can breach institutional keys.